+ All Categories
Home > Documents > A Map of the Universe - J Richard Gott, M Juric, et al

A Map of the Universe - J Richard Gott, M Juric, et al

Date post: 10-Mar-2016
Category:
Upload: ucaptd-three
View: 215 times
Download: 1 times
Share this document with a friend
Description:
A Map of the Universe - J Richard Gott, M Juric, et al, research paper, cosmology, astrophysics
51
Transcript
Page 1: A Map of the Universe - J Richard Gott, M Juric, et al

� � ���������� ��������� �����

���� "!$#&%�')(+*-,�.)/+/10�2+232&054768')(+!$.9�):�(+!<;#)054>=�'@?A!$*-BA#&%�CEDGFHD1CI0J4LKM!E.HN�'PO".@Q�C$D)0�RS68!E#&%�')D1CUT�.HF)D1CED<QH0�R6-'WVYXZD1F)[\')(3]^0�_S`"DG/a'cb>'d%�#e')C$Cf0 4 �).HNYb�(3!EN�]g[c')N�Nh

ijckmloniqprl

stDq%�'e?HDqu�(+.A*�:�#1DG*v'8N�D<wx#1.HN�yz.)(+[c')C�[\')ut.)yL/a%�D\:�N�!{?HDG(+|+D\!ECEC$:�|3/+(a'd/+!EN�F}(3D1#1DGN~/*�!$|+#G.�?)D1(3!ED1|G0�(+')N�FH!$N�Foyz(3.H[���:�!Eu�D1(���D1C{/�.)�A�3D1#</a|>!$N9/+%�D�BA.HC�')(�|�Q�|�/aDG[80A/a.�/+%�D"F~')C�'�V�!$D1|')N�*��g:�')|a'd(+|�yz(+.)[�/a%�D�BACE.~')N-=�!EFH!{/&')CZBA]gQ�B�:�(�?HD<QH��XL%�!$|�[\'du-u�(3.W�3D1#</a!E.)NU05��'d|+D1*�.)N/+%�D�C$.HF~')(3!$/+%�[�[c')u9.)y5/+%�D�#G.H[9u�CED�V�u�C�'dN�D)0Au�(+DG|+DG(3?HDG|>|+%�')uJDG|�C$.�#1')CEC{QH0~')N�*cQHD</�!$|�'d��CED/+.r*�!E|3u�C�'eQ�/a%�DSD1N~/+!E(+DS(a')N�F)DS.)yZ')|�/a(3.HN�.H[9!E#1')C^|+#e'dCED1|�yz(+.H[�/+%�D���')(3/+%U��|>N�D1!$FH%g�J.)(+%�.A.�*/+.Y/+%�Dc#G.H|+[9!E#�[9!E#G(+.@w>'e?)D\��')#&]gFH(3.H:�N�*5�XL%�Dc#G.HN�yz.H(3[\'dC�N�'d/a:�(+D9.)y�/+%�Dcu�(+.W�3DG#G/a!$.HNU0u�(3D1|3D1(3?A!$N�F�|+%�')u�D1|�C$.�#1')CEC{QH0�[\'eQ��JD>.dyJu�')(3/+!E#1:�C�')(M:�|+D>yz.H(�')N�')C{Q��G!EN�FSC�')(3FHD�|3#e')C$DL|3/a(3:�#<�/+:�(+Dd�r��(+.H[9!EN�D1N~/�!EN�/+%�DP[c')u�!E|�'}BACE.~')N�,�(+D1'd/�s�')CECM.)y�F~')CE'WV�!ED1|��H� �H¡\��!EC$CE!E.)N8C$!EFH%~/Q)De')(3|�C$.HN�F�0g¢H£H¤¥CE.)N�FHD1(�/+%�')N�/a%�D�,�(+D1'd/�s¦'dCEC�*�!$|+#G.�?)D1(3D1*q�~Q9,�D1C$CED1(�')N�*cO�:�#&%�(+'�')N�*/+%�D1(3DGyz.H(3D�/+%�D�C�')(3FHD1|�/7.H��|3D1(3?)D1*8|3/a(3:�#G/+:�(+Do!EN/+%�D�:�N�!$?)D1(3|+D)�

§^¨�©Iªe«&¬<­�®�«+¯~°)±³²A´Wµ1¶ [9DG/a%�.�*�|G·�*�'d/&'�')N�')C$QA|+!$|10�CE')(+F)D<��|3#e')C$D�|3/+(+:�#</a:�(3D�.dy¸:�N�!$?HDG(+|3D

¹^º »1¼�½@¾�¿mÀMÁZÂ)½�Ãz¿�¼

Ä ')(�/a.HFH(+')u�%�DG(+|>[c')u�u�!EN�Fo/a%�D���')(�/a%U��|L|+:�(3yÅ')#GDSw�DG(+D�yÅ')#GD1*qw7!{/a%\/+%�D�#&%�')C$CEDGN�FHDS.dy�[\')u�u�!EN�F�'#1:�(3?HDG*\|3:�(3yÅ')#GD7.HN~/a.�'�u�C�'dN�D)�¸`�.�|+:�#&%cu�(+.��3D1#G/+!E.HNP#1')N9�JDLu�D1(�yzD1#G/10g��:�/�!$/�#e')N�#e'du�/a:�(3D7!E[9uJ.H(�/&')N~/yzDe'W/a:�(3D1|1���ZD1(+%�')u�|�/+%�D�[9.H|3/�yÅ')[c.):�|�[c')uqu�(+.W�3DG#G/a!$.HNq!$|�/a%�D�68D1(3#e'd/+.H(�u�(+.W�3DG#G/a!$.HN�ÆÅu�(+D1|3D1N~/aDG*}�gQ,�D1(+%�')(+*�:�|L68DG(+#e'W/a.H(�!EN8��Ç)ÈHÉ~Ê��¸XL%�!$|�!$|�'o#1.HN�yz.H(+[c')C�u�(3.W�3D1#</a!E.)Ncw7%�!$#&%\u�(3D1|+DG(3?)D1|L|+%�')uJDG|>CE.A#e'dCEC$Q)�Ëm!EN�DG|c.dy�C�'d/+!$/+:�*�DY')(+DY|+%�.�w7NÌ')|c|�/a(+')!EFH%~/c%�.H(3!E�1.)Ng/a')CLCE!$N�D1|G0�w7%�!$CED}[cDG(+!$*�!�')N�|9.dy�CE.)N�FH!$/+:�*�DY')(3D|+%�.�w7N8')|>|�/a(+')!EFH%~/�?HD1(�/a!$#e')CUC$!EN�DG|1��2Íy�/+%�Do68D1(3#e'd/+.H(Lu�(3.W�3D1#</a!E.)N!E|�u�CE.)/3/aD1*.)N}')N�ÆzÎ�ÏaÐ�Ê�u�C�')N�Dd0�/a%�D#1.A.H(3*�!EN�'W/aD1|S')(+D�u�CE.)/3/aDG*�')|Syz.HC$CE.@w7|1·>ÎÒÑÔÓ�05')N�*�Ð}Ñ¥CENmƳ/&')NmÆzÕZÖd×�ØÚÙ5ÖHÛ)Ê+Ê7w7%�D1(+D9ÙÜÆÅu�.H|+!{/a!{?HD�!{yN�.H(�/a%U0mN�D1F~'d/+!$?)Dr!$y�|+.):�/a%^ÊS!$|S/a%�DPC�'d/+!$/a:�*�D�!$N�(a')*�!E')N�|G05w7%�!EC$D�ÓÝÆzuJ.)|+!$/+!$?)Dr!$y�D1')|3/+D1(+C{QH0mN�DGF~'d/+!$?HDP!{yw�D1|3/+D1(3C$Q�Ê�!E|¸/+%�D>CE.)N�FH!$/+:�*�D�!ENP(a'd*�!�')N�|7ÆÅ|3D1D"B�N~QA*�D1(�ÆÞ�@ÉHÉH�~Êmyz.H(�')NPD�V�#1D1C$CEDGNg/�*�!E|+#G:�|+|3!E.HN�.)y^/+%�!E|�'dN�*

ßÞàZá3âWã�äIåIæ>á3çGå�è<é�êMëzåfäIèGâ�ìeí@ëÅîðï�ã<ñ~ò�ïÞî á�çWï�á3ë3ó�ô^äfîõçWï�áÞåfè<ç�ö�ç�î ÷<á3äfëIî�åzíGó@ô^äfîõçWï�áÞåfè<çgó�øMù7ú<û1ü&ý<ýþ3àZá3âWã�äIåIæ>á3çGå�è<é�ô�ìeíeëIîðï�ë3óeàMäfáÞÿ@á�ñgöZç�îõ÷Gá�äÍëÅîõåzí<ó�ô�ì�î ñ ã��@á�ñ â�ì�îðã�ó�ô~ê������3ú<ý�3àZá3âWã�äIåIæ>á3çGå�è<é�ô�ìeíeëIîðï�ë3óeöZç�î ÷<á�äÍëIî�åzí7è<é�ô�á3ç�çWëIí1ñ ÷&ã�ç�îðã�ó@ô�ì�îõñðã���á�ñ â�ì�îðã�ó�ô~ê�����3ú<ý ê�âWãGïÍì�á�ô�è<î ç1å��� dëÅá3äI÷&ã&åfè<äfí<ó���úGú��¸ê�âWãGïÍì�á�ô�è<î ç1å��mè1ã��~ó�ô������5èaÿSü���ó ò���çWëIâ)è�å3ó�ø��PóWûGû���ý��

Page 2: A Map of the Universe - J Richard Gott, M Juric, et al

� Û �

.)/+%�D1(�[c')uru�(3.W�3D1#</a!$.HN�|�.)y^/a%�D7��'d(3/a%5�ðÊ�XL%�!$|�#1.HN�yz.H(+[c')CA[\')uPu�(+.W�3DG#G/a!$.HNPu�(3D1|+DG(3?)D1|�')N�FHC$D1|�CE.A#e'dCEC$Q)0')N�*Ò'dCE|+.c#1.H[9u�')|3|�*�!$(+D1#</a!$.HN�|1�SËm.�#1')CM|3%�')u�D1|�')(3D�FH.A.A*U0�w7%�!ECEDo/a%�D�|+#1')CED�?d')(3!EDG|�')|S'\yz:�N�#G/+!E.HN8.)yC�'W/a!$/+:�*�Dd��XL%g:�|10�/a%�D|3%�')u�D1|9.)y"�J.d/a%v2�#1DGC�')N�* ')N�*ÝBA.H:�/a%��S[9D1(3!E#1'�')(+D|3%�.@w7N w�D1C$Cf0�')C$/+%�.H:�F)%2�#1DGC�')N�*!E|>|3%�.@w7N8CE')(+FHDG(�/+%�')N!$/�|+%�.):�CE*��D�(+DGC�'d/+!$?HD"/a.9B�.):�/a%��S[9D1(3!E#1'����S/a%�DG(>[c')uu�(+.��3D1#G/+!E.HN�|u�(3D1|+DG(3?)D�.)/a%�DG(>u�(3.HuJDG(3/+!ED1|G��XL%�D�|�/aDG(+D1.)FH(a')u�%�!E#�u�(+.W�3DG#G/a!$.HNcw7%�!E#&%U0�C$!E]dD"/+%�D�68DG(+#e'W/a.H(�u�(+.W�3DG#G/+!E.HNU0!E|�#G.HN�yz.H(3[\')C¸!E|�.)y³/aDGNt:�|+D1*�/a.Y[\'dut%�DG[c!$|+u�%�D1(+DG|1�cXL%�DcF)N�.H[9.HN�!E#P[c')uÒu�(3.W�3D1#</a!E.)NÌÆzD��JD1#G/+!$?)D1C$Qyz(+.)[�'�HCE!$FH%~/�P'W/L/a%�D�#1DGN~/aD1(".)yZ/a%�D�F)CE.H��D�.HN~/a.c'r/&')N�FHD1N~/7u�CE')N�D@Ê�[c')u�|LF)D1.A*�D1|3!E#1|7!$Ng/+.�|3/a(+')!EF)%g/CE!$N�D1|�.HN�/a%�D��^'d/o[c')uU0Z��:�/�*�.AD1|oN�.)/�u�(+DG|+D1(�?HDq|3%�')u�D1|�.H(o')(+D1')|1�}���g:�')C�')(3De'8[c')u�u�(+.��3D1#G/+!E.HN�|CE!$])D�/+%�DoËZ'd[r�JDG(3/10^68.HC$C$w�D1!E*�D)0�')N�*8O�')[9[cDG(Lu�(+.W�3DG#G/+!E.HN�|Lu�(+D1|3D1(�?HDr'd(+De'd|"��:�/"N�.)/7|+%�')uJDG|1�

� Ë�')[r��D1(�/�')�1!$[r:�/+%�')C�D1�g:�')CL'd(+De'�u�(3.W�3D1#</a!$.HNU0�#1DGN~/aD1(3D1*Ü.HN¦/a%�DN�.H(3/+% uJ.HC$Dq%�')|P!$N uJ.)C�')(#1.A.H(3*�!EN�'W/aD1|SÆ� A0��HÊ<0��oÑ Óm0� �Ñ�Û� ���|+!$N��$ƳÕZÖHÛ���ÙJÊ+ÖHÛ��I0~w7%�D1(3D� ��L!$|�/+%�DS(+')*�!E:�|�.)yU/+%�D�|3u�%�D1(3D)��XL%�!$|u�(3.W�3D1#</a!E.)NYu�(+D1|3D1(�?HD1|�')(+D1')|1��XL%�DoN�.H(�/a%�DG(+NY%�D1[9!E|3u�%�DG(+D�!E|>/+%A:�|�[c')u�u�D1*}.HN~/a.9'P#1!$(+#G:�C�')(L*�!E|+]c.)y(a'd*�!E:�|�� Û� ���')N�*�')(+D1'ÛWÕ� R� ���SN�.H��CE!E�g:�D�?)D1(+|3!E.HN�.dy�/a%�!$|10�#1DGNg/+D1(3D1*�'d/S'\uJ.)!EN~/S.)N8/a%�D�D1�g:�'W/a.H(G0!E|7'dCE|+.�u�.H|+|3!E��C$D)�

XL%�D�O�')[9[cDG(9u�(+.W�3DG#G/a!$.HNÌ|3%�.@w7|\/a%�D���'d(3/a%Ì')|q'�%�.H(+!$�1.HN~/a')C7D1CEC$!Eu�|3DYw7!{/a%ÌÛ�·$��'WV�!E|9(a'd/+!E.��XL%�D9D1�g:�'d/+.H(o!E|�|+%�.@w7N�')|�'}|3/+(a')!$FH%~/o%�.H(+!$�1.HN~/a')C�CE!$N�DP[c')(+]g!EN�F}/+%�D9CE.HN�FY'WV�!$|o.dy�/a%�DcDGCECE!$u�|+Dd��2Í/!E|�u�(3.�*�:�#1DG*Ý!EN /+%�DYyz.)CECE.@w7!$N�F�w>'eQ�·-[c')u /a%�D8DGNg/+!E(3DY|3u�%�DG(+D-.)Ng/+.t!{/a|Pw�D1|3/+D1(3NÌ%�D1[9!E|3u�%�DG(+DY�gQ|+!$[cu�C$Q #1.H[9u�(3D1|+|3!EN�F D1')#&% CE.HN�FH!$/+:�*�DY�gQÚ'tyÅ')#G/+.H(q.)y�Û��¥`".�w [c')uÌ/a%�!E|cw�D1|�/aDG(+N %�D1[9!E|+u�%�D1(3D.HN~/a.q'\u�C�'dN�D��~QY/a%�DPË�')[��JDG(3/�DG�g:�')C�'d(+De'\')�1!$[r:�/a%�')C�u�(+.W�3DG#G/+!E.HNU�SXL%�!E|�[\')u-!E|�'c#1!E(3#1:�CE')("*�!E|3]��XL%�!$|9!$|�/a%�D1NÝ|�/a(3DG/a#&%�D1*Ý�~Qv'�yÅ')#</a.H(P.dy�ÛvÆÅ:�N�*�.H!$N�F�/a%�D}u�(3DG?A!E.H:�|9#G.H[9u�(+DG|+|+!$.HNv�~Qv'�yÅ')#G/+.H(P.)yÛHÊS!$NÒ/+%�D�D1�g:�'d/+.H(+!E')C�*�!$(+D1#</a!$.HN�/a.Y[\'d])D�')N�D1C$CE!Eu�|+D�w7!{/a%t'8ÛA·$�9'WV�!E|�(+'d/a!$.��rXL%g:�|10Z/a%�D9O�')[c[9D1(u�(3.W�3D1#</a!E.)Nu�(+DG|+D1(�?HDG|S')(3De')|G��XL%�Do68.HC$C$w�D1!$*�DSu�(3.W�3D1#</a!$.HN}')CE|3.P|+%�.@w7|>/+%�D�|+u�%�D1(+D�'d|"Û�·$��'�V�!$|�(+'d/a!$.D1C$CE!$u�|+Dd�oÆzÎ�ÏaÐ�Ê>#1.A.H(+*�!$N�'d/+D1|".HN-/a%�D�[c')u-'d(+D)·>Î-ÑxÆfÛ�� ÛHÖWÕZÊ ���Ó�#G.H|!�A05')N�*�ÐqÑ"� Û� ��^|+!EN#��w7%�D1(3DÛ$��ئ|+!EN"Û%��ÑÚÕo|+!EN"ÙJÊ<��XL%�!$|>u�(3.W�3D1#</a!E.)N!E|>DG�A:�')Cm')(3De'P')|>w�D1C$Cf��Ë�'d/+!$/a:�*�D�CE!$N�D1|�.HNq/a%�Do68.HCEC{w�DG!E*�Du�(3.W�3D1#</a!E.)N8'd(+D�|3/+(a')!$FH%~/e0�w7%�DG(+D1')|"/+%�DGQY'd(+D�#1:�(3?HDG*�')(3#1|7.HN}/a%�DoO�')[c[9D1(�u�(+.W�3DG#G/+!E.HNU�

�S|�/a(3.HN�.H[9D1(3|�[\')u�u�!EN�FÜ/a%�D |3]gQ�%�'e?HD ')CE|3.Ú:�|+DG* |3:�#&%¥[\')u u�(+.W�3DG#G/a!$.HN�|�.)y�/+%�D |+u�%�D1(+Dd�,�N�.H[9.HN�!E#�[\'du�|L.)yZ/a%�D�#GD1CEDG|3/+!�')CU|3u�%�DG(+D�.HN~/a.9'P#1:���D�*�'d/+D�yz(+.H[ �@È~¡d×��¸2�NY(3D1#GD1N~/�/+!E[9D1|G0�XZ:�(+N�DG(')N�*q,�.d/+/�Æ��@É~¡dÈ~Ê�:�|+DG*\/a%�D�|3/+D1(+DG.HFH(+')u�%�!$#S[c')ucu�(+.W�3DG#G/a!$.HNc/+.�#&%�'d(3/>F)(+.H:�u�|�.)yUF~')C�'�V�!$D1|�ÆÅ:�/a!EC$!E�G!EN�F!$/+|�u�(+.Hu�D1(�/�Q�.)yJ[\')u�u�!EN�F�#G!E(+#GCEDG|�!$NP/a%�D"|+]~Q9.HN~/a.o#1!$(+#1C$D1|�.HN9/a%�D7[c')uU� Ê�XL%�D Ä ��b���|a'd/+D1C$CE!$/+DL[\'duÆfBA[c.A.)/MDG/�'dCf��Æ��@É)É~ÛHÊ+Êm.)y�/+%�D>#1.)|+[9!E#�[c!$#1(+.@w�'e?HD>��'d#&]AF)(+.H:�N�*P:�|+DG*c'dNrD1�g:�')C�')(+D1'S[c')u�u�(3.W�3D1#</a!$.HN.)yJ/a%�D"#1DGCED1|�/a!E')C^|+u�%�DG(+D�.HN~/a.r'�#1:��JDd��XL%�D�s 6&�S�¦|a'd/+D1C$CE!$/+DoÆIb�DGN�N�D</+/>D</>'dCf��ÆfÛd£H£H�~Ê3ʸ[\')u�uJDG*c/a%�D#1DGCEDG|3/a!E')CZ|+u�%�DG(+Dr.)Ng/+.'\(3%�.H[r��!$#�*�.A*�DG#e')%�DG*�(+.)N�:�|+!$N�F\/a%�DrO�D1')CEu�!{V8D1�g:�')C¸')(+D1'\[c')u-u�(3.W�3D1#</a!$.HNÆf,�;.H(3|+]g!�D</')CI�"Æ��@É)ÉHÉ~Ê+Ê�� 2Í/a|\(3D1|3:�C$/+|cw�D1(+D-*�!E|3u�C�'eQHDG*Ú')C$|+.�.)NÜ/a%�DÒ68.HC$C$w�D1!E*�DY[c')uÜu�(+.W�3DG#G/+!E.HNU0|+%�.�w7!$N�F�/a%�D�#1DGCEDG|3/a!E')Cm|+u�%�D1(3D�')|"')NYD1C$CE!$u�|+Dd0�w7%�!E#&%}w�')|�#&%�.H|+DGN8yz.H(L!{/a|7D1�g:�')CZ')(3De'Pu�(3.HuJDG(3/�Q)0J'dN�*/a%�D�yÅ'd#G/L/a%�'d/"CE!EN�D1|>.)y¸#1.HN�|3/&'dNg/"F~'dC�')#</a!E#SC�'d/+!$/a:�*�D�')(3D�|+%�.@w7N�'d|"|�/a(+')!EFH%~/7C$!EN�DG|1�

*�DcË�')u�u�')(3D1N~/e0M,�D1C$CED1(G0�'�O�:�#&%�(a'�Æ��@ÉH¢)È~ÊSu�!E.)N�D1DG(+D1*�:�|3Dc.)y�|+C$!E#GD9[c')u�|�.dy�/a%�D9:�N�!$?)D1(+|3D9/+.

Page 3: A Map of the Universe - J Richard Gott, M Juric, et al

� � �

[c')])D �^'d/�[c')u�|G��XL%�DGQ9|3:�(3?)DGQHDG*}'o|3CE!$#1D7.)yJ|+]~QH0J�H��¡ � CE.HN�F�'dN�*\È � w7!E*�D)0g.)yU#G.HN�|�/&')N~/�*�D1#GCE!EN�'d/a!$.HNU�2�NÒ�H= /+%�!E|�|+C$!E#1D�%�')*�/+%�DrFHDG.H[cD</a(�Q8.dy�'\#1.HN�D)0m')N�*-/a%�D<Q �^'W/+/aDGN�D1*�/+%�!E|�.HN~/a.'cu�C�')N�D)��Æ ��#1.)N�D%�')|��1DG(+.�,�'):�|3|+!�'dNc#G:�(3?d'd/+:�(+D�'dN�*\#1')N\/a%�D1(+D<yz.H(+D��JD"#1.)N�|3/+(+:�#</aD1*qyz(3.H[x'�u�!$D1#GD�.)yUu�')u�D1(1� � #1.)N�D#1:�/o')CE.HN�F'CE!EN�Dr')N�* �^'W/+/aDGN�D1*Ò.HN~/+.8'qu�C�')N�D�CE.A.H]g|�CE!$])DP'qu�!$�1�1'w7!{/a%Ò'q|3CE!E#GDr[9!E|+|3!EN�F-�ðÊt2Íy�/a%�D#1.)N�D�!E|�'d/>*�D1#1C$!EN�'W/a!E.)N��g0A/+%�D�[c')uq!ENc/a%�D�u�C�')N�D"w7!EC$C���D�Î}Ñ ¸#G.H|�ÆIÓ�#1.H|eÆ��dÊ+Ê�0�Ð�Ñ ¸|+!$N�ÆfÓ"#1.H|eÆ��dÊ+Ê<0w7%�DG(+DoÓY!$|�/a%�D�(+!$FH%~/L')|3#1D1N�|+!E.)N�Æz!ENq(+')*�!E')N�|&Ê�0�')N�* �!$|�/a%�DS#1.d�Í[c.@?A!EN�F�*�!E|�/&')N�#GD�ÆI'd|>!EN�*�!E#e'W/aD1*\�gQ/a%�Dr(+DG*�|+%�!{y³/�.)y�/+%�Dr.H�A�3DG#G/&Ê<��XL%�!$|Sw7!EC$CMu�(3D1|3D1(3?)D�|+%�')u�D1|G�o6-')N~Q-/+!E[9D1|S'q�HÈH£ � |3CE!$#1D�!$|S|3%�.@w7Nt'd|'q#1!$(+#GCED�w7!{/a%�/+%�DP��')(3/+%�!EN-/+%�DP#1DGN~/aD1(G0Uw7%�D1(3DrÎ�Ñ" ¸#G.H|�ÆIÓJÊ�05ÐYÑ �|3!ENUÆfÓ�Ê<��2Íy \!E|�[cD1')|+:�(+D1*Ò!$N#1.W��[9.�?A!$N�F�*�!E|�/&')N�#1D)0~/+%�!E|�w7!EC$C�u�(3D1|3D1(3?)D�|+%�')uJDG|�.HN�C$Qr!$y^/a%�D":�N�!{?HDG(+|+D"!E| ��'d/SÆ���Ñ £~Ê�0g')N�*�/a%�D"|+C$!E#1D!E|�!$N9/+%�D7D1�g:�'d/+.H(+!E')C�u�CE')N�D�Æ���Ñ £~Ê<0�Æz!$y���Ñ £�0g|�/a(+:�#G/a:�(+D1|SÆÅ|3:�#&%')|�?).H!E*�|aʸw7!ECEC�')u�u�De')(�C$D1N�F)/+%�D1N�D1*!ENÒ/a%�Dc*�!$(+DG#G/a!$.HN�/&')N�FHD1N~/a!E')C�/a.Y/a%�D9CE!$N�DP.)y�|+!EF)%g/o�~Qt'}yÅ'd#G/a.)(o.dy���Ö�#1.)|@Æ��dÊ+Ê��\XL%�!$|�#G.H(+(3D1#</a!E.)Nt!$|!E[9u�.H(3/a')N~/�yz.H(�|3/+:�*�Q\.)ym/a%�D �SCE#G.�#&]H���¸')#G�GQAN�|+]g!mD �5DG#G/e0�w7%�!E#&%|+'@QA|>/+%�'d/>|�/a(3:�#G/+:�(+DG|L|+:�#&%Y')|�?).H!E*�|w7!EC$C�N�.d/���D7|+%�.@w7Nc!EN�u�(+.)uJDG(�|3%�')u�D�!{y^w�D7/&')]dD�|3!E[9u�C$Q �Ñ�cÆ���CE#G.�#&]P'dN�*\�M')#1�<QAN�|+]g!�ÆÞ�@É~¡)ÉHÊ+Ê<�M2�NyÅ')#</e0^ LQ�*�D1NvÆÞ�@ÉHÉ~ÇHÊ>'dN�*- LQA*�D1N '�68D1C$.)/+/�ÆÞ�@ÉHÉHÈHÊ�%�'e?HD�DG[cu�%�')|+!$�1DG*8/a%�'d/7/a%�!$|"|3%�')u�D�*�!E|3/+.H(3/+!E.HN!EN�(3D1*�|3%�!$y³/�|3u�')#GDP#e')NÒ��DP:�|+DG*�/+.q/aD1|�/�/a%�DP#G.H|+[9.HCE.)FH!E#1')C�[c.A*�D1CM!ENÒ'qCE')(+FHD�|a')[9u�CED�|+:�#&%t')|�/a%�DB�C$.~')N}=�!EF)!$/&'dC5BA]gQ}B�:�(3?)DGQtÆ ��.H(+]cDG/"')CI�mÆfÛd£H£H£~Ê���,�:�N�N}DG/"'dCf�mÆÞ�@ÉHÉH¢HÊ���K�:�]g:�F)!$/&'rD</"')Cf�UÆ��@É)ÉHÈ~Ê+Ê���2Íy?H.)!E*�|�(3:�N�!EN~/a.D1')#&%Ò.)/a%�D1(10U/+%�Drw�')CEC$|�w7!EC$C¸.HNÒ'e?)D1(a'dFHDPN�.)/�%�'e?)DP|3QA|3/+D1[c'd/a!$#PuJDG#1:�C$!�')("?HD1C$.�#G!$/+!ED1|')N�*t/a%�DG(+DGyz.)(+D\?).H!E*�|�|+%�.):�CE*¦%�'@?)D}')u�u�(3.eV�!$[\'W/aD1C{Q�(+.):�N�* |+%�')uJDG|}ÆI'8u�(+.Hu�.H|3!$/a!$.HNÒw7%�!E#&%¦#1')N ��D#&%�DG#&])D1* !$Nt*�DG/&'d!EC¸w7!{/a%t`7����.A*�Q�|+!$[r:�CE'd/a!$.HN�|&Ê��PXL%�D1(3DGyz.H(3D)0M!$/�!E|�!$[cu�.H(�/&')N~/�/a.Y!EN~?)D1|3/+!EF~'W/aD�[\'duu�(3.W�3D1#</a!E.)N�|�w7%�!$#&%¦w7!ECEC�u�(3D1|3D1(3?)D}|+%�')u�D1|PC$.�#1')CEC{QH�}2Íy".HN�Dc%�')|�/+%�Dq#1.)(+(+DG#G/P#G.H|+[9.HC$.HFH!E#1')C�[9.�*�DGCf0')N�*\:�|+DG|�|+:�#&%}'�#1.)N�yz.H(+[c')C^[c')ucu�(+.W�3DG#G/a!$.HNU0A!E|3.)/a(3.Hu�!E#LyzD1'd/a:�(3D1|�!ENc/+%�DSCE')(+F)D"|3#e')C$DS|�/a(+:�#G/a:�(+D�w7!$CEC')u�u�De'd(L!E|+.d/a(+.)u�!E#�.HN/+%�D�[\')u5�

�S|�/a(3.HN�.H[9D1(3|�[c')u�u�!$N�F�/+%�DS:�N�!$?HDG(+|3D�')(+D�#1.HN�yz(+.HN~/aDG*qw7!$/+%\/a%�D�#&%�')C$CED1N�FHDS.)yU|+%�.@w7!EN�FP'�w7!E*�D?d')(+!$DG/�QÚ.dyr|+#1')CEDG|1�xs %�'d/8|+%�.H:�CE* ' [c')u .)y�/+%�D�:�N�!$?)D1(3|+D�|3%�.@w�� 2Í/Y|+%�.H:�CE* |+%�.�w C$.�#1'd/a!$.HN�|.)y�')C$C�/a%�D�yÅ')[c.):�|c/+%�!EN�F)|q!ENÚ|3u�')#1Dd·¦/a%�DÒO":�����C$DÒB�u�'d#1DÒXMDGCEDG|+#1.)uJDd0�/a%�D�2�Ng/+D1(3N�'d/a!$.HN�')C�B�u�')#GDBA/a'd/a!$.HNU0�.)/a%�D1(�|a'd/+D1C$CE!$/+D1|r.)(+��!{/a!EN�F-/a%�DY��')(�/a%U0�/a%�D?d')N �SC$CEDGN (+')*�!E'd/a!$.HN¦��D1C$/+|10�/a%�D868.A.HNU0�/a%�DB�:�N50�u�C�')N�DG/a|G0�')|3/+D1(3.H!E*�|G0���:�!Eu�D1(��JDGC$/P.H�g�3D1#G/+|10�N�D1')(+�~Q¦|�/&')(3|r|+:�#&%Ü'd|�� Ä D1N~/a'):�(+!I0�')N�* B�!$(+!$:�|10|3/a')(+|w7!{/a%Úu�CE')N�DG/+||+:�#&% ')|YÇ��Ò�ZD1F�0�|�/&')(3|!EN .H:�(\F~')C�'�V�Q)0"yÅ'd[c.H:�|��C�')#&]Ü%�.HC$D1|}')N�* u�:�CE|a'd(+|10/a%�D8F~'dC�')#</a!E##GD1N~/aDG(107Ë�')(3FHDY')N�*ÚBA[\')C$C76-')F)D1CECE')N�!$# Ä CE.H:�*�|10L68���H0�yÅ')[9.H:�|�F~'dC�'WV�!EDG|PCE!$])D86-¢~¡�0/a%�D�,�(+D1'd/7s¦'dCECf0AyÅ')[9.H:�|7�g:�')|a'd(+|"CE!E]dD�� Ä ÛH¡)�8ÆfBA#&%�[c!$*�/�Æ��eÉHÈH�~Ê3Ê>')N�*}/a%�DoFH(a'e?A!$/a'd/a!$.HN�')C$C$Q�C$D1N�|3D1*�g:�')|+')(S£)É~ÇH¡ÆI��:�N�*�!E#�DG/�')CI��Æ��eÉHÉ~¡HÊ3Ê<0�*�!$|3/a')N~/�BACE.~')NY=�!$FH!$/a')CUBA]gQ8BA:�(3?)DGQYF~')CE'WV�!ED1|G0�')N�*Y�g:�')|+')(+|G0/a%�D[c.H|�/P*�!$|3/&'dNg/�]gN�.@w7N �g:�')|a'd(�')N�*vF~')CE'WVAQ¦')N�*���N�')CEC{QÒ/a%�D#G.H|+[9!E#q[9!E#G(+.@w�'@?)D}��')#&]gFH(+.):�N�*(a'd*�!�'d/+!E.HN5�qXL%�!E|o!E|o�g:�!$/+D\'8#&%�')CEC$D1N�F)D)�}�MDG(+%�'du�|�/a%�D���(3|3/��J.A.H]�/a.-')*�*�(3D1|3|�/a%�!$|�#&%�')CEC$D1N�FHD�w�')|Ä .H|3[c!$#�T�!ED<w�·�XL%�D���N�!{?HD1(3|+Do!EN}×~£9�):�[9u�| �~Q-��D1D1|Sb�.AD1])D�u�:���C$!E|+%�D1*�!$N��@É~Ç)¡-ÆIb�.�DG])D}ÆÞ�@É~ÇH¡HÊ3Ê<�XL%�!$|���(3!EC$CE!�'dNg/S�J.A.H]�|�/&')(�/aDG*tw7!$/+%�'}u�!$#G/a:�(+D9.)yL'}CE!{/+/aC$DrFH!$(+C�|+%�.�w7N�'d/c��Ö��@£d/+%Ò|+#e'dCED)�\XL%�DcN�D<VA/u�!$#G/a:�(+D\|3%�.@w�DG* /+%�Dq|+')[cDcCE!{/+/aC$D�FH!E(3C�'W/q��Ö��e£H£d/a%t|+#1')CED\w7%�.�N�.@w #G.H:�C$*¦�JDc|+DGD1Nv|+!{/+/a!$N�F-!$N¦%�DG(|+#&%�.�.HC�#G.H:�(�/�Q~')(3*U�9��'d#&%t|3:�#1#GD1|+|3!$?)Dqu�!E#</a:�(3Drw>'d|ou�CE.)/3/aD1*�'d/�/+D1NÒ/a!$[cDG|�|+[c')CEC$D1(�|3#e')C$D)�PXL%�D9¢d/+%

Page 4: A Map of the Universe - J Richard Gott, M Juric, et al

� × �

u�!$#G/a:�(+D)0J'd/�'c|+#1')CED�.)yL��ÖA�@£��e0�|+%�.@w7|�/+%�D�DGNg/+!E(3Dr��')(3/+%U�"XL%�D\�e×d/a%�u�!$#G/+:�(+Dd05'd/�'c|3#e')C$D�.)yL�@Ö��@£A4 h 0|+%�.�w7|�/+%�D�DGN~/a!E(3DPB�.)C�')("|3QA|3/+D1[Y��XL%�Dq�e¢d/a%�u�!E#G/+:�(+Dd0U'd/�'\|+#1')CED�.)yL��ÖA�@£ 4�� 0J!EN�#GCE:�*�DG| � Ä D1N~/&'):�(+!f0XL%�DYÛHÛ����u�!$#G/a:�(+D)0�'W/�'-|+#1')CED\.)yo��Ö��@£)R�R�|+%�.@w7|9')CEC�.)yL/+%�D}68!$CE]~Qts�'eQ ,�')CE'WVAQH��XL%�DYÛ)È���}'dN�*C�'d|3/�u�!$#G/a:�(+D�!EN�/a%�Dc|3D1�g:�D1N�#1D\|3%�.@w7|�F~'dC�'WV�!EDG|�.H:�/�/a.Y'}*�!E|�/&')N�#1D�.)y7¡)Ç)£[c!$CECE!$.HN-C$!EFH%~/�Q)De')(3|1� �yz:�(�/a%�DG(9|3D1�g:�DGN�#1D�.dySu�!$#G/+:�(+DG|cCE')�JDGCEDG*v£�Ï��o�HÏ��SÛ�Ï�� �¥�@��0�|3/&'d(3/a!$N�F�w7!$/+%Ü'ÒCE!{yzDq|+!$�1D}u�!$#G/a:�(+D}.)y/a%�DoF)!E(+CI�õ|�%�')N�*50�|+%�.@w7|�'�|3D1�g:�DGN�#1D�.)y¸[9!E#G(+.H|3#1.Hu�!E#S?A!ED<w7|10�D1')#&%8/+D1N/a!$[cDG|LC�')(3FHD1(>!$N|+!$�1D)0�DGN�*�!$N�Fw7!$/+%Ý'�?A!ED<w�.)y�/a%�D}Ng:�#1C$D1:�|c.)yS'�|3.�*�!$:�[ 'd/+.H[ 'd/9'Ò|+#1')CED}.)y��@£A4 _ ÖA�H� � [9.�*�D1(+Nv?HDG(+|3!E.HN .)y/a%�!E|o�J.A.H]^0��Z.�w�D1(3|�.dy¸XZD1N ÆI68.H(+(3!E|3.HNtD</P')CI��Æ��@É)¢~ÛHÊ+Ê��~Qt��%�!EC$CE!Eu�')N�*¦��%~Q�C$!E|�68.H(3(+!E|3.HN¦'dN�*�/a%�D���9#1D�.)y Ä %�')(3CEDG|#' "'eQ��')[9D1|10�!E|>u�(3.H��')��C$Q9yÅ')[c!$CE!E')(�/a.P[9.H|3/7'd|3/a(3.HN�.H[9D1(3|1��XL%�!$|L|+:�#G#1DG|+|3yz:�CEC$Q')*�*�(+D1|3|+DG|�/a%�D�|3#e')C$Dou�(+.H��C$D1[Y0���:�/�!E|7'dN�'d/+C�')|L.)yM[c')u�|10�N�.)/�'P|3!EN�FHC$D�[\'duU��O".@w *�.AD1|7.HN�Do|+%�.@w/a%�DoDGN~/a!E(3D�.H��|+DG(3?d')��C$D�:�N�!{?HD1(3|+Do!ENY'P|+!$N�FHCED�[c')u �

XL%�Dc[c.A*�D1(3N��Z.@w�DG(+|S.dy¸XZD1N ��.A.H]�*�DG|+#1(3!E��D1* 'd�J.@?HDc!E|���')|3D1*¦.)N¦'}[c.@?A!EDd0¸�Z.�w�D1(3|S.)yMXZD1NÆI��')[9D1|Y')N�*���')[9D1|tÆ��@ÉH¡H¡HÊ+Ê�0S�~Q Ä %�')(3CEDG|-')N�* "'eQ ��')[cDG|Yw7%�!E#&% !EN /a:�(3N w�')|Y!EN�|3u�!E(3D1* �gQ��D1DG|rb�.AD1]dD)��|���.�.H]^�cXL%�D\[9.@?�!$D�!E|o')(+F):�')��C{QÒ')N�DG?HDGN [c.)(+D���(+!$CEC$!�')N~/�u�(+D1|3D1N~/&'W/a!E.)Nt/a%�')N¦��D1DG|b�.AD1]dD)��|q.H(+!$FH!EN�')CL�J.A.H]^� XL%�D�#1')[cDG(a'�|3/&'d(3/a|9w7!$/+%Ì'�u�!$#G/+:�(+DY.)yo't#G.H:�u�C$D-|3!$/+/+!EN�F�.HNÝ'�u�!E#GN�!E#��CE')N�])D</"!EN Ä %�!E#1')FH.�0�'dN�*Y/+%�D1NY/a%�Do#e'd[cDG(a'P[c.@?)D1|".H:�/�w�')(+*U0^!$N�#1(3De')|3!EN�F�!$/+|7*�!E|�/&')N�#GD�yz(+.H[ /+%�D1[D<V�u�.HN�DGNg/+!�')C$C$Q¦')|9'Òyz:�N�#G/a!$.HN .)y�/+!E[9D)�vXL%g:�|107'du�u�(+.eV�!E[c'd/+D1C$QtDG?)D1(�Q /+D1NÜ|+D1#G.HN�*�|G0�/a%�DY?A!ED<w�!$|yz(+.)[ /aDGNt/a!$[cDG|�yz:�(3/+%�D1(�'ew>'eQ�')N�*�#1.)(+(+DG|+u�.HN�*�|�/a.}/a%�DcN�D�VA/�u�!$#G/+:�(+D�!ENÒ/a%�D9��.A.H]^�\XL%�D9[c.@?A!EDFH!{?HD1|S.HN�D�C$.HN�Fq#G.HN~/a!$NA:�.H:�|�|3%�.)/e0�w7%�!E#&%�!$|S��(3De'd/+%~/&')]g!EN�F')|�!{/S[9.@?HD1|�.):�/e��XL%�DP[c.@?A!EDo!E|�#e')C$CEDG*�M.@w�D1(3|S.)yMXMDGN ÆI')N�*�(3D1#GD1N~/aC{QH0�')N�2�6&����?HDG(+|+!$.HNÒ.)y�/a%�!E|�!$*�De'q%�'d|��JDGD1NÒ[c')*�D)05#e')C$CED1* � Ä .H|+[9!E#T�.@Q~')F)D �gÊ�0���:�/9!{/�#1.H:�C$*vD1�g:�')C$C$Q¦w�D1C$CL�JD/a!{/aC$D1*v�M.@w�D1(3|q.)y�X>w�.�0�.H(9�M.@w�D1(+|c.)y��H0���D1#e'd:�|+DY!$/+|D<V�u�.HN�DGNg/+!�')CM#&%�')N�F)DP.)y�|+#1')CED�w7!{/a%-/+!E[9D)0�u�(+.A*�:�#GD1|�'\(3D1*�:�#G/a!$.HN��~Q�'cyÅ'd#G/a.)(S.)y�/�w�.!EN�#G.HN�|3/a')N~//a!$[cD�!$N~/aD1(�?d')CE|G0�')N�*-')CE|3.c'PyÅ')#</a.H(L.)y���!$N8#G.HN�|3/a')N~/�/+!E[9D�!EN~/+D1(3?d')C$|1��XL%�D�/a!E[9D�!EN~/+D1(3?d')C$|L�JD</�w�DGD1NyÅ')#</a.H(3|�.)yZ�@£�0HyÅ')#</a.H(3|�.)y5Û�'dN�*PyÅ')#G/+.H(+|�.)y��7!ENr/+%�D7[c.@?A!EDL'd(+DL(+DGC�'d/+D1*P�~Qr/+%�DL(a'd/+!E.H|¸CEN��@£P·~CEN"Ûr·��H�BA/+!ECECI0�/a%�!$|S!E|�N�.)/�'c|+!EN�FHCED�[\')u8w7%�!E#&%�#1')N��JD�|3/a:�*�!EDG*Ò')CECM'd/�.)N�#1Dd0U.H(�w7%�!E#&%Ò#e')N-�JDr%g:�N�FY.)N�'w�')CECI�

stD�w�')N~/�/a.c|+D1D�/a%�D�C�')(3FHD�|3#e')C$D�|�/a(+:�#G/a:�(+Dr.)y�F~')C�'�V�Q}#GCE:�|�/aDG(+!EN�F\��:�/�')(+D�')CE|3.\!$Ng/+D1(3D1|3/+D1*�!$N|3/a')(+|m!$N�.H:�(m.@w7N�F~')CE'WVAQ�')N�*�/+%�D�68.A.HN�')N�*�u�CE')N�DG/+|1� ���A�3D1#</a|�#1C$.H|+D�/+.L:�|�[\'eQ��JD�!$N�#1.HN�|+D1�g:�DGN~/a!�'dC!ENY/aDG(+[9|S.)y�/+%�D�w7%�.HCED�:�N�!$?)D1(3|+Dr��:�/S/a%�DGQ8')(+D�!E[9uJ.)(3/&'dNg/7/+.\:�|G�S2Í/�(3D1[9!EN�*�|�.HN�D�.)y�/+%�D�yÅ')[9.H:�|#e'd(3/a.A.HN-`�DGw ��.)(+])DG(�#1.@?)D1(��)TS!ED<w .)y�/+%�D�st.H(+C$*8yz(3.H[ É�� � ��?)D1Ng:�D��Y�~Q�B�'):�CMBA/+D1!$NA��D1(3Fq.)y�68'@QÛ)É�0M�@É~¡)È�ÆfBA/+D1!ENg��D1(3F Æ��@É~¡dÈ~Ê+Ê���2Í/�%g:�[9.H(+.H:�|+C$QY|3%�.@w7|�'\`�DGw ��.H(3])D1(G�õ|�?A!$DGw¥.)y�/a%�D�w�.)(+CE*5��XL%�D/a(+'��9#)0A|+!$*�DGw�')CE]g|�')N�*\��:�!EC$*�!EN�F)|�')CE.HN�F�É�� ����?HDGNg:�D�')(3D"?A!E|3!E��C$D7!EN�/a%�D"yz.H(+DGFH(+.H:�N�*U��b�DG%�!EN�*\!E|�/a%�DO�:�*�|+.HN�(3!$?)D1(10�w7!$/+%�`�D<wÔ�)DG(+|3DGQ�'d|�'c/+%�!EN�|�/a(3!Eu-.)N�/a%�DoyÅ')(S��'dN�]^��XL%�D1NÒ'W/�DG?)D1NÒ|+[c')C$CED1(7|3#e')C$D!E|�/a%�Dc(3D1|3/�.)y>/+%�D �"N�!$/+D1*¦BA/&'d/+D1|ow7!$/a%Ò/a%�Dq 7.�#&]~Q�[c.):�N~/&')!$N�|�|3/a!$#&]g!EN�F8:�u�C$!E])D9|+[c')C$C�%�!EC$CE|1�c2�N/a%�D���'d#&]AF)(+.H:�N�*U0���:�/�N�.d/�[r:�#&%cw7!E*�D1(�/a%�')N9/a%�D�O�:�*�|+.HNq "!{?HD1(G0�!$|�/a%�D"D1N~/a!$(+D��¸')#G! ��#".A#1De'dNcw7!$/+%Ä %�!$N�'r')N�*�H')u�')Nq!$Nc/+%�DS*�!$|3/a')N�#1Dd��XL%�!E|�!E|G0�.)y�#G.H:�(3|+D�'ou�')(+.A#&%�!E')C�?A!$DGw�0A��:�/L!{/�!$|m�3:�|�/�/+%�'d/>]g!$N�*.)y�?A!ED<w /+%�'d/�w�DPw>')N~/�.)y�/+%�DP:�N�!{?HD1(3|+Dd��s�Drw�.H:�C$*ÒCE!E]dDr'|+!$N�FHC$D�[c')u�/a%�'W/�w�.):�CE*ÒD1�g:�'dCEC$QYw�D1CEC

Page 5: A Map of the Universe - J Richard Gott, M Juric, et al

� Ç �

|+%�.�w ��.)/+%q!EN~/aDG(+DG|3/a!$N�Fo.H�A�3D1#</a|>!$Nc/+%�D�|3.HC�'d(�|�Q�|�/aDG[80�N�De')(3�~Qc|�/&')(3|10�F~')C�'�V�!$D1|�!EN9/a%�D�Ëm.�#1')CJ,�(3.H:�uU0')N�*YC�'d(+FHD�|3#e')C$D�|3/a(3:�#G/+:�(+Do.H:�/L/+.P/a%�D�#1.)|+[9!E#�[9!E#1(3.@w>'e?HD���'d#&]AF)(+.H:�N�*U�

�mº p ¿�����¿���ÃI¼��¦ÂH¿5¿�¾WÀZÃI¼��½�����:�(S.)�A�3D1#</a!$?)DP%�D1(3Dr!E|7/a.\u�(+.A*�:�#GDP'\#1.)N�yz.H(+[c')C�[c')u�.)y�/+%�Dr:�N�!$?HDG(+|3D�w7%�!E#&%�w7!$CEC�|+%�.�w¥/a%�D

w7!E*�Do(+')N�FHD�.dy¸|3#e')C$D1|7D1N�#G.H:�N~/aDG(+DG*-w7%�!EC$D�|3/+!ECECJ|+%�.@w7!$N�Fc|3%�')u�D1|L/a%�'d/�')(+D�C$.�#1')CEC{Qc#G.H(+(3D1#</e�Ä .HN�|3!E*�DG(L/a%�D�FHDGN�D1(+')C�K�(+!EDG*�[c')N�N[9DG/a(3!E#G|1·

�� R Ñ � �� R Ø�� R Æ � Ê1Æ �� R Øv|+!EN R � Æ � R Ø |+!$N R � Ù R Ê+Ê<Ï �9Ñ�Ør� Æ��@Ê �� R Ñ � �� R Ø�� R Æ � Ê1Æ �� R Ø � R Æ � R Ø |3!EN R � Ù R Ê+Ê�Ï �9Ñ £ ÆfÛ)Ê �� R Ñ � �� R Ø�� R Æ � Ê1Æ �� R Øv|+!EN�% R � Æ � R ØÜ|+!$N R � Ù R Ê+Ê�Ï �9Ñ �o� ÆI�HÊ

w7%�DG(+D � !E|m/a%�D�#1.)|+[9!E#�/a!$[cD�|3!EN�#GD�/+%�D�b�!EF"b>')N�F�0���Æ � Êm!E|m/a%�D�D�V�u�')N�|+!$.HN�u�')(a')[9DG/+D1(G0)')N�*�!EN�*�!$?A!E*�:�')CF~')CE'WV�!EDG|�u�')(�/a!$#1!Eu�'d/a!$N�F�!$Nq/a%�D�#G.H|+[9!E#�D�V�u�')N�|3!E.HNyz.HC$CE.@w FHD1.A*�DG|+!E#G|>w7!$/+%Y#G.HN�|�/&')N~/L?d')CE:�D1|L.)y � 0!��0')N�*\ÙZ�¸XL%�D1|3D�/a%�(+D1D"')(3D7#e')C$CED1*�#G.d��[9.@?�!$N�F�#1.A.H(+*�!EN�'d/+D1|G��`�DGFHCEDG#G/+!EN�F�u�D1#1:�CE!�'d(�?HD1C$.�#G!$/+!ED1|G0~F~')CE'WV�!ED1|(+DG[\'d!EN�'d/�#1.HN�|�/&')N~/�uJ.)|+!$/+!E.HN�|o!$Nt#G.d��[9.@?A!EN�F}#1.A.H(3*�!EN�'W/aD1|o')|�/a%�D\:�N�!{?HDG(+|+DcD<V�u�')N�*�|1�}`".�w���Æ � Ê.H��DGQA|�K^(3!EDG*�[\'dN�NU��|>D1�g:�'d/+!E.HN�|1·

Æ ��� �� Ê R Ñ � �� R Ø�� � Ø ¢dÕ����� Ø ¢dÕ����

� ÆÅ×~Ê

Û�Æ ��� ���� Ê Ñ Û �� � ¢dÕ ���� � �@ÈdÕ ���

� ÆfÇ)Ê

w7%�DG(+D � Ñ"!$#&% �'� $0�!$|�/a%�D\#1.H|3[c.HC$.HFH!$#e')C�#1.)N�|3/a')N~/e0(���*)"��+ _ 0�!E|�/+%�D}'e?HDG(a')FHD[c'd/3/aD1(�*�D1N�|+!$/�Q!EN¦/+%�D}:�N�!{?HD1(3|+Dd0�!EN�#1CE:�*�!EN�F-#1.HC$* *�')(+]�[\'d/3/aDG(10(���,)-� + hc!E|�/+%�DY'@?)D1(+')FHD}(a')*�!�'d/+!E.HN¦*�D1N�|3!$/�Q !$N/a%�D\:�N�!{?HDG(+|+Dd0�u�(3!E[c')(+!$C$QY/a%�D9#1.H|3[c!$#c[9!E#G(+.@w�'@?)D\��'d#&]AF)(+.H:�N�*¦(a')*�!�'d/+!E.HNU�cXL%�D\|3D1#G.HN�*¦DG�A:�'d/a!$.HN|+%�.�w7|�/a%�'d/�/+%�D\#G.H|+[9.HCE.)FH!E#1')C¸#G.HN�|3/a')N~/ru�(3.�*�:�#1DG|r')N�')#1#GD1CEDG(a'd/+!E.HN�!ENÒ/a%�DcD�V�u�')N�|+!$.HNtw7%�!ECED�/a%�D[c'd/+/+D1(M')N�*r(+')*�!�'W/a!E.)N�u�(3.�*�:�#1DL'"*�D1#GD1C$D1(a'W/a!E.)NU���ZD1(�:�N�!$/M[\')|3|¸*�DGN�|+!{/�QH0~(+')*�!�'W/a!E.)Nou�(+.A*�:�#1DG|�/�w7!E#GD/a%�D9*�D1#1DGCEDG(a'd/+!E.HN�.)y�N�.H(3[\'dC¸[c'd/+/+D1(���D1#1'):�|+D�u�.H|+!{/a!{?HDPu�(3D1|+|3:�(+D9!E|SFH(a'e?A!$/a'd/a!$.HN�')C$C$QY'd/3/a(a'd#G/a!{?HDP!$N��!EN�|�/aDG!ENU��|L/a%�DG.H(3Q}'dN�*}(a')*�!E'd/a!$.HN%�')|"'Pu�(3D1|+|3:�(+Do!EN}D1')#&%8.dyM/+%�D�/a%�(3D1Do*�!E(3D1#G/+!E.HN�|�ÆzÎ�ÏaÐ�Ï ~Ê�w7%�!E#&%!E|��@Ö)�/. � /+%�D�D1N�DG(+F)Qq*�D1N�|3!$/�Q)�

stDo#1')NY*�D ��N�D�'P#1.)N�yz.H(+[c')C5/+!E[9D10q�~Qq/+%�D�(+D1CE'd/a!$.HN 0�Ñ �� Ö2��0�|3.9/+%�'d/0UÆ � Ê�Ñ43 �

� ��� ÆIÈHÊ

Ëm!EFH%~/�/a(+'e?HD1C$|\.HNÜ(a')*�!�')CLFHDG.�*�D1|+!$#1|9w7!$/a% 0 Ñ65 �� |+.¦'�F~')CE'WVAQv'd/\'t#1.W��[9.�?A!$N�FÒ*�!E|�/&')N�#GD �yz(+.)[ :�|�D1[9!$/3/aDG*v/+%�D}CE!$FH%~/rw�D}|3D1D}/a.A*�'eQv'd/9'�#1.HN�yz.H(+[c')C�/+!E[9D,0UÆ � ÊcÑ"05Æ � �<Ê � � � XL%A:�|10�w�D

Page 6: A Map of the Universe - J Richard Gott, M Juric, et al

� È �

#e'dN #e')C$#1:�CE'd/aD�/a%�Dc/a!E[9D � 'dN�*¦(+DG*�|+%�!$y³/ �Ñ �JÆ � ��Ê+Ö/�JÆ � Ê � �'d/�w7%�!E#&%¦/a%�'d/PCE!$FH%~/�w>')|PDG[c!{/+/+D1*U�Ä .HN~?HDG(+|3D1C$Q)0�!$y�w�Dc]gN�.@wÔ/+%�Dc(3D1*�|3%�!$y³/10�FH!$?)D1Nt'Y#G.H|+[9.HCE.)FH!E#1')C¸[9.�*�D1C"ÆÅ!I�õDd�P?)'dCE:�DG|o.dy���e0 � 0����S0���e0^'dN�* �q/a.A*�'eQ�Ê�w�Do#e')NY#e'dCE#1:�C�'d/+DS/a%�Do#1.W��[9.�?A!$N�FP(a')*�!�')CJ*�!E|�/&')N�#GD�.dyM/+%�D�F~')C�'�V�Qcyz(+.H[ :�|Lyz(+.H[!$/+|r(+DG*�|+%�!$y³/e0�')FH')!EN¦!$FHN�.H(3!EN�F8uJDG#1:�C$!�')(�?HD1C$.�#G!$/+!ED1|G��K^.)(P'�[c.)(+Dq*�D</&')!$CEDG* *�!E|3#1:�|3|+!E.)N .dy�*�!E|3/a')N�#GD[9De')|3:�(+DG|"!$N}#1.H|3[c.HC$.HF)Q)0�|+DGD�O".HFHF8Æ��eÉHÉHÉ~Ê��

XL%�D>s 6&�S�t|+'d/aDGCECE!{/aD�%�')|�[9De')|3:�(+DG*P/a%�D>#G.H|+[9!E#�[c!$#1(+.@w�'e?HD>��'d#&]AF)(+.H:�N�*c!$NrD<V��g:�!E|3!$/+DL*�DG/a')!ECÆIb�D1N�N�D</+/�DG/�')CI�^ÆfÛ)£)£H�~Ê+Ê�'dN�*c#G.H[r��!$N�D1*P/+%�!E|�*�'d/a'�w7!$/a%9.)/+%�D1(�*�'d/a'9ÆI�MDG(+#G!$?d')C�DG/�')CI�^ÆfÛd£H£���Ê��)T�D1(3*�DDG/�')CI��ÆfÛd£H£~ÛHÊ�� Ä (+.dy³/�D</�')Cf��ÆIÛ)£H£~Û)Ê���,�N�DG*�!EN&'�O�')[c!$C$/+.HNÒÆfÛd£H£~ÛHÊ��^,o'd(+N�'e?A!E#&%}DG/�')CI��Æ��eÉHÉH¢~Ê��� "!$D1|3|DG/9'dCf�LÆIÛ)£H£��@Ê���K�(3D1D1*�[\')NvD</\'dCf�LÆIÛ)£H£��@Ê����ZD1(3CE[r:�/3/aDG(PDG/9')CI�LÆ��eÉHÉHÉ~Ê3Êo/a.Òu�(3.�*�:�#1DY')#1#G:�(a'W/aD*�'d/a'.HN�/a%�DP#1.H|3[c.HC$.HFH!$#e')C�[9.�*�DGCLÆIB�uJDG(+FHDGC�DG/o'dCf�¸ÆfÛ)£H£)�~Ê+Ê��ostD�')*�.Hu�/��JDG|3/ ��/�?d')C$:�D1|�'W/�/a%�DPu�(+D1|3D1N~/D1u�.A#&%U0 � Ñ � �10���')|+DG*8.)NY/+%�D�s 6&���Ì*�'W/&'P.)yÞ·

���� ��� �� Ñ ¡�� ]A[|3D1#�68uJ# Ï

��� � ���� R� Ñ £ ð¡d��Ï

� � Ñ ¢ õ�~Ç~�@£ +�� Ï� � � ¢dÕ����

� � R� Ñ £  ÛH¡�� � �eÏ� Ñ £

XL%�D�s 6&���Ò*�'d/a'�!E[9u�C$!ED1|U/+%�'d/����"����yz.H(�*�')(+]�DGN�D1(3F)Q\ÆÅ!EDd����������Ñ�� ���������"� �������aÊ�0)|+:�FHFHD1|�/a!$N�F/a%�'d/9'�#1.H|3[c.HC$.HFH!$#e')C�#1.HN�|3/&'dNg/9!$|�')NvD<V�#1DGCECEDGN~/�[c.A*�D1C�yz.H(r/a%�D*�')(+]¦DGN�D1(3F)QH0�|+.Òw�D8'd(+D|+!$[cu�C$Q')*�.)u�/a!$N�F�/a%�'d/e��XL%�D�#1:�(3(+D1N~/"O":�����C$D�(a')*�!E:�|���� �>Ñ4!!� +�4" Ñ ×gÛHÛd£�6YuJ#d��XL%�D�#1.)|+[9!E#S[9!E#G(+.@w�'@?)D��')#&]gFH(3.H:�N�*8!E|7'd/�'P(+DG*�|+%�!$y³/�rÑ��@£H¢HÉ���B�:���|3/+!$/a:�/a!EN�F�0�:�|3!EN�F�FHDG.H[cD</a(3!E�1DG*}:�N�!$/+|7!ENw7%�!E#&% !7Ñ �H0')N�*!$N~/aD1F)(a'd/+!EN�Fo/a%�D ��(+|3/"K�(3!ED1*�[\')N�N\D1�g:�'W/a!E.)N\w�D ��N�*/a%�D�#G.HN�yz.H(3[\'dC�/+!E[9D�[c'eQ\��D�#e'dCE#1:�C�'d/+D1*U·

0UÆ � Ê�Ñ 3 �� ��� Ñ 3 �$# �&%

� ' � ��� R Ø ¢dÕ� � h � ����Æ ��ÊmØ ���WÆ �AÊ �AØ � � � h)( +�4+*ÍR � Æf¡)Ê

w7%�DG(+D ����) ��+ _ ')N�* ��� ) � + h �MXL%�!E|�yz.)(+[r:�CE'"w7!$CEC�'d#1#1:�(a'd/+D1C$Qo/a(+')#&]�/+%�D�?d')CE:�D>.)y 0UÆ � Ê<0~u�(3.@?�!$*�!EN�F/a%�'d/S/+%�!E|�!E|S!$N~/aD1(3u�(+D</aDG*Ò')|S/a%�D�?d')CE:�D�.)y�/+%�Dr#1.)N�yz.H(+[c')Cm/a!$[cDo|+!$N�#1D�/a%�DrDGN�*�.)y�/+%�Dr!EN��^'d/a!$.HN�')(�Qu�D1(+!$.�*}'W/>/a%�D���D1FH!$N�N�!$N�Fr.)y�/a%�Do:�N�!$?)D1(+|3D)��ÆI=�:�(+!EN�Fr/a%�D�!$N��^'d/+!E.HN�'d(3Q9uJDG(+!$.�*}'d/L/+%�D���D1FH!$N�N�!EN�Fr.)y/a%�D�:�N�!$?HDG(+|3D)0^/a%�D�#1.H|3[c.HC$.HFH!$#e')CJ#1.HN�|�/&')N~/S')|+|3:�[9D1*�'�C�')(3FHD�?d')CE:�Dd0�*�! �JD1(3D1N~/"yz(+.H[ /+%�'d/�.H��|3D1(3?)D1*/a.A*�'eQH0^'dN�*/a%�D�yz.H(3[r:�C�'�w�.H:�C$*}%�'e?HD�/a.��JD�#&%�'dN�FHD1*-')#1#G.H(+*�!EN�FHC{QH��BA.9w�D�|+!E[9u�C{Q\|�/&')(�/"/+%�D�#1C$.�#&]'d/r/+%�DD1N�* .)y7/a%�D!$N��^'d/+!E.HN�'d(3QÒu�D1(+!$.�*¦w7%�D1(+Dq/+%�DD1N�D1(+FdQ¦*�DGN�|+!{/�Q¦!EN¦/+%�D\yÅ')C$|+D\?d')#G:�:�[ � CE')(+FHD#1.)|+[9.HCE.HF)!E#e'dC"#G.HN�|�/&')N~/ ��!$|q*�:�[9u�D1*Ú!ENÌ/+%�D�yz.H(3[ .)yo[c'd/+/+D1('dN�* (a')*�!E'd/a!$.HNU� XL%g:�|G0�w7%�DGN w�D/a(+')#1D���'d#&]}/+.P/a%�Do��!EF���'dN�F�0�w�D�')(3D�(+De'dCEC$Qc/a(+')#1!$N�F���')#&]q/a.�/a%�D�DGN�*8.dy¸/a%�Do!$N��^'d/+!E.HN�')(3Q\uJDG(+!E.A*U���y³/+D1(�/a%�'d/10A/+%�DS[9.A*�D1C^*�.AD1|��JDG%�'e?HD��3:�|�/LCE!$])D"'�|�/&')N�*�')(+*q%�.)/3��K^(3!EDG*�[\'dN�Nc��!EFo��')N�Fr[9.A*�D1CI�¸XL%�!$||3/a')N�*�'d(+*�[c.A*�D1C¸[c!$FH%~/��JD�u�(3.Hu�D1(+C{Q�(3DGyzD1(3(+DG*t/a.Y')|o')N�!EN��^'d/a!$.HN�')(�Q~����!$F\��')N�F8[9.�*�D1Cf0Jw7!$/a%Ò/a%�D

Page 7: A Map of the Universe - J Richard Gott, M Juric, et al

� ¡ �

!EN��^'d/a!$.HN�')(�Q}D1u�.�#&%�u�(+.A*�:�#1!$N�F\/+%�DPb�!$Fqb>')N�FqD<V�u�C$.H|+!$.HN�'d/�/a%�Dr|�/&')(�/e� Ê�`�.@w�0 ��Æ � Ê7!E|�/+%�Dr(+')*�!E:�|.)yZ#1:�(3?d'd/a:�(+D�.)y�/a%�D�:�N�!$?)D1(+|3D�yz.H(�/a%�D �cÑ ØP�o')N�* �cÑ �o��#e'd|+D1|G0^��:�/Lyz.H(�/+%�D �9Ñ £P#e')|3D)0�w7%�!E#&%w�DSw7!EC$C��JD�!$N~?HD1|�/a!$F~'d/a!$N�F ��(+|�/7')N�*cu�(+!$[\')(3!EC{QH0H/a%�D1(+D�!E|�N�.�|3#e')C$D�')N�*\|+.�w�D�')(3D�yz(+DGD�/+.rN�.H(3[\')C$!E�GD)0|+D</+/+!EN�F ��Æ � �<Ê�Ñ �� � Ñ"! � +�4� Ñ ×gÛHÛ)£�68u�#)��XL%�D1N50 � [cD1')|+:�(3D1|P#G.d��[9.@?�!$N�F�*�!$|3/a')N�#1DG|�'d/P/a%�Du�(3D1|+DGN~/rD1u�.A#&%�!ENÒ:�N�!$/a|�.)y�/a%�D9#1:�(+(+DGN~/rO":�����C$D9(+')*�!$:�| ��� �@�cXL%g:�|10Zyz.H(�/a%�D���Ñ £}#e')|3D)0Z:�|+!$N�FFHDG.H[cD</a(3!E�1DG*}:�N�!$/+|10�w�Do%�'e?HD)·

05Æ �AÊ�Ñ405Æ ��Æ � Ê3Ê�Ñ 3 �� Æ �� � � ��Ø � �MØ Æ �� � Ê h ��� Ê +�4+*ÍR �� � ÆI¢HÊ

w7%�DG(+D � ��0 ��� 0 � �')(3D8/+%�D-?d')CE:�D1|q'W/\/a%�D�#1:�(3(+DGNg/qD1u�.�#&%U� ,�!{?HD1NÜ/a%�D-?d')C$:�D1|\')*�.Hu�/aD1*Üyz(+.H[s 6&�S�Ýw�D ��N�*5· 05Æ � ��Ê�Ñ �  �H¢ ÆIÉHÊXL%�'d/�[9De')N�|�/a%�'d/�w7%�D1N\w�DSC$.�.)]�.H:�/�N�.@w 'd/ � Ñ � ��Ƴw7%�D1N �PÑ � �<ʸw�D�#e')Nc|+D1D".H:�/�/a.�'�*�!E|3/a')N�#GD.)y � Ñ � õ�H¢ Æ��@£~Ê.H(7'�#1.d�Í[c.@?A!EN�FP*�!E|�/&')N�#GD�.)y

� ��� � Ñ �  �H¢ ��� � Ñ �e×�Ï&�H£H£�68u�#� Æ��H��Ê

XL%�!$|r!E|�/+%�DD��JD1#</a!{?HDu�')(�/a!$#1CEDc%�.H(3!E�1.)NU0�w7%�D1(3Dqw�D}'d(+Dq|3D1D1!$N�FÒu�')(�/a!E#GCEDG|r'd/r/+%�D[9.H[cDGN~/r.)y7/a%�Db�!$F�b>')N�F���XL%�!$|L!E|7'PC�'d(+FHDG(L(a')*�!$:�|>/a%�')NÒ�@��� ¡P��!ECEC$!E.HNcCE!$FH%~/>QHD1')(+| � /a%�Do')FHD�.dyM/+%�D�:�N�!$?)D1(3|+D\Æz/a%�DCE.A.H]g��')#&]9/a!$[cDeÊ�/a!$[cDG|>/a%�D�|3uJDGD1*Y.)yMCE!EF)%g/ � �JDG#e'):�|3D�!$/L|3%�.@w7|"/+%�D�#1.d�Í[c.@?A!EN�FP*�!E|�/&')N�#GD�/a%�D�[9.H|3/*�!$|3/&'dNg/Mu�')(�/a!$#1CEDG|mw�D>#1')N�.)��|+DG(3?HD�N�.@w w7!ECEC~%�'@?)D�yz(+.)[ :�|Zw7%�D1Nr/a%�DGQ�')(+D�')|M.HCE*�')|�w�D�')(+D�N�.@w�0)!f��D)�[9De')|3:�(+DG*�'d/L/+%�D�#G:�(+(3D1N~/�#1.H|3[c.HC$.HFH!$#e')C�D1u�.�#&%5��stDo[c'eQ#e'dCE#1:�C�'d/+D�/a%�D�?d')CE:�D�.)y 0}')|"'ryz:�N�#</a!$.HN.)y��^0A.H(�D1�g:�!{?d')CEDGNg/+C$Q�'d|�'�yz:�N�#</a!$.HNc.dyU.H��|3D1(�?HD1*(3D1*�|3%�!$y³/ �Ñ�Æ � �<Ö2�AÊ!�Ò�H�� 7D1#1.)[r��!EN�'d/a!$.HNP.�#G#1:�(3|'d/ '� � ��Ñ¥�@£H¢HÉ�0�w7%�!E#&%Y!E|>/+%�D�(+D1*�|+%�!{y³/7.)y¸/+%�D�#1.H|3[c!$#�[c!$#1(3.�w�'e?HDo��')#&]gFH(3.H:�N�*Y|+DGD1N-�~Qs 6&�S�M�

0UÆ '� � �ÞÊ�Ñ £  £)È~¡�� Æ���ÛHÊ

B�.�0�/+%�D�#1.d�Í[c.@?A!EN�FP(a')*�!$:�|L.)yZ/a%�D�#G.H|+[9!E#�[9!E#G(+.@w>'e?)Do��')#&]gFH(+.H:�N�*-!$|1·

� ��� � Ñ Æ 0%� � 0&� � �ÞÊ���� � Ñ¥�1×�Ï&£H£H£�68u�# Æ��@�~Ê

XL%�'d/M!E|m/+%�D�(+')*�!$:�|Z'd/�/a%�D�#1:�(3(+DGNg/¸D1u�.�#&%50)|+.S'd/Z(+DG#1.H[r��!EN�'d/+!E.HN�/+%�D�s 6 ����|+u�%�D1(+D�%�')|M'"u�%gQA|3!E#e'dC(a'd*�!E:�|>/+%�'d/"!E|��e£HÉH£�/a!$[cDG|L|+[c')CEC$D1(�.H("')�J.):�/��@�968u�#)�

�S#G#1.H(3*�!EN�Fv/+. B�=�B�BÌCE:�[c!$N�.H|+!{/�Qvyz:�N�#G/+!E.HN *�'W/&' Æf6Y!E#&%�')DGC�b�C�'dNg/+.HNU0"u�(+!{?d'd/aD�#G.H[9[r:�N�!$#e'W�/a!$.HN^Ê�0�����!$N�/a%�D ��(+DG|+|t')N�* B�#&%�DG#&%~/aD1(tCE:�[9!EN�.H|+!{/�Q yz:�N�#G/+!E.HN�!EN�b ��'dN�* !$|�¡ {� ¸�@£�����yz.)(��>Ñ ¡���]g[qÖd|�6YuJ# +�4 ')N�*�/a%�D�[9De')N9|+DGu�')(+'d/a!$.HNc��DG/�w�D1DGNF~')CE'WV�!ED1|���(+!EF)%g/+D1(�/a%�')N�����!$|�× $�Z6YuJ#d�XL%�Do68!$CE]~Q9s¦'eQq%�')|7É �×W�@£ � ���!ENb��^B�!EN�#1DS/+%�D�(a')*�!E:�|>.dyZ/+%�D�.H��|+D1(�?d')��CED�:�N�!$?)D1(+|3D9ÆÅ.H:�/L/a.r/a%�D

Page 8: A Map of the Universe - J Richard Gott, M Juric, et al

� ¢ �

#1.)|+[9!E#\[9!E#G(+.@w�'@?)Dq��')#&]gFH(3.H:�N�*�Ê�!E|c�e×Ò,�uJ#d0¸/a%�'W/r[9De')N�|�/a%�'d/�/a%�D\NA:�[r�JDG(�.)y7��(+!EF)%g/�F~')CE'WV�!ED1|ÆÅ[9.H(3D9C$:�[9!EN�.H:�|�/a%�')N ����Ê�yz.H(3[c!$N�Fw7!$/+%�!EN�/a%�D\#1:�(+(+DGN~/aC$QÒ.)��|+DG(3?d')��C$D\:�N�!{?HDG(+|+Dc!E|�.)yL.)(+*�DG(c��¡d£��!$CECE!$.HNU�U2Íy�.H:�(ZF~')C�'�V�Q�%�')|M.dy�.H(+*�D1(�Ûd£H£"��!ECEC$!E.HN�|�/&')(3|10W/a%�D�[cD1')N���C$:�D�|3/aDGCECE')(mCE:�[9!EN�.H|+!{/�Q�!E|Z.)y�.)(+*�DG(£��õ£~Ç ���')N�*q/a%�D�[cD1')NqNg:�[r��D1(>*�D1N�|3!$/�Qc.)y�|3/a')(+|>!$|>'d/�CED1')|3/�.)y�.H(3*�D1(7Û  È�@�@£ � 68uJ# + _ ����CEC$!Eu�/+!E#e'dCE|')N�*-B�£�F~')CE'WV�!ED1|�%�'e?HD�'9%�!$FH%�DG(LNA:�[r�JDG(7.)y�|�/&')(3|"u�D1(�B�.)C�')(>C$:�[9!EN�.H|3!$/�Q9/a%�'dNY/+%�D�68!EC$]gQcs¦'eQ)0�|3.'}#1.HN�|3D1(�?)'W/a!$?)D�D1|3/+!E[c'd/aDPyz.H(�/+%�D�[cD1')N�NA:�[r�JDG(�*�D1N�|3!$/�QÒ.)y�|3/a')(+|�[9!EFH%~/���DcÇ ��@£ � |�/&')(3|&ÖH6YuJ# _ �XL%g:�|10�/+%�D�#1:�(3(+D1N~/+C$Q}.H��|3D1(�?)'d��CED�:�N�!$?HDG(+|3D�!$|L%�.H[9D�/a.9.)y¸.)(+*�DG(7È ~�e£)R�R�|�/&')(3|1�

stD�[\'eQq#G.H[9u�:�/aD�#G.d��[9.@?A!EN�Fr(+')*�!$! �Ñ � ��� � yz.H(L*�! �5DG(+D1N~/7(3D1*�|3%�!$y³/+|10�')|L|3%�.@w7N8!$Nq/&')��CEDr�H�stD�#1')N')C$|+.o#e')C$#1:�CE'd/aD>/+%�D�?d')C$:�D7.)y 05Æ � Ñ � Ê�Ñ ×  Ç)£�w7%�!E#&%c|+%�.@w7|>%�.@wÚyÅ')(�'ou�%�.)/+.HN\#1')Nc/+(a'e?HDGC!EN8#1.d�Í[c.@?A!EN�Fc#G.�.H(3*�!EN�'d/aDG|7yz(3.H[ /a%�Do!EN��^'d/a!$.HN�')(�Q}b�!$F\b>'dN�F\/a.9/a%�Do!EN ��N�!$/+Doyz:�/a:�(3D)�7XL%g:�|10U!{y¸w�Dw�')!$/�:�N~/a!EC^/a%�DS!EN ��N�!$/+D"yz:�/a:�(3DSw�D�w7!ECEC^D<?HD1N~/+:�')CEC{Q\��D�'d��CED7/a.r|3D1D�.H:�/�/a.�'�#1.W��[9.�?A!$N�F�*�!$|3/a')N�#1D�.)y

'� ��� Ñ ×  Ç)£���� � Ñ �@É�Ï&£)£H£�68uJ# Æ��e×gÊXL%�!$|�!$|�/+%�D9#1.d�Í[c.@?A!EN�Fyz:�/+:�(+D�?A!E|3!E��!$CE!$/�Q8CE!$[c!{/e��`".-[c'd/+/+D1(�%�.@w�CE.)N�Fw�D9w>')!{/e0mw�Dcw7!EC$C�N�.)/���D')��C$Dq/a.�|3D1D}yz:�(3/+%�D1(r/+%�')Nv/a%�!$|1�¦XL%�!$|P!E|P|3:�(+u�(3!E|3!EN�FHC{Q�#GCE.H|3D)�¦XL%�D8Ng:�[r��D1(P.dySF~'dC�'WV�!EDG|�w�D}w7!$CECDG?)D1N~/a:�')CEC{QtD<?HDG(P�JD\')��CED�/a.-|+D1D\!E|�.)N�C$QÒCE')(+FHDG(o/+%�')N¦Ng:�[��JDG(�.H��|3D1(�?)'d��CED9/a.A*�'eQt�~Q�'8yÅ')#</a.H(o.)yÆ� � ��� Ö% '� � Ê _ Ñ�Û  �HÈ��

XL%�!$|o#1')CE#G:�C�'W/a!E.)N�')|+|3:�[9D1|�/a%�DPyÅ')C$|+Dr?d')#1:�:�[�|3/a'd/aD8Æz#1.H|3[c.HC$.HFH!$#e')CZ#1.HN�|3/&'dNg/&Ê�?A!$|+!E��CED�/+.�*�'eQ(+DG[\'d!EN�|r:�N�#&%�')N�F)D1*U� ÆzXL%�Ds 6&���¥*�'d/a'Ò!$|r#1.)N�|+!$|3/aDGN~/Pw7!$/a% '-?d')C$:�Dq.)y � Ñ �o�H0�!EN�*�!$#e'd/+!EN�F/a%�'d/7/a%�D�?d')#1:�:�[ |�/&'d/+DcÆÅ*�')(3]D1N�DG(+F)Q�ÊL/a.A*�'eQ!E|Lw�D1CECZ')u�u�(+.eV�!E[c'd/aDG*8�~QY'�uJ.)|+!$/+!$?)Do#G.H|+[9.HC$.HFH!E#1')C#1.)N�|3/a')N~/e�ÚXL%�!$|9yÅ')C$|+D}?d')#1:�:�[ |3/&'W/aD Ƴw7!$/+% �������Ñ � �������\Ñ �o� �������aÊr[c'@Qv*�D1#e'eQ �~Qvyz.H(+[9!EN�F��:�����CEDG|�.)y�N�.H(+[c')CA�1DG(+.�*�DGN�|+!{/�Qr?d')#1:�:�[ Æ � Ñ £~ÊM.H(MDG?HDGNc*�D1#e'eQP�~Q�yz.H(+[9!EN�F���:�����CED1|�.dyJN�D1F~'d/+!$?)DD1N�D1(+FdQÚ*�D1N�|+!$/�QÜ?d')#1:�:�[ Æ ���

£~Ê�� 2Íy�/a%�D�u�(+DG|+D1N~/YyÅ')CE|3D-?d')#1:�:�[ !$|q.HN�C{QÝ[9DG/a')|3/a')��CED-!$/\w7!$CECDG?)D1N~/a:�')CEC{Q8*�D1#e'eQY�~Q}/a%�Doyz.H(+[c'd/a!$.HN}.)y���:�����CEDG|�.dy�N�.H(3[\')Cm.)(�N�DGF~'d/+!$?HD�D1N�DG(+F)QY*�DGN�|+!{/�Q}?)'d#1:�:�[')N�*�DG?)D1N~/a:�')CEC{Q�.HN�D�.)y�/a%�DG|+D9��:�����CED1|�w7!EC$C¸DGN�FH:�C{y�/+%�D�#1.d�Í[c.@?A!EN�FC$.�#1'd/a!$.HN�.)y�.H:�(�F~')CE'WVAQH��b�:�/!$y¸/a%�DG|+DP��:�����CEDG|�.�#G#1:�(�CE'd/aD\Æ����@£ 4 � � QA(+|aÊS')|�D�V�u�D1#</aDG*�/+%�DGQYw7!EC$CM[c')])D�'qN�D1F)CE!EF)!E��C$D�#1.H(3(+D1#</a!$.HN/a.�%�.@w�yÅ')(9'ew�'@Q !$NÜ#G.H[c.@?A!EN�F�#G.�.)(+*�!$N�'d/aDG|Pw�DYw7!ECEC�DG?HDGN~/a:�')C$C$Qv��DY')��CED/+.t|3D1D)� K�.H(�'Òyz:�CEC$D1(*�!$|+#1:�|+|+!$.HNU0�|3D1D�,�.)/3/e0��):�(+!<;#oD</"')Cf�"ÆÅ')|3/+(+.d�Íu�%)£)���@£~ÇH¡A�1?���Ê�')N�*8(3DGyzD1(3D1N�#GD1|"/a%�DG(+D1!$NU�

Ëm!EN�*�DvÆ��@É)ÉH£~Ê�')N�* ,�')(+(3!EF~'t')N�*ÌT�!$CEDGN�]g!EN ÆÞ�@ÉHÉH¢HÊ9%�'e?HD�u�.H!$Ng/+D1*Ú.H:�/\/a%�'d/!$y�/+%�D�#G:�(+(3D1N~/?d')#1:�:�[ |�/&'d/+Dr!E|S/+%�DrC$.�w�D1|�/�|3/a')��CED�D1�g:�!$CE!E��(+!E:�[�/a%�DGN��g:�'dNg/+:�[ ��:�#G/+:�'d/a!$.HN�|�#1')N�yz.H(+[ ��:�����CEDG|.)y5%�!EFH%9*�DGN�|+!{/�QP?)'d#1:�:�[�/+%�'d/�w7!EC$C�|3/a')(3/�'oN�DGw !EN��^'d/a!$.HN�')(�Q�DGuJ.A#&%U0AN�DGw ��')�~Q�:�N�!$?)D1(3|+D1|�FH(+.@w7!EN�FCE!$])D}��(+')N�#&%�DG|\.$� '�/a(3D1D)�ÚBA/a!$CECf0�')|�!$N /+%�D-'d�J.@?HDY#e'd|+D)0�w�D8D<V�uJDG#G/c/a.��JDYD1N�F):�C$yzDG*Ü�~Qv|+:�#&%Ú'N�D<w !EN���'d/a!$N�F�(+D1F)!E.HN}.HN�C{Q}'d/"C�'W/aD�/a!$[cDG|oÆÅ|a'eQY'd/"C$De')|�/��e£ 4 � � Q)De')(3|�yz(+.)[�N�.@w�Ê"'dN�*Y/+%�Do.H��|+DG(3?)D1(w7!EC$C�|�/a!$CEC��JD\|+:�(3(+.H:�N�*�D1*v�~Q ')N D<?HDGNg/�%�.H(+!$�1.HN�w7!{/a%v'-C$!E[9!$/o.)yLyz:�/+:�(+Dc?�!$|+!$��!EC$!$/�Q�!$N¦#1.d�Í[c.@?A!EN�F#1.A.H(3*�!EN�'W/aD1|�!$NÜ.H:�(c:�N�!$?HDG(+|3D8/a%�'d/9!E|P?A!E(3/+:�')C$C$Q¦!$*�D1N~/+!E#e'dC>w7!$/a%vw7%�'d/9w�D-%�'e?HD8u�CE.d/+/aDG*U�ÝXL%g:�|G0')C{/a%�.H:�FH%8/+%�D�yz:�/+:�(+D�%�!E|�/a.H(�QY.)y�/a%�D�:�N�!{?HDG(+|+D�w7!ECEC���D�*�DG/aDG(+[9!EN�DG*��~Q8/+%�D�|3:���|3D1�g:�D1N~/oDG?).HCE:�/a!E.)N.)yM/a%�D��g:�')N~/a:�[�?)'d#1:�:�[ |�/&'d/+DcÆI')|�')CE|3.�N�.)/aDG*8�~QY��(a'd:�|+| '�BA/a')(+]g[c')N�ÆfÛ)£H£)£~Ê+Ê�0�!EN}u�(+')#G/+!E#1D�w�D

Page 9: A Map of the Universe - J Richard Gott, M Juric, et al

� É �

D<V�u�D1#</�/+%�D7#1:�(3(+D1N~/�?d')#1:�:�[�/a.o|3/a'@QP')|�!E|�yz.H(�#1.)N�|+!$*�D1(+')��C$Q�CE.HN�FHD1(�/+%�')N�/a%�D"O�:�����CEDL/+!E[9D)0~')N�*c!$N[c')N~QP|+#GD1N�')(3!E.H|�/+%�!E|�C$De'e?HDG|�:�|�w7!{/a%c'�C$!E[9!$/M.)y5yz:�/a:�(3D7?A!$|+!E��!ECE!{/�Q�/a%�'d/�!$|�yz.H(�')CEC�u�(a'd#G/a!$#e')C�u�:�(+u�.H|+DG|�3:�|�/"w7%�'d/7w�D�%�'e?HDou�C$.)/+/+D1*U�

2Íy�w�D7|+DGN�*9.H:�/�'�CE!$FH%~/�|+!$FHN�')C�N�.@w�0g�gQ � Ñ � !{/�w7!EC$C�(+D1')#&%c'�(a')*�!$:�| � Ñ 0UÆ � Ñ � Ê � 05Æ � ��Ê�Ñ×  Ç)£�� � õ�H¢oÑ � {��Û�0�.)(

�Ñ ×�Ï�¡d×H£�6YuJ# Æ���ÇHÊ/a.�w7%�!E#&%¦w�D(+DGyzDG(�/a.Ò'd|�/a%�D��3.H:�/�w�')(+* C$!E[9!$/o.)y7(3De')#&%�'d��!EC$!$/�Q ���-stDq#e'dN�N�.)/P(3De')#&% Ƴw7!$/a% C$!EFH%~/|+!$FHN�')C$|�.H(�(+.A#&])D</a|&ÊL')N~Q\F~')C�'�V�!$D1|�/a%�'W/7')(+D�yz:�(3/+%�D1(L'ew�'eQq/a%�'dNq/a%�!$|�ÆIb�:�|+%�'PD</7')Cf�5ÆfÛd£H£H�~Ê3Ê<�¸s %�'W/(+DG*�|+%�!$y³/"*�.AD1|7/a%�!$|"#G.H(+(3D1|3uJ.HN�*8/a. �t,�')C�'�V�!$D1|>w�D�.)��|+DG(3?HD�/a.A*�'eQqw7!$/+%-'�(+DG*�|+%�!{y³/S.dy PÑ��� ÈHÉ9')(3D'd/7/a%�!E|"#1.d�Í[c.@?A!EN�F�*�!$|3/a')N�#1Dd�7,�')C�'WV�!$D1|Lw7!$/+%8(3D1*�|3%�!$y³/+|�CE')(+FHDG(L/a%�')N�� õÈHÉ9/+.�*�'@Q')(+Do:�N�(3De')#&%�'d��CEDd�XL%�!$|"!$|7'P|+:�(3u�(+!$|+!EN�FHC$Q\|+[c')CECJ(+D1*�|+%�!{y³/e�

stDq#e')N�|+D1D\[\')N~Q�F~')CE'WV�!EDG|�'d/�(+DG*�|+%�!{y³/a|�C�')(3FHD1(�/a%�'dNÚ�  È)ÉY/a%�'d/�w�D\w7!EC$C�N�DG?)D1(P��Dq')��C$D9/+.?A!E|3!$/".H(7|+!$FHN�')CI��2�N}/a%�D�')#G#1D1C$D1(+'d/a!$N�Fc:�N�!$?)D1(+|3D)0^/a%�DG|+D�F~')C�'�V�!$D1|7')(3D�'d#1#1DGCEDG(a'd/+!EN�F9'ew>'eQ}yz(+.)[ :�|�|3.yÅ')|�/�/+%�'d/�w�D"#e'dN\N�D<?HD1(�#e'd/+#&%c/+%�D1[Y��XL%�D"/a.)/a')C�Ng:�[r��D1(�.)yU|�/&')(3|�/+%�'d/�.H:�(�(a'd*�!E.�|+!$FHN�')C$|�w7!EC$C�DG?HDG(u�')|3|7!E|7.)yM.H(+*�DG("Û��¦�@£)R+4��

�Uº i�� ��o¾�¿�� �Â)½@ÃÅ¿�¼� f¿�¾c½�� ��}¼Mà � A¾&�'stD�w7!EC$C�#&%�.A.H|3DL'�#1.HN�yz.H(+[c')CA[\')u�/a%�'d/Mw7!EC$C�#G.�?)D1(�/+%�D�w7!E*�D>(a')N�FHD>.)y^|3#e')C$D1|¸yz(3.H[¥/+%�DL��')(�/a%U��|

N�DG!EFH%g��.H(+%�.A.A*Ý/a.�/+%�D�#1.)|+[9!E#-[9!E#G(+.@w�'@?)D���')#&]gFH(3.H:�N�*5��K¸!$(+|�/\w�D�w7!ECEC"#1.)N�|+!$*�D1(\/+%�D �^'W/#e')|3DÆ��9Ñ £HÊ�w7%�!E#&%c/+%�D7s 6&���¦*�'W/&'�/aD1C$CE|�:�|�!E|�/+%�D�')u�u�(3.Hu�(+!E'd/aDL#G.H|+[9.HC$.HFH!E#1')C�[9.A*�D1CI� ��:�(�[\'du�w7!$CEC��D"/�w�.r*�!$[cDGN�|+!$.HN�')C�|3.�/+%�'d/�!$/�#e'dN\��D�|3%�[email protected]\'�w>'dCEC�#&%�')(�/e��*�D�Ë�')u�u�'d(+D1N~/10�,�D1C$CED1(G0�' O�:�#&%�(a'Æ��eÉH¢HÈ~Ê�|+%�.@w�D1*w7!$/+%\/a%�DG!E(�|+CE!$#1D�.)ym/a%�DS:�N�!$?)D1(3|+D)0d�3:�|3/L%�.@w |+:�#1#1DG|+|�yz:�C�'r|+C$!E#1D�.)ym/a%�D�:�N�!{?HD1(3|+D�#1')N��D�!EN-!ECEC$:�|3/+(a'd/+!EN�FPCE')(+F)D�|3#e')C$D�|3/+(+:�#</a:�(3D)��XL%�DPB�CE.~'dN�=�!EF)!$/&'dC�B�:�(�?HDGQ-|+%�.):�CE*�D<?HDGNg/+:�')C$C$Q8!EN�#GCE:�*�D|+u�D1#</a(+' ')N�* ')#G#1:�(+'d/aD�u�.H|+!{/a!$.HN�|�yz.H(')��.H:�/-��[c!$CEC$!E.HNvF~')CE'WV�!EDG|\')N�*Ú�A:�')|a')(3|!ENÚ' �)=�|a')[9u�CEDÆÅ|3D1DcBA/+.H:�FH%~/a.)N�D</o')Cf��ÆfÛ)£)£~ÛHÊ�� �S��'d�e'��3!E')N�DG/o')CI��ÆIÛ)£H£H�~Ê��mBA/+(a'):�|+|�DG/o')CI��ÆIÛ)£H£~ÛHÊ��U 7!E#&%�'d(+*�|�D</o')Cf�ÆfÛd£H£~ÛHÊ��U��!E|3D1N�|�/aD1!$NtD</�')Cf��ÆfÛ)£H£���Ê"yz.H(oB�=�B�BÒ|3#1!EDGN~/a! ��#P(+D1|3:�C$/+|o')N�*tb�C�')N~/+.HN�DG/�')CI��ÆfÛd£H£H�~Ê��mO�.HF)FDG/9'dCf�LÆIÛ)£H£H�HÊ���BA[c!{/a% DG/9'dCf�LÆIÛ)£H£~Û)Ê�����!$D1(PDG/9'dCf�LÆIÛ)£H£H�HÊoyz.H(�yz:�(�/a%�DG(P/aD1#&%�N�!E#1')C>(+D<yzD1(3D1N�#GD@Ê<� b�:�/?A!E(�/a:�')C$C$Q\#1.H[9u�CED</aD�')CE(3De')*�Q}!E|�')N-DG�A:�'d/a.H(3!�')Cm|3CE!$#1Do×\*�DGFH(+DGD1|Sw7!$*�DqÆ ��Û �

���Û � Ê7#GD1N~/aDG(+DG*�.HN

/a%�D�#1D1C$D1|�/a!�'dC5D1�g:�'W/a.H(L#G.�?)D1(3!EN�F���.)/a%N�.)(3/a%�D1(+NY')N�*Y|3.H:�/+%�D1(3NYFH')C�')#</a!$#S%�DG[c!$|+u�%�DG(+DG|1��XL%�!E|�|+%�.@w7|[c')N~Q!EN~/aDG(+DG|3/a!$N�FPyzDe'd/+:�(+DG|7!EN�#GCE:�*�!$N�FP[c')N~Qu�(+.)[c!$N�D1N~/L?H.)!E*�|"')N�*8'PFH(+D1'd/7w>'dCECUC$.HN�FHDG(>/a%�')N}/a%�DFH(3De'd/Lw�')CECUyz.):�N�*}�~Q8,�DGCECEDG(L')N�*YO":�#&%�(a'-Æ��@É)¢HÉ~Ê<�

B�!$N�#1DY/a%�D8.H��|+DG(3?)D1*Ú|+C$!E#GD8!$|\')C$(+D1')*�Qv!ENÝ' �^'W/qu�CE')N�D�Æ�� Ñ £t[9.�*�D1Cf0�')CE.)N�F�/+%�D-#GD1C$D1|3/+!�')CD1�g:�'W/a.H(aÊ�w�D�[\'eQ9u�(3.W�3D1#</>/a%�!$|�|3CE!$#1D"*�!E(3D1#G/+C$Q9.HN~/a.�' �^'d/�|+%�DGDG/L.dymu�')u�D1(�:�|+!$N�Fru�.HC�')(�#G.�.H(3*�!EN�'d/aDG|w7!$/+% Ñ � ��� � ��D1!$N�F /a%�DÒ#1.W��[9.�?A!$N�F *�!E|�/&')N�#1D)0S')N�* � �JDG!EN�F¦/+%�DÒ(+!$FH%~/Y')|+#GD1N�|3!E.HNU� Æ Ä 6-b

Page 10: A Map of the Universe - J Richard Gott, M Juric, et al

� �@£ �

.H��|3D1(�?)'W/a!E.)N�|�yz(3.H[xb�.�.)[cDG(a')N�F�0�=#��B�2&0�6&����2�6&��')N�*\s 6&���v!EN�*�!E#1'd/aD7/a%�'W/�/a%�D�#e')|3D �9Ñ £�!$|/a%�DP')u�u�(3.Hu�(3!�'d/+Dr.HN�D�yz.)(�/a%�DP:�N�!$?)D1(3|+D)��K�.H(S[c'd/+%�D1[c'd/a!$#e')C�#G.H[cu�CEDG/+D1N�DG|+|�w�Drw7!EC$C¸')C$|+.q#G.HN�|3!E*�DG(/a%�D � Ñ ØP�-')N�* � Ñ �o�-#e'd|+D1|c!ENÜ')NÜ')u�u�D1N�*�! VJ�ðÊ stDYw7!$|+% /a.�|3%�.@w C�'d(+FHD}|+#1')CEDY|3/+(+:�#</a:�(3D')N�*9/a%�D"D<VA/+D1N~/>.)y5/a%�D".H��|3D1(3?d')��CED":�N�!$?)D1(3|+DS.):�/�/a.�/+%�D"#1.H|3[c!$#"[9!E#G(+.@w�'@?)D���')#&]gFH(+.H:�N�*q(a'd*�!�'d/+!E.HN!EN�#1CE:�*�!EN�F9')C$CU/a%�D�B�=�B�B}F~')CE'WV�!ED1|"')N�*-�g:�')|+')(+|�!EN}/a%�DoD1�g:�'d/+.H(+!E')Cm|+C$!E#GD)�>2�N ��FH:�(3D\�H0^.HN�Do#e'dN-|+DGD/a%�D�#1.H|3[c!$#S[9!E#1(3.@w>'e?HD���')#&]gFH(+.H:�N�*-'W/>/a%�D�|3:�(3yÅ'd#1D�.)yZC�'d|3/>|3#e'd/3/aDG(+!EN�Fc'd|L'r#1!$(+#1C$D)��2Í/+|>#1.d�Í[c.@?A!EN�F(a'd*�!E:�|"!E|o�e× õ£q,�u�#)��ÆfB�!$N�#1Do/a%�D�|+!$�1Do.)y�/a%�D�:�N�!{?HDG(+|+Dr'd/�/+%�D�DGuJ.A#&%�.)y�(+D1#G.H[r��!$N�'d/+!E.HNY!E|"|+[c')CEC$D1(/a%�'d/q/a%�'d/'¦u�(3D1|3D1N~/}�~QÚ'tyÅ')#</a.H(\.)y��oØ Ñ �@£)ÉH£�0>/a%�D-/a(3:�D�(a'd*�!E:�|\.)y�/a%�!$|\#G!E(+#GCED8!E|q'd�J.H:�/��Û õ¢)×c68u�#)� Ê\B�C$!EFH%~/+C$Qc�JD<QH.HN�*Y/a%�Do#1.)|+[9!E#�[9!E#1(3.@w>'e?HD���'d#&]AF)(+.H:�N�*-!ENY#1.W��[9.�?A!$N�FP#1.A.H(+*�!EN�'d/+D1|L!$|/a%�D�b�!EF�b>')N�F\'d/"'P#G.d��[9.@?�!$N�FP*�!$|3/&'dN�#1D�.)y��e× õ�9,�u�#)�

ÆÅ2�[c')FH!$N�Dc'�uJ.H!$N~/r.HN¦/+%�Dq#1.)|+[9!E#\[9!E#G(+.@w�'@?)Dq��')#&]gFH(3.H:�N�*v#G!E(+#GCEDd��=�(a'ew '�(a')*�!E:�|�')(+.H:�N�*/a%�'d/ouJ.H!$N~/o/+%�'d/o!E|�/a')N�FHDGNg/o/a.Y/a%�D9.H:�/+D1(�#1!$(+#GCED�C�')��D1C$D1*�b�!$F-b>'dN�F�0M')|�|+%�.@w7N¦!$N�/+%�D ��FH:�(+Dd0¸!$N.)/+%�D1(7w�.)(+*�|G0U'c#G!E(3#1CED�/a%�'d/S%�')|S'9(a')*�!E:�|"D1�g:�')CZ/a.�/a%�D�*�! �JD1(3D1N�#GD�!$N-(a'd*�!E:�|"��DG/�w�D1D1N�/+%�D�#G.H|+[9!E#[9!E#1(3.@w>'e?HDS��')#&]gFH(+.):�N�*}#1!$(+#1C$DS'dN�*q/a%�D�b�!EF�b>')N�FP#G!E(+#GCEDd��XL%�'d/�#1!E(3#1C$DS%�')|>'�#1.d�Í[c.@?A!EN�F�(a'd*�!E:�|�.)yÛ)¢H�c68u�#)��XL%�'d/�!E|L/a%�Do#1.W��[9.�?A!$N�F�%�.H(+!$�1.HN}(+')*�!E:�|�'W/S(3D1#1.)[r��!EN�'d/a!$.HNU��2Íy¸/+%�D�b�!EF9b>')N�F9[9.�*�DGC �w7!$/+%�.H:�/�!$N��^'d/+!E.HN � w�D1(+D�#1.)(+(+DG#G/�w�D�w�.H:�C$*oD�V�uJDG#G/¸'"u�.H!EN~/�.HN�/+%�D�#1.H|3[c!$#�[c!$#1(+.@w�'e?HD���')#&]gFH(+.):�N�*#1!$(+#GCED�/+.q��Dr#e'):�|a')C$C$QY!EN���:�D1N�#GD1*�.HN�C$QY�~Q-/a%�!EN�FH|�!EN�|3!E*�Do/a%�'W/�%�.H(3!E�G.HN�(a'd*�!E:�|S'd/�(3D1#1.)[r��!EN�'d/a!$.HNU�XL%�D�'dN�FH:�CE')(c(+')*�!$:�|\.)y�/+%�!E|c|+[c')CEC7#G!E(+#GCED-')|\|3D1D1NÚyz(3.H[ /a%�D���')(�/a%Ì!$|�ÆIÛ)¢H��68u�#eÖ��1×�Ï&£H£H£�68u�#1Ê(a'd*�!�')N�|P.H(}� $�eÈ � � 2ÍyS/a%�D8b�!EF�b>')N�F�[9.�*�DGC�w7!$/+%�.H:�/9!$N��^'d/+!E.HN¦w�D1(3D8#G.H(+(3D1#G/9w�DYw�.H:�C$*ÜD�V�u�D1#<//a%�D�#1.)|+[9!E#�[c!$#1(3.�w�'e?HD���')#&]gFH(+.):�N�*-/+.\��D�#1.)(+(+DGC�'d/+D1*8.HN-|3#e')C$D1|".)y�'d/�[c.)|3/�� $�eÈ � �L2�N��^'W/a!E.)NU0^�gQ%�'e?A!EN�F�'�|+%�.H(�/�uJDG(+!E.A*�.)ym'd#1#1DGCEDG(a'd/+D1*\D�V�u�')N�|3!E.HN9*�:�(3!EN�F�/a%�D ��(3|3/��@£�+ _Íh |+DG#1.HN�*�|�.)yJ/a%�D":�N�!{?HD1(3|+Dd0u�:�/+|�*�!$|3/a')N~/�(3D1FH!$.HN�|�!EN9#e'):�|a')C�#1.HN~/a')#G/��JDG#e'):�|+DS.dyU/a%�D"|+C$!EFH%~/�')*�*�!$/a!$.HN�')C�/a!E[9D7')C$CE.@w�DG*9w7%�D1Nq/a%�D:�N�!{?HDG(+|+DPw�')|�?HDG(3Q�|3[\')C$Cf��B�.�0Uw7!{/a%�!$N��^'d/+!E.HNU0Jw�DP#1')Nt:�N�*�D1(3|3/a')N�*Òw7%gQ-/a%�DP#G.H|+[9!E#r[9!E#G(+.@w�'@?)D��')#&]gFH(3.H:�N�*�!E|Z:�N�!$yz.)(+[ /+.S.HN�D�u�')(�/¸!$Nc�@£)£�0 £)£H£�'dCEC~.@?HDG(M/a%�D�|+]~Q)��K�:�(3/+%�D1(3[c.H(3D)0W(a')N�*�.H[��g:�')N~/a:�[��:�#</a:�'W/a!E.)N�|7u�(+DG*�!E#</aD1*8�~Q}!EN��^'W/a!E.)N}')*�*�'P|3D1(+!$D1|".)y�'d*�!�')��'d/a!$# ��:�#</a:�'d/+!E.HN�|7w7%�!E#&%�'d(+D�D<V�u�D1#G/+D1*/a.�%�'@?)D"'�uJD1')]�!$Nr/a%�DLu�.@w�DG(�|+u�D1#G/+(+:�[Ô'd/�')N�')N�FH:�C�'d(�|+#1')CEDL'd�J.H:�/�/a%�DL|3!E�GDL.)y^/a%�DL%�.)(+!E�G.HNr(+')*�!E:�|'d/7(3D1#1.)[r��!EN�'d/a!$.HN#e')C$#1:�CE'd/aDG*Y')�J.@?)D)0���£ õ¢HÈP*�D1F)(+D1DG|1� Ê

b�D<QH.HN�*Ò/a%�Dcb�!EF}b>')N�F#1!E(3#1C$DP!E|S/+%�D�#1!E(3#1C$Dr|+%�.@w7!$N�F/a%�Dryz:�/+:�(+D�#G.d��[9.@?�!$N�F\?A!E|3!E��!$CE!{/�Q}CE!E[9!$/1�2ÍyZw�D�w�')!$/7:�N~/+!EC5/+%�D�!EN ��N�!$/+DSyz:�/a:�(+D)0�w�D�w7!EC$C5��D�')��CED�/a.�|+DGDo.):�/L/a.P/a%�!E|L#1!$(+#GCED)�LÆÅ2�NY.)/a%�DG(>w�.)(+*�|G0!ENq/+%�D�!EN ��N�!$/+DSyz:�/a:�(+D)0�w�D�w7!EC$C5��D�')��CED�/+.�|+D1D�u�'d(3/a!$#1C$D1|L'd/L/+%�D�yz:�/a:�(+D�#1.W��[9.�?A!$N�Fr?A!E|+!$��!EC$!$/�Q�C$!E[9!$/')|L/a%�DGQ}')u�uJD1')(+DG*-'d/L/+%�Dob�!EF9b>'dN�F�� Ê

XL%�DrB�=�B�BY�g:�'d|a')(3|�D�V�/+D1N�*�.):�/�')�J.):�/"%�')C$y³w�'eQ}.H:�/"/a.�/a%�Do#1.)|+[9!E#�[c!$#1(3.�w�'e?HD���')#&]gFH(+.):�N�*(a'd*�!�'d/+!E.HN5�¸XL%�D�*�!$|3/+(+!E��:�/a!$.HNq.)yZ�g:�')|+')(+|7|+%�.�w7|7|3DG?HDG(a')CUyzD1'd/a:�(+D1|G��XL%�D�(a')*�!�')CJ*�!E|�/a(+!$��:�/+!E.HNc|+%�.@w7||+D<?HDG(a')CZ|+%�DGC$?)D1|"*�:�D�/a.9|+D1C$D1#</a!E.)NYD �5DG#G/+|�')|7*�! �5DG(+D1N~/"|+u�D1#</a(+')CmyzDe'd/+:�(+DG|�:�|3D1*Y/a.�!E*�DGN~/a!$y³Qq�A:�')|a')(3|#1.)[cDP!$Ng/+.q?A!EDGw !EN�/+%�Dr?A!E|3!E��C$D)��B�DG?)D1(a'dC�(a')*�!E')C¸|3uJ.)])D1|o')u�uJD1')(�*�:�DP/a.!$N�#1.)[cu�C$DG/+D1N�DG|+|�!EN�|3.H[9DN�')(3(+.@w�(3!EFH%~/"')|3#1DGN�|+!$.HN8!$N~/aD1(�?d')CE|G��X>w�.9C�')(3FHD�yÅ')N}|+%�'duJDG*-(+DGFH!E.)N�|7')(+D�DG[cu�/�Q')N�*YN�.)/"|+:�(�?HD<QHD1*

Page 11: A Map of the Universe - J Richard Gott, M Juric, et al

� �H� �

��D1#e'd:�|+D�/a%�D<Q�#1.@?)D1(�/a%�D��1.)N�D�.)y>'e?).H!E*�'dN�#1D�#1C$.H|+Dr/+./a%�D�F~')CE')#G/+!E#�u�C�')N�Drw7%�!E#&%�!E|�N�.d/�!EN�#GCE:�*�DG*!ENY/a%�DrB�CE.H')N8|3:�(3?)DGQ)��XL%�D1|3DrD<V�#GCE:�*�DG*�(+DGFH!E.HN�|�(3:�N8yz(3.H[ ')u�u�(3.@V�!$[\'d/+D1C{Q}�  ¡�%�� ����¢ ð¡�%�'dN�*')u�u�(+.eV�!E[c'd/aDGC$Q��@È ð¡�%�� ���ÔÛ)£  ¡�%U�LXL%�Dr�g:�')|+')(+|S*�.\N�.d/S|3%�.@w N�.)/a!$#1De'd��CEDo#1C$:�|3/+D1(+!$N�F\.)(�CE')(+FHD|+#1')CEDc|3/+(+:�#</a:�(3D)��XL%�!$|r!E|o��D1#e'd:�|+Dq/+%�D\�g:�')|+')(+|r')(+Dc|+.�w7!E*�D1C$QÒ|3u�')#GD1* /a%�'W/�/+%�Dq[9De')N¦*�!E|3/a')N�#GD��DG/�w�D1D1N-�A:�')|a')(3|7!E|LC�'d(+FHDG(>/a%�')N/+%�D�#1.H(3(+D1CE'd/a!$.HNCEDGN�F)/+%8'W/L/a%�'d/"DGuJ.A#&%U�

XL%�D}#1!$(+#GCEDq.)y"(3De')#&%�'d��!EC$!$/�Q�!E|P'dCE|+.�|3%�.@w7NU����:�')|+')(+|���DGQ).HN�* /a%�!$|P#1!$(+#1C$Dq')(3D:�N�(3De')#&%�'d��CEDd� "')*�!E.�|+!EF)N�')CE|�D1[9!$/+/+D1*�~Q:�|7N�.@w w7!EC$C5.HN�C{Q\(3De')#&%Y.H:�/"'d|>yÅ')(L')|>/+%�!E|L#G!E(+#GCEDd0�DG?)D1NY!EN/a%�D�!EN ��N�!$/aDyz:�/+:�(+Dd�

XL%�DSB�=�B�B�F~')C�'�V�!$D1|�')u�uJD1')(�')|�'o��CE')#&]r��C$.H�9!ENP/a%�D"#1DGN~/aD1(G��XL%�D1(3DS!$|�[r:�#&%\!$N~/aD1(3D1|�/a!EN�F�CE')(+FHD|+#1')CEDP|�/a(3:�#G/+:�(+D�%�DG(+D���:�/�/+%�D ��D1C$*Ò!E|S/+.�.#G(+.@w7*�D1*�')N�*Ò|+[c')C$CZ/+.Y|3%�.@wÔ!{/e�oXL%�!E|�!$CECE:�|3/a(+'d/aDG|S/a%�Du�(3.H��CEDG[ .dyJ|3#e')C$D>!EN�*�D1u�!$#G/+!EN�FS/+%�DL:�N�!{?HDG(+|+Dd��2Íy^w�D>w�')N~/�'�[\'dur.)y^/a%�D�D1N~/a!$(+D>.H��|+D1(�?d')��CEDL:�N�!$?)D1(+|3D.HN�.HN�D�u�')FHDd0)'d/M'"N�!E#GD�|3#e')C$D)0�/a%�D�F~')CE'WV�!ED1|Z')(3D�#1(a'd[c[9D1*o!EN~/a.�'���CE.H��!EN�/a%�D�#GD1N~/aDG(1��ËmDG/M:�|MD1N�CE')(+FHD/a%�D�#1D1N~/+(a')Cm#G!E(+#GCED�.)yZ(a')*�!$:�|7£ õ£HÈ�/a!$[cDG|�/+%�D�*�!E|�/&')N�#1D�/a.P/+%�D�b�!EFrb>')N�F�#1!$(+#GCEDS�~Q}'�yÅ'd#G/a.)(>.)y��@È��õÈ')N�*}u�C$.)/L!{/7')F~')!$Nq!EN���FH:�(+D�Û���XL%�!E|LN�.@w�|3%�.@w7|"'�#G!E(3#1CEDS.)yZ#1.d�Í[c.@?A!EN�FP(+')*�!$:�|L¢~Ç)¢�6YuJ#d� ��CE[9.H|3/')C$CU.)y¸/+%�D1|3D�u�.H!$Ng/+|"')(+D�F~')CE'WV�!EDG|>yz(+.H[ /+%�DoF~')C�'�V�Q')N�*Y��(+!$FH%~/7(+D1*8F~')CE'WVAQ|a')[9u�C$D1|L.)yM/a%�D�B�=�B�BJ�`�.@w w�D�#e'dN8|3D1D�'�C$.)/L.)yM!EN~/+D1(+DG|3/+!EN�F�|3/+(+:�#</a:�(3D)��XL%�D�[c.)|3/7u�(3.H[c!$N�D1N~/>yzD1'd/a:�(+D�!E|7'9B�C$.~')NY,�(+De'W/s�')CECm'W/"'9[9D1*�!E')N*�!$|3/&'dN�#1Do.)y¸')�J.):�/"���@£968u�#�|�/a(3DG/a#&%�!EN�F�yz(+.H[ ¢  ¡d%Y/+.8�1×H%}!ENY o� ����XL%�D1(+D�')(3DNg:�[9D1(+.):�|�?H.)!E*�|G� ��u�')(�/a!E#G:�C�'d(+C$Q�!EN~/aDG(+D1|�/a!$N�F�.HN�D\!E|�#GCE.H|3D\!$N 'd/P'�#G.d��[9.@?A!EN�F8*�!E|�/&')N�#GDq.)y���Û)Ç68u�#r'd/��H� Çd%� �� ��� �>/S/a%�D�yÅ')("D1N�*-.)y�/a%�!E|7?H.H!$*�')(+D�'\#G.H:�u�C$D�.)y�u�(+.H[9!EN�D1N~/S#GCE:�|�/aDG(+|S.dy�F~')CE'WV�!ED1|w7%�!$#&%�')(3D�(+D1#G.HFHN�!$�e')��CED�')| � ��N�FHD1(3|�.)y>,�.�* �}u�.H!EN~/+!EN�F}'d/�/+%�Dc��'d(3/a%5�c 7D1*�|+%�!{y³/�!$N�/a%�!$|�[\')uÒ!$|/&'d])D1Nv'd|�/a%�D\#1.W��[9.�?A!$N�F8*�!E|3/a')N�#GD\!EN�*�!E#1'd/a.H(o')|3|+:�[9!EN�F-u�')(�/a!$#1!Eu�'d/a!$.HNÒ!ENt/+%�DO":�����C$D ��.@w�0���:�/F~')CE'WV�!EDG|�')C$|+.q%�'e?)DPuJDG#1:�C$!�')("?HD1C$.�#G!$/+!ED1|S')N�*�!$N�'q*�D1N�|+D�#1C$:�|3/+D1(Sw7!{/a%Ò'\%�!$FH%�?HDGCE.A#1!{/�Q8*�!E|+u�D1(3|+!$.HN/a%�!E|�#e'):�|3D1|�/+%�DS*�!E|3/a')N�#GDSD1(3(+.H(3|�*�:�D�/a.o/a%�DG|+D�u�D1#G:�CE!E')(�?HDGCE.A#1!$/+!EDG|�/+.�|+u�(+De'd*\/a%�D�F~')CE'WVAQ�uJ.H|3!$/+!E.HN�|.H:�/�!EN}/a%�D�(+')*�!�'dCm*�!E(3D1#G/+!E.HNYu�(3.�*�:�#1!EN�F9/+%�D � ��N�FHD1(".)y�,�.A* �cu�.H!$Ng/+!EN�F9'd/7/+%�Dr��')(�/a%U�7`":�[cDG(+.H:�|.)/+%�D1("#1C$:�|3/+D1(+|S#e')N8�JD�|+!E[9!ECE')(+C{Q9!E*�DGNg/+! ��DG*U�7XL%�!E|"!E|�'c#G.HN�yz.H(3[\'dCm[\')u50�/+%�'d/�u�(+DG|+D1(�?HDG|�|+%�')u�D1| �D<V�#GCE:�*�!$N�F}/a%�D9|+[c')CEC�D �5DG#G/+|�.)y>uJDG#1:�C$!�')(�?)D1CE.A#1!{/a!$D1|1�9XL%�Dc.H(+!$FH!EN�'dC Ä y �x|+:�(�?HDGQt!ENÒw7%�!$#&% ,�D1CEC$D1(')N�*cO�:�#&%�(a'�*�!E|3#1.@?HDG(+DG*c/a%�DS,�(+D1'd/�s�')CEC�%�')*c'�#G.d��[9.@?A!EN�F�(+')*�!E:�|�.)y5.)N�C$QPÛ��H��68u�#)0~w7%�!E#&%9!E|�C$D1|3|/a%�')NY'r�A:�')(3/+D1(7.)y�/a%�D�(+')*�!$:�|>|+%�.�w7NY!EN���FH:�(+D�Û���KM!EFH:�(3D�Ûr!E|>'r�A:�!$/aD�!$[cu�(+D1|3|+!{?HD�u�!$#G/a:�(+D)0���:�/7!$/*�.AD1|�N�.)/�#1')u�/+:�(+D9')C$C¸.)y�/a%�D9BACE.~')NtB�:�(3?HD<QH��2Íy�w�D9*�!E|3u�C�'eQ)D1* ��FH:�(3D}�c'W/o'}|3#e')C$DPD1N�CE')(+F)D1*Ò�~QÒ'yÅ')#</a.H(�.dy��@È��õÈS/a%�D>#GD1N~/a(+')C�u�.H(3/+!E.HN�.)y^/a%�D>[c')urw�.H:�C$*P�JDL'd|¸QH.H:�|3D1D7*�!E|3u�C�'eQ)D1*�'d/�/+%�D>|3#e')C$DL|+%�.@w7N!EN ��F):�(+DcÛ\w7%�!E#&%�!E|�'d*�D1�g:�'d/+D)0Z��:�/�/a%�Dcb�!EFYb>')N�F}#G!E(+#GCEDrw�.H:�C$*t%�'e?)D\'*�!E')[cD</aDG(�.)y�È��ð¡)ÇqyzDGDG/1���.H:q#G.H:�C$*\u�:�/�/a%�!$|�.HNcQH.H:�(�w>'dCECf0A��:�/�!$yUw�DSw�D1(3DS/a.�u�(+!$Ng/�!$/�!EN9/a%�D��3.H:�(+N�')C�yz.)(�Q).H:q/a.P'd|+|+DG[r��C$D!$/7w�.H:�C$*-(+DG�g:�!E(3D�/a%�D�N�D�VA/�ÛHÇ)È9u�')FHDG|1�LXL%�!$|�u�.H!$Ng/+|�.):�/�/+%�D�u�(+.H��C$D1[ .)y¸|+#1')CED�yz.H("DG?HDGN�|+%�.@w7!$N�F/a%�D�B�CE.H')N�B�:�(3?HD<Q�')C$C�.HN�.HN�D�u�')FHDd��B�[c')CEC�|+#1')CEDG|�')(3Dr')C$|+.\N�.)/�(+DGu�(+DG|+DGNg/+D1*�w�D1CECI�SXL%�DP*�!E|3/a')N�#GD/a.o/a%�D"T�!$(+FH. Ä CE:�|�/aD1(�!EN ��FH:�(3D�Ûo!$|�.)N�C$Qc')��.H:�/>Ûo[9[�')N�*\/+%�DS*�!E|3/a')N�#GD�yz(+.)[�/+%�D�6Y!ECE]~QPs�'eQ9/+.6-���L!$|�.HN�C{Q\�@Ö��@�d/+%P.)yJ'�[c!$CECE!$[cD</aDG(�')N�*P/a%�DG(+D<yz.H(+DL!$Ng?A!$|+!E��CED�.)Nr/a%�!$|�6-')uU��K¸!EFH:�(+DLÛA0~*�(a')[c'd/+!E#>'d|!$/7!$|10�yÅ'd!ECE|�/a.�#e')u�/a:�(3D�'Pu�!$#G/+:�(+D�.)y¸')CECJ/a%�D�D<VA/+D1(+N�')CmF~')CE'WV�!ED1|7'dN�*}�A:�')|a')(3|1��XL%�D�N�De'd(+�~Q}F~')CE'WV�!ED1|

Page 12: A Map of the Universe - J Richard Gott, M Juric, et al

� ��Û �

')(3D�/+.�.P#GCE.H|3D�/a.�|+DGD�')N�*}/+%�D��g:�')|a'd(+|�')(+D���DGQH.)N�*Y/+%�D�CE!$[c!{/a|�.dyM/+%�D�u�')FHDd�stD�[c'eQq/a(�Qu�CE.d/+/a!$N�Fr/a%�D�:�N�!$?HDG(+|3D�!EN}C$.�.H]g��'d#&]\/a!$[cD�(+'d/a%�DG(L/a%�')N8#1.d�Í[c.@?A!EN�FP#1.A.H(+*�!$N�'d/+D1|1�

XL%�DP(3D1|+:�C$/�!$|S!$N ��FH:�(3DP����XL%�DP.H:�/aDG(S#G!E(+#GCED�!E|�/+%�Dr#G.H|+[9!E#�[c!$#1(+.@w�'e?HDr��'d#&]AF)(+.H:�N�*U��2Í/�!E|�!EN�*�!E|��/a!$N�FH:�!$|+%�'d��CED�yz(3.H[�/a%�D�b�!$F\b>'dN�Fq')|7/a%�D�/�w�.q')(3D�|3D1u�')(+'d/aDG*��~QY.HN�C$QY�)¢H£�Ï&£H£)£PQ)De')(3|S.H:�/S.)y>�@�  ¡��!$CECE!$.HNtQ)De')(3|1�vXL%�D8B�=�B�B¦�g:�')|+')(+|9N�.@w�D�VA/aD1N�*Ý��')#&]�N�De')(3C$Qt/a.�/a%�D}#G.H|+[9!E#q[9!E#G(+.@w�'@?)D}��')#&]H�FH(3.H:�N�* (+')*�!�'W/a!E.)NÚÆÅ|3!EN�#GDq!$/�!E|o/a(+:�Dq/a%�'d/�w�D}'d(+Dq|3D1D1!$N�F���')#&]�/a.�w7!{/a%�!$N '-��!$CECE!$.HNÒQHDe'd(+|P.)y7/a%�Db�!$Frb>')N�FgÊ<��Ëm.A.H]g��')#&]�/a!$[cD"!E|�De')|3!EDG(�/a.�D<V�u�C�'d!ENc/+.r'�CE'eQ\'d:�*�!EDGN�#1D"/a%�'dNq#1.d�Í[c.@?A!EN�F�#G.�.H(3*�!EN�'d/aDG|')N�*}!{/L[\'d])D1|>/+%�DoB�=�B�Bq*�'W/&'PCE.A.H]�[c.)(+D�!$[cu�(3D1|3|+!$?)D)0���:�/7!$/>!$|7'r[c!$|+C$De')*�!$N�F�u�.H(�/a(a'eQH')Cm')|>yÅ')(7'd||+%�')uJDG|r')N�*t/a%�DcFHDG.H[9DG/a(�Q�.)y�|+u�')#GDq')(3Dc#G.HN�#GD1(+N�D1*U�2Í/�[c!$|+C$De')*�|�:�|�')|�/a.Y%�.@w�yÅ')(�.H:�/�w�Dq')(3D|+DGD1!$N�FP!EN|3u�')#1Dd��K^.)(�/a%�'d/e0�#1.d�Í[c.@?A!EN�F�#1.A.H(+*�!$N�'d/+D1|L')(3D�')u�u�(+.Hu�(3!�'d/+D)� ��FH:�(+D��r*�.�DG|LN�.)/Lu�(+D1|3D1(�?HD|+%�')uJDG| � !$/7#G.H[cu�(+D1|3|+DG|�/a%�D�CE')(+FHD�'d(+De'���DG/�w�D1D1N�/+%�D�B�=�B�B}�A:�')|a')(3|S'dN�*8/+%�D�#G.H|+[9!E#�[9!E#G(+.@w�'@?)D��')#&]gFH(3.H:�N�*Ò!$Ng/+.q'c/+%�!EN-(+!E[Y�SXL%�!E|S!$|SN�.d/�'\#1.)N�yz.H(+[c')C�[c')uU�SXL%�D9B�=�B�B8F~'dC�'WV�!EDG|SN�.@w¥.A#1#1:�ugQ'�C�')(3FHD1(L|3u�')#1Do!EN/+%�D�#GD1N~/aDG(10^��:�/"/a%�DGQY')(3Do|�/a!$CECU|3.c#G(+.@w7*�D1*Y/a.HF)DG/a%�D1(7/a%�'d/".HN�Do#1')NYN�.)/"|+DGD�/a%�DC�'d(+FHD�|3#e')C$D�|3/+(+:�#</a:�(3Do#GCED1')(+C{QH��K¸!$FH:�(+DS×P|+%�.@w7|7/a%�D�#1DGN~/a(a'dC�£��ðÛ�(+')*�!$:�|L#1!$(+#1C$D�ÆÅ|3%�.@w7N�')|7'P*�.d/+/aDG*#1!$(+#GCEDq!$N ��FH:�(3D�~Ê�D1N�C�')(3FHD1* �~Q '�yÅ')#</a.H(�.)ySÇ��tXL%g:�|�!{y"w�Dqw�D1(+D/+.�[\')]dD}'-w>'dCEC>[c')u¦.)y"/a%�D.H��|3D1(�?)'d��CEDq:�N�!$?)D1(+|3D:�|+!$N�F�CE.A.H]g��')#&]Ò/a!$[cDc'd/r/+%�Dq|3#e')C$Dq.)y ��FH:�(3Dq×�!$/�w�.):�CE* .HN�C$Q�N�D1DG* /a.���DÛYyzDGDG/P'd#1(+.)|+|P')N�*�w�.):�CE*¦.)N�C$QÒ(3D1�g:�!E(3Dc/+%�DqN�D�V�/PÛHÇ8u�'dFHD1|�!ENt/+%�Do�3.H:�(+N�')C�/+.�u�CE.d/e�}XL%�!E|�!E|�')N')*�?d')N~/a')FHDo.)y¸/+%�D�C$.�.)]A��')#&]q/a!$[cD�[c')uU��2Í/S[c')])DG|"/+%�Do!EN~/aDG(+D1|�/a!$N�FcCE')(+F)Do|3#e')C$D�|�/a(3:�#G/+:�(+D�/a%�'W/�w�D|+DGDSC$.�#1')CEC{QÆ ��FH:�(3D�×gÊ�'�yÅ')#G/+.H(�.dyU|+C$!EFH%~/+C$Qr.@?)D1(>�oC�')(3FHD1(�!$Nc|3!E�GD�(3D1C�'W/a!$?)DL/a.�/+%�D"#1.H|3[c!$#"[9!E#G(+.@w�'@?)D��')#&]gFH(3.H:�N�*Ò#G!E(+#GCEDo/a%�')N�!{y�w�DP%�')*�:�|+DG*Ò#1.d�Í[c.@?A!EN�F\#1.A.H(+*�!$N�'d/+D1|1��KM!EFH:�(3D�×C$.�.H]g|��A:�!$/aD�|+!E[9!ECE')(/a. ��FH:�(+D�Û�� �>/�#G.d��[9.@?A!EN�FP(+')*�!E!5CED1|3|"/+%�')N8¢~Ç)¢968u�#)0�/a%�DoC$.�.)]A��')#&]\/a!$[cD�'dN�*8#G.d��[9.@?A!EN�FP(+')*�!E:�|')(3D�(+'d/a%�DG(7|+!E[9!ECE')(1��Bg/a!EC$Cf0 ��FH:�(+Do×9!E|7N�.)/�uJDG(3yzDG#G/aC{Q#1.)N�yz.H(+[c')CI��`"De')(L/a%�D�.H:�/aD1("D1*�FHD1|"/a%�DG(+Do!E|"'|+C$!EFH%~/�(+')*�!E')CM#G.H[9u�(+DG|+|+!$.HN�/a%�'W/�!E|���D1FH!$N�N�!$N�Fq/a..A#1#G:�(�!EN�/a%�DPCE.A.H]g��')#&]8/+!E[9D�[c')u�')|�.HN�DPF).�DG|/a.@w�')(+*¦/+%�D}b�!$F�b>')N�F���XL%�DD��JD1#</a|P.)y"(+')*�!�'dC�#G.H[9u�(+DG|+|+!$.HNv')(3Dq!EC$CE:�|�/a(a'W/aD1*t!EN ��FH:�(+DÇ�0�w7%�D1(3Dw�D�%�'e?)D�u�C$.)/+/+D1*8'9|3�A:�')(+D�FH(+!$*Y!$N8#G.d��[9.@?A!EN�FP#G.�.H(3*�!EN�'d/aDG|"!$NY/+D1(3[c|7.)y¸CE.A.H]g��')#&]\/+!E[9D�')|"w�.H:�C$*��Dc*�DGu�!E#</aDG*�!EN ��FH:�(+D9���q��')#&%�FH(+!$*�|3�g:�')(+D9w�.):�CE*�#1.HN~/a')!EN�')NtDG�g:�')C�Ng:�[r��D1(o.)y>F~'dC�'WV�!EDG|�!ENt'�^'d/"|3CE!E#GD�.)y�#1.)N�|3/a')N~/�?)D1(3/+!E#1')Cm/a%�!$#&]AN�D1|+|G�7XL%�!E|7|+%�.�w7|�/a%�Do*�!E|�/a.H(�/a!$.HN}.)y�|3u�')#1Do/a%�'W/�!$|7u�(+.A*�:�#GD1*�~Q-:�|+!EN�Fc/a%�D�CE.A.H]g��')#&]/+!E[9D)�LXL%�Dr|3�g:�')(+DG|���D1#1.)[cDo[c.)(+D�')N�*�[9.H(+Do*�!$|3/a.)(3/aDG*�!EN8|+%�'duJD�')|S.HN�D')u�u�(+.~')#&%�D1|7/a%�D�D1*�FHD)�

XL%g:�|10A!$/�w�.H:�C$*c��D7:�|+D<yz:�C�/a.�%�'e?HD�'�#1.HN�yz.)(+[c')C�[c')u�u�(+.��3D1#G/+!E.HN�/a%�'d/�w�.):�CE*9|+%�.@wÌ/+%�DLw7%�.HC$DB�=�B�BY|+:�(�?HDGQ)0m!EN�#GCE:�*�!EN�FcF~')C�'�V�!$D1|G0��g:�'d|a')(3|�')N�*-/+%�Dr#1.)|+[9!E#o[c!$#1(+.@w�'e?HDr��'d#&]AF)(+.H:�N�*U0m')|"w�DGCEC�'d||+[c')C$CED1(�|3#e')C$D1|10~#G.@?HD1(3!EN�F�/a%�D>C$.�#1')Cg|+:�u�D1(3#1C$:�|3/+D1(10H/+%�DLËm.A#e')C�,�(3.H:�uU0W/a%�DL68!EC$]gQ�s�'eQH0HN�D1')(+�~Q�|3/a')(+|G0/a%�D�BA:�N-'dN�*8u�C�')N�D</a|G0�/a%�D�68.A.HN8')N�*Y')(�/a! ��#1!�'dCU��')(3/+%8|+'d/aDGCEC$!$/aDG|1��BA:�#&%�'P[c')u}!E|Lu�.H|+|3!E��C$D)�

Ä .HN�|3!E*�DG(M/+%�D�#G.H[cu�CED<V�u�C�')N�D�Æ��ZÏ���Ê�Ñ��MØ�����w7%�D1(3D��MÑ � �o�>'dN�*��')N�*��')(+D�(+D1')CgNA:�[r�JDG(+|G���?HDG(3Qc#1.H[9u�CED�V�Ng:�[r��D1(�� Ñ��"Ø ����w7!EC$C���D�(3D1u�(3D1|+DGN~/aD1*}'d|�'�uJ.)!EN~/�!EN�/a%�D�Æ���Ï���ʸu�CE')N�D7w7%�D1(3D��')N�*��q'd(+D�/a%�D�:�|3:�')C Ä ')(�/aD1|3!�')N}#G.�.H(3*�!EN�'d/aDG|1��XL%�D�yz:�N�#G/+!E.HN�� Ñ��~CENUÆ���Ê�[c')u�|L/a%�D�u�CE')N�D9Æ��ZÏ���Ê

Page 13: A Map of the Universe - J Richard Gott, M Juric, et al

� �@� �

.HN~/a.r/+%�D�u�CE')N�DrÆzÎ�ÏaÐ�Ê�w7%�DG(+D � Ñ Î�Ø �fÐ���XL%�D�Æ��ZÏ���Ê�u�C�'dN�DS(3D1u�(3D1|+DGN~/a|"'�|+C$!E#GDS.)y�/a%�D�:�N�!{?HD1(3|+D�!$N!E|3.)/a(3.Hu�!$#�#G.�.H(3*�!EN�'d/aDG|rÆz!EN8/+%�!E|�#e')|3Dr#1.W��[9.�?A!$N�F\#G.�.H(3*�!EN�'d/aDG|�|3!EN�#GD �}Ñ¥£~Ê�0U')N�*-/a%�DqÆzÎ�ÏaÐ�ÊLu�C�')N�D(+DGu�(+DG|+DGNg/+|�.H:�("[\'du8.)y¸/a%�Do:�N�!{?HD1(3|+Dd��XL%�D�!EN~?HDG(+|3D�yz:�N�#</a!E.)N � Ñ�D<V�uZÆ��>Ö ��ÊL!E|L/a%�D�!EN~?HDG(+|3Dr[\'du/a%�'d/�/a')])DG|P'8u�.H!EN~/�!EN�.):�(�[c')u¦u�C�')N�D-ÆzÎ�Ï+Ð�Ê���')#&]Ò/a.-/+%�D\u�.H!$Ng/�!$/�(+DGu�(+DG|+DGNg/+|P!EN�/a%�Dq:�N�!$?)D1(+|3DÆ���Ï���Ê���2�NY/+%�D�:�N�!{?HD1(3|+Do!$/7!$|L:�|+D<yz:�CU/a.9D1|�/&')��C$!E|3%Yu�.HCE')(>#1.A.H(3*�!EN�'W/aD1|oÆ �Ï �HÊ�w7%�DG(+D

� Ñ �#G.H| � Æ��@È~Ê� Ñ �|3!EN#� Æ���¡HÊ

')N�* Ñ Æ�� R Ø � R Ê 4+*ÍR !$|9/+%�D Æz#1.d�Í[c.@?A!EN�FgÊr*�!E|�/&')N�#GD8yz(3.H[ /a%�D8#1DGNg/+D1(q.dy�/a%�D-��')(3/+%Ú')N�* � Ñ')(3#G/&'dN�Æ���Ö �JÊ�!$|>/a%�D�(+!$FH%~/"')|+#GD1N�|3!E.HNY[9De')|3:�(+DG*-!EN(+')*�!E')N�|1��BA!EN�#GD

#1.H| �oÑ � ��� Ø �/+ ���Û Ï |+!$N ��Ñ � ��� � �/+ ���

Û � Æ��@¢~Ê

!$/7!$|L#1C$De')(>/+%�'d/

� Ñ���Ø ����Ñ �ÆÅ#G.H| �"Ø �~|+!$N#�HÊ Ñ �� ��� Æ��@É~Ê� Ñ��~CENUÆ���Ê�Ñ �&ÆzCEN 7Ø � �)Ê�Ñ � �"Ø �~C$N Ñ ÎrØ �IÐ ÆfÛ)£~Ê

|+.�·

Î Ñ � � ÆfÛ���ÊÐ Ñ CEN ÆfÛHÛHÊ

XL%g:�|10A/a%�D7DGNg/+!E(3D�Æ���Ï���ʸu�C�')N�D)0gD<V�#1DGu�/�/+%�D7.H(+!$FH!ENYÆÅ£�Ï&£~Ê�0~!E|�[c')u�u�D1*9!EN~/a.o')N9!EN ��N�!$/+D>?HD1(�/a!$#e')C�|�/a(+!$u.)yM%�.H(3!E�1.)Ng/a')C5w7!$*�/a%8ÛWÕ�0�!I�õDd�

��ÛWÕ�Î�� £�Ï � � �

� �

ÆfÛ)�~Ê

ÆIKM!EFH:�(3D�È�|+%�.@w7|¸/+%�D>#1.)[cu�C$D<Vou�CE')N�D ��Ø ����[\'du�uJDG*r.HN~/a.�/a%�D�Î�Ø �fÐ�u�C�'dN�D��~Qo/a%�!$|M[c')uU� ��N�D#e'dN9/a')])DL/a%�!E|�[c')u9')N�*9[\')]dDL!$/�!$Ng/+.�'o|3CE!$*�D>(+:�CED>yz.H(�[r:�C$/a!$u�C$QA!$N�FS#G.H[cu�CED<VrNg:�[r��D1(+|G����%�.)/a.A#1.)ugQ/a%�D�[c')u�.HN�/a%�!$|�u�')FHD"')N�*c#1:�/�!$/�.H:�/e��XM')u�D7/+%�D"CEDGy³/�%�')N�*\DG*�FHD7/a.�/a%�D�(3!EFH%~/�%�')N�*9D1*�FHD"/+.�[c')]dD'-u�'duJDG(�#GQAC$!EN�*�DG(1�YXL%�D �Y#1.A.H(+*�!$N�'d/+DcN�.@w�[9De')|3:�(+DG|rCE.)N�FH!$/+:�*�Dc')N�FHC$Dc.)Nt/a%�'d/r#<Q�C$!EN�*�D1(1�8`�.@wu�%�.d/a.A#1.Hu~Qr/+%�D�[c')u�.HN~/a.�'�/a(+')N�|+u�')(+DGN�#GQ)0�')N�*c#G:�/�!{/�.H:�/10g')N�*c')F~')!$N�/a')u�D>/a%�D"CED<y³/�%�')N�*9D1*�F)D7/+./a%�D�(+!$FH%~/S%�')N�*�DG*�FHD�/+.\[c')])D�'9/+(a')N�|3u�')(3D1N~/�#<Q�C$!EN�*�D1(1�72�N�#G:�/+/+!EN�Fc.H:�/�/a%�D�CEDGy³/�')N�*�(+!$FH%~/S%�'dN�*|+!$*�D1|�.)y�/a%�D�[c')u�#&%�De'W/�'�CE!{/+/+CED)0d#1:�/�')C$.HN�F�/+%�D7.H:�/a|3!E*�D7DG*�FHD1|�.)y�/a%�D7[c')u��J.)(+*�DG(+CE!$N�D1|�|3.o/+%�'d/�/a%�D#1!$(+#G:�[9yzDG(+DGN�#1Dr.dy�/a%�D�/+(a')N�|+u�')(3D1N�#<Q�#<Q�C$!EN�*�D1(�!$|��3:�|�/�'c/a!$N~Q-��!{/SCE')(+F)D1(�/+%�')N�/+%�Dru�')u�D1(�#GQACE!$N�*�DG(')N�*8|+.9/a%�'d/"!{/"w7!$CEC���/S|3NA:�FHC$Q}.@?HDG(S!{/e��s !$/a%Y/a%�Dou�')u�D1(7#<Q�C$!EN�*�D1("|+Ng:�FHC{Q}!EN�|3!E*�D�/a%�Do/+(a')N�|3u�')(3D1N~/#GQAC$!EN�*�DG(�QH.H: 'd(+D�(+D1')*�QÒ/a.Y[r:�C{/a!Eu�C$QH��2Íy>Q).H:tw�')N~/�/+.8[�:�C$/+!Eu�C{Q-/�w�.-Ng:�[r��D1(3|�� Ñ ��Ø� ��'dN�* Ñ !LØ ��')C$C�Q).H: *�.�!E|�(+.)/a'd/aD\')N�* |+C$!E*�D9/a%�Dq/+(a')N�|+u�')(3D1N~/�#GQAC$!EN�*�DG(�:�N~/+!EC�/+%�D\/+(a')N�|3u�')(3D1N�#<Q

Page 14: A Map of the Universe - J Richard Gott, M Juric, et al

� �e× �

Ng:�[r��D1(��8ÆÅ!I�õDd�q�"ØÚ£ ��ÊS!$|�*�!E(3D1#G/+C$Q-.�?)D1(�/a%�D9Ng:�[��JDG( ��Ø � �".)NÒ/+%�D�u�')u�D1(�#GQAC$!EN�*�DG(10U/+%�D1N�CE.A.H]:�u�/+%�DqNg:�[r��D1( !LØ �S.)N�/a%�Dc/a(a'dN�|+u�'d(+D1N~/P#<QACE!EN�*�D1(G0¸��D1CE.@w�!{/�.HNt/a%�Dqu�')uJDG(�#<Q�C$!EN�*�D1(�w7!$CEC���D/a%�D\u�(3.�*�:�#G/ � ��c�8XL%�D\CE.HF~'d(+!$/+%�[ .dy ��� !$|�DG�A:�')C�/+.-/a%�D\|+:�[ .dyL/a%�DcCE.HF~'d(+!$/+%�[9|�.)y ��'dN�*�\� �Sy�#1.H:�(+|+Dd0m.HN�/a%�Dr(+D1')C�'WV�!$|10��9ÑÔ£�ƳÎ�Ñ�£~Ê�05/a%�D�[\')u-CE.A.H]g|SCE!$])D�/+%�Dr|3#e')C$Dr.HNÒ'\|3CE!E*�D�(+:�CED)��SC{/aDG(+N�'d/+!$?)D1C$Qr[\')]dDS' �^'d/�|+C$!E*�D7(+:�CEDLyz.H(�[r:�C$/+!Eu�C{QA!EN�F�#G.H[9u�CED�V9NA:�[r�JDG(+|G·�[\'d])D�/�w�.�u�%�.)/a.A#1.)u�!EDG|.)y�/a%�D�[c')ut.)N�w7%�!{/aD�u�')u�D1(o')N�*t/&'duJDP/a%�D1[�/a.)FHDG/+%�D1(�/a.Y[c')])DP/�w�.-#GQA#GCED1|o!EN �qyz(+.H[ (+!EF)%g/�/+.CED<y³/e��XL%�D1N8[\'d])Do.HN�D�u�%�.)/+.�#G.Hu~Q}.)y¸/+%�Do[\')uY.HN~/a.c'P/a(a'dN�|+u�'d(+D1N�#GQH�>ËZ'eQ/+%�D�Ng:�[��JDG(o�\ÆÅ.)N8/a%�D/a(+')N�|3u�')(+DGN�#GQ�Ê�.HN9/a.Hu\.)ym/a%�D�Ng:�[r��D1( � !ENc/+%�D�(3!EFH%~/�%�')N�*q#<QA#1CEDS.)yU/a%�D�u�')u�D1(�[\')u\')N�*qC$.�.)]P.HN/a%�D�/+(a')N�|+u�')(3D1N�#<Qyz.H(>/a%�DoNg:�[��JDG(��c0��JDGCE.@w !{/7.HN/a%�D�u�'duJDG("[c')uw7!EC$C5��D�/a%�D�u�(3.�*�:�#G/ ���\� Ê

K�.H(�#G.HN~?HD1N�!ED1N�#1D".HN�.H:�(�[c')uP.)y�/a%�DL:�N�!$?)D1(+|3D)0gCED</ oÑ�Æ � ��� � Ê3Ö% ��tÆÅ#G.d��[9.@?A!EN�F�#G.H|+[9.HC$.HFH!E#1')C*�!$|3/&'dN�#1D d(a')*�!E:�|�.)y>/a%�D��')(3/+%^Êo��D\[9De')|3:�(+DG* !ENt:�N�!$/+|�.)yL/+%�Dq��')(�/a%U��|rDG�A:�'d/a.H(3!�')C�(+')*�!E:�| �� ÑÈH�~¡d¢)]g[8�ÚXL%g:�|G0"#G!E(3#1CEDG|c.dy�#1.)N�|3/a')N~/(a')*�!E:�|-Æ� vÑ ! # % �'�  ÊPyz(3.H[ /a%�D8#1DGNg/+D1(q.dy�/a%�D8��')(3/+%Ú')(3D|+%�.�w7N 'd|\%�.H(3!E�G.HN~/&')CLC$!EN�DG|�ÆzÐ Ñ6!$#&% � �  Ê9!$N /+%�D-[c')uU0>')N�*Ì(+'@QA|c.)y�#1.)N�|3/a')N~/(+!$FH%~/\'d|+#1DGN�|+!$.HNÆ �9Ñ !$# % �'� ðÊ"')(+D�|+%�.@w7N�')|S?)D1(3/+!E#1')C¸C$!EN�DG|rƳÎ�Ñ !$#&% �'� ðÊ�!$N-/a%�Dr[\'duU��XL%�Dr|3:�(3yÅ'd#1DP.)y�/+%�DP��')(3/+%ÆI'W/P!$/+|�D1�g:�'W/a.H(aÊ�!E|P'8#1!E(3#1C$D\.)y":�N�!{/r(+')*�!E:�|r!EN�/+%�DÒÆ��ZÏ���Ê�u�C�'dN�D)0�'dN�*v!E|�/+%�DqC$!EN�DcÐ Ñ £8!EN¦/a%�D[c')uU��XL%�D�(3D1FH!$.HNqÐ

�£r!ENq/a%�D�[\')u\(+D1u�(+D1|3D1N~/a|7/a%�D�!EN~/aDG(+!E.)(�.)y�/a%�D���')(3/+%U0�|+.�.HN�D�#e')N}|3%�.@w /a%�D

��')(3/+%U��|o[c')N~/aC$DP')N�*ÒC$!E�g:�!E*�')N�*Ò|+.HC$!E*�#G.H(+Dd�PXL%�D�|+.HC$!E*�!$N�N�D1(�#G.H(+D�%�'d|�'}(+')*�!$:�|�')��.H:�/�£ {�@É ���0/a%g:�|G0�/+%�DSC$.�w�D1(�D1*�FHDS.)y5/a%�D�[\')uc[r:�|�/�D�V�/+D1N�*q/+.�Ð�Ñ CENmÆÅ£ {�@É~Ê�Ñ �o� õÈHÈ�/+.�|+%�.�w !{/e��XL%�DS(+DGFH!E.)NÐ � £c|+%�.@w7|�/a%�Dr:�N�!{?HD1(3|+DP��DGQ).HN�*�/a%�Dr��'d(3/a%5��XL%�Dr#1.W��[9.�?A!$N�F\yz:�/+:�(+Dr.)��|+DG(3?d')��!$CE!$/�Q}C$!E[9!$/"'d/�'(a'd*�!E:�|�.)y��@ÉP,�u�#S!E|�'d/7É  Û ���@£ 4 � ��')(�/a%(a'd*�!E!I0�'dN�*q|+.r/+%�D�:�u�uJDG(>D1*�F)D�.)ym/a%�D�[\'duq[r:�|�/>D<VA/+D1N�*/a.8ÐÒÑ CENUÆIÉ  Û �Ý�@£g4 � ÊoÑ ×~Ç  ÉH¡/+.8|3%�.@w�!$/e�\XL%A:�|�/a%�D9*�!$[cDGN�|+!$.HN�|�.)y>/+%�Dc[c')ut')(+D��rÎÜÑ�ÛWÕ�0')N�*�PÐ�Ñ�×g¡ õÈH����XL%�Dc')|+u�D1#</�(+'d/a!$.yz.H(�/a%�D�[c')u�!E|�%�DG!EFH%~/�Ö�w7!E*�/+%�Ñ ¡  Ç)¢��cB�DGD ��F):�(+Dc¡qyz.H(�'|+[c')C$Cm|+#e'dCED�?)D1(3|+!E.)N�.)y�/+%�!E|7/a%�'W/�w7!$CEC ��/S.HN-.HN�D�u�')F)D)��Æ��¥|+�g:�')(3Dr[\'du8w�.H:�CE*8%�'e?HDr*�!E[9D1N�|3!E.HN�|ÛWÕ �YÛWÕÒ')N�*\w�.):�CE*#G.�?)D1(7'�|3#e')C$DS(+'d/a!$.�yz(+.)[x��.)/3/a.H[�/a.�/a.Hu.)y�D�V�uZÆfÛWÕZÊ�Ñ Ç)�~Ç �×~É�� ��[\'ducw7!$/+%')NY')|3uJDG#G/�(a'd/+!E.P%�DG!EFH%~/�Ö�w7!E*�/+%\Ñ ¡ ðÇd¢r#1.@?HDG(+|�'P|3#e')C$Do(+'d/a!$.ryz(+.H[ �J.d/+/a.)[ /a.�/a.)uY.dy�Ç)�HÇ õ×HÉ� � � � � Ê

�>/�'�|+#1')CED�.)yJ')�J.):�/L�L(a'd*�!�')NPu�D1(¸!EN�#&%Pyz.H(¸/+%�D7')N�F):�C�')(M|+#1')CEDd0H/a%�!$|¸w�.):�CE*P[c')])D7'�[c')uP'd�J.H:�/È�� Û)¢�!EN�#&%�D1|�w7!E*�D7�~QP×g¡��õÈ�!EN�#&%�D1|�/&')C$Cf0)w7%�!$#&%c#G.H:�C$*9��D7De')|3!EC{Qr*�!$|+u�CE'@Q)D1*c')|�'�w�')C$C�#&%�')(�/e�¸stD�%�'@?)Du�(3D1|+DGN~/aD1*8/a%�D�[c')uY'd/"')u�u�(3.eV�!$[\'W/aD1C{Qc/+%�!E|L|3#e')C$D�C�'d/+D1(>!$N}/+%�!E|7'd(3/a!$#1C$D)�

XL%�!$|!E|N�.)/\/a%�D ��(3|3//a!$[cD-CE.HF~'d(+!$/+%�[9!E#}#1.A.H(+*�!EN�'d/+D1|q%�'@?)DÒ�JDGD1N :�|+DG* yz.H(q'v[c')uÚ.)yo/a%�D:�N�!{?HDG(+|+Dd��XL%�D ��[c.A#1.�6-')uq.dyZB�u�')#GD�6YQA|�/aD1(3!EDG|�ÆI=�D��MD<Q�N�FYÆ��@É~Çd¢~Ê+Ê�u�C$.)/+/+D1*c/+%�DS#G:�(3?)D1*|3:�(3yÅ')#GD.)y�/+%�Dr��')(�/a%�'dN�*�')��.@?HD�!{/�'dC$/a!{/a:�*�D\Ƴyz(+.H[�/+%�D�|3:�(3yÅ'd#1D)0JN�.)/�*�!E|�/&')N�#1D�yz(3.H[ /a%�D�#1DGNg/+D1(aÊ�[\'d(+])DG*.$�t!EN�DG�g:�')C�!$Ng/+D1(�?)'dCE|SCE')��D1CEDG*¦�r[9!EC$D)0��@£q[9!ECEDG|10Z�@£H£\[9!EC$D1|G0M�H0õ£H£H£c[c!$CED1|G0M�e£�0 £)£H£c[9!EC$D1|10Z�@£H£�0 £H£)£[9!ECEDG|10��9[c!$CECE!$.HN-[9!EC$D1|G0��e£Y[9!EC$CE!E.)N-[9!ECEDG|10Z')N�* �@£H£}[9!ECEC$!E.HN-[c!$CED1|G�c2�N�/a%�!$|�(a')N�F)DqB�.)C�')(�|�Q�|�/aDG[.H�A�3DG#G/+|cyz(+.)[ /a%�DY[c.A.HN /a.�T�D1Ng:�|G0"6-')(+|c')N�* /a%�D-B�:�NÌ')(+D}u�C$.)/+/+D1*Ýu�(+.Hu�D1(3C$QH�Ýb�:�/\')C$/+%�.H:�F)%� Ä D1N~/a'):�(+!I0�/a%�D�68!$CE]~Qqs�'eQ}')N�*-6-���o')(3Do|3%�.@w7N-��DGQ).HN�*8/+%�DGQ')(+D�N�.)/7|3%�.@w7N�'d/"#G.H(+(3D1#G/"|3#e')C$DÆÅD<?HDGN�CE.HFH')(+!{/a%�[9!E#1')CEC{Q�Ê��¸XL%�D���')(3/+%U��|�|3:�(3yÅ')#GD�!$|"u�CE.)/3/aD1*w7%�DG(+D�')N-'dC$/a!{/a:�*�D�.)y�£��{�o[c!$CED1|L|3%�.H:�C$*

Page 15: A Map of the Universe - J Richard Gott, M Juric, et al

� ��Ç �

%�'e?HDo��D1D1N5��2�N�'dNgQ}#1')|+Dd0^�JDG#e'):�|3D�.dy¸/a%�D�#G:�(3?d'd/+:�(+D�.)yM/a%�D���')(3/+%U�õ|"|+:�(3yÅ')#GDo!$NY/+%�D�[\'duU0�DG?)D1N�!$N/a%�D�(a'dN�FHDo�JD</�w�DGD1NÒ')N-')C$/+!$/a:�*�D�.)yL�@£�[c!$CEDG|�'dN�*��@£)£9[9!EC$CE!E.)Nq[c!$CEDG|10�/a%�D�[c')u8!$|�N�.)/S#G.HN�yz.H(3[\'dCf�2�N ��#G/+.H�JDG(>�@ÉHÉ)É�0~`S'W/a!E.)N�')C�,�DG.HFH(a'du�%�!E#�u�(+DG|+DGNg/+D1*c'�[\'dur.)y�/a%�DL:�N�!$?)D1(3|+DoÆz/+%�'d/�.)N�D>.)y�:�|7ÆI�H L,oÊu�')(�/a!$#1!Eu�'d/aDG*�!EN�u�(3.�*�:�#1!$N�FgÊ"w7%�!$#&%�w>')|�'}�H=�?A!$DGw¥w7!$/a%Ò'|3u�%�D1(3!E#1')C���')(3/+%Ò'd/�/+%�DP#1DGNg/+D1(�w7!$/+%D1�g:�'dC�w7!E*�/+%9|3%�D1C$CE|�|3:�(+(3.H:�N�*�!EN�F�!$/�C$!E]dDL')N�.HN�!$.HNrw7!$/+%9(+')*�!$!�.)y�×~£H£�0 £H£)£�[c!$CED1|G0)×~£�[9!EC$CE!E.)N�[9!EC$D1|10d×��!$CECE!$.HN9[c!$CED1|G0�×r/+(+!$CECE!$.HN�[c!$CEDG|10��@£rCE!$FH%~/�Q)De')(3|10m�H0õ£H£H£rC$!EFH%~/�QHDe'd(+|10m�e£H£�0õ£H£H£�C$!EFH%~/�Q)De')(3|10m�@£�[c!$CECE!$.HNCE!$FH%~/�Q)De')(3|107���!$CECE!$.HNÒCE!$FH%~/�QHD1')(+|G07�H�G�&�@ÇY��!$CECE!$.HN�CE!EF)%g/oQHD1')(+|YÆIB�CE.H')N¦DG/P')Cf��Æ��@É)ÉHÉ~Ê+Ê���XL%�!$|r[\'du*�!$|+u�CE'@QA|7.H�A�3DG#G/+|7yz(3.H[ /+%�D�[c.A.HNq/a.P/+%�D�[c!$#1(+.@w�'e?HD���')#&]gFH(3.H:�N�*8��:�/"!E|7')C$|+.�N�.)/7#G.HN�yz.H(3[\'dCf�

XL%�D�[\'duou�(+.W�3DG#G/a!$.HN�w�D�')(+D�u�(3.Hu�.H|+!$N�F�!$|m#1.HN�yz.H(+[c')CH��D1#1'):�|+D�/a%�D�*�DG(+!{?)'W/a!$?)D1|�.)y�/a%�D�#1.)[cu�C$D<Vyz:�N�#</a!$.HN ��Ñ �~CEN � %�'@?)DPN�.u�.HCEDG|S.H(��1D1(3.H|�!$N8/a%�Dr[\'du�uJDG*�(+DGFH!E.)NU�S2Íy�w�D�w>'dNg/�/+.q|+DGDr%�.@w 'CE!{/+/+CED�')(+D1'�.dyJ/+%�DL:�N�!{?HD1(3|+D"|+C$!E#1D�!E|�[c')u�u�D1*�.HN~/a.�.H:�(�|+CE!$#1D�w�D7|+%�.):�CE*�*�.o'�X¸'eQACE.)(�D<V�u�')N�|+!E.)NU·¸/a%�Du�.H!EN~/ � Ø � � !E|"[\'du�uJDG*�.HN~/a.9/a%�D�uJ.)!EN~/ � Ø � � Ñ �ÝØ�Æ ��Ö �¥Ê � � !ENY/a%�D�CE!$[c!{/>w7%�D1(3D� � � £�u�(+.@?A!E*�!EN�F�/+%�'d/ �>Ö � �Ñ � |3.r/a%�D�[c')uq*�.�DG|+NU� /L��C$.�w :�uq/+%�D1(3D�')N�* �>Ö � �Ñ £r|3./a%�'d/�/a%�DP|+D1#G.HN�*t')N�*�%�!$FH%�DG(�.H(+*�D1(�/aDG(+[9|�!EN8/a%�DPXM'eQ�C$.H(�D�V�u�')N�|+!$.HNÒ#e')NÒ��Dr!EF)N�.H(+DG* ÆÅu�(3.@?�!$*�!EN�F/a%�'d/7N�.HN�D�.dyM/+%�D�%�!EF)%�D1(L*�DG(+!{?)'W/a!$?)D1| �� �>Ö � � ��D1#G.H[cD�!$N ��N�!{/aD�'d/�/a%�D�u�.H!EN~/ ��Ê<��2�N/+%�!E|L#1')|+Dd0!EN/+%�D�CE!E[9!$/�')| � � � £�0�/a%�DoXM'eQACE.H(L|3D1(+!$D1|7!E|>?d')C$!E*:�|3!EN�FS�3:�|�/7/a%�D ��(3|3/"*�D1(3!$?d'd/+!$?HD�/+D1(+[Y·

� � Ñ � � � � ÆfÛd×gÊ � � Ñ Æ��~CEN �¥Ê � Ñ �

�ÆfÛHÇHÊ

XL%g:�|�yz.H( � �Ñ¥£q')N�* ��N�!$/+DÆÅ!I�õDd��D�V�#1CE:�*�!EN�Fc/a%�Dr#GD1N~/aDG(�.)y�/+%�Dr��')(�/a%Ò')N�*8/a%�D�uJ.H!$N~/�'d/S!EN ��N�!$/�Qw7%�!$#&%Ò')(+DrN�.)/�[c')u�u�D1*�')N~Qgw�'@Q�Ê �>Ö � !E|�N�D1!{/a%�DG(��1DG(+.N�.)(�!EN ��N�!$/�Q)��XL%�DP%�!EF)%�D1(�*�D1(3!$?d'd/a!{?HDG|Æ %�� ÛHÊ�· �� ��Ö � � Ñ �&Æ ����Ê � %�� � + �� 4"')(+D�')C$|+.���N�!$/+Dow7%�DGN � !E| ��N�!{/aD�')N�*�N�.HN-�GD1(+.��"XL%g:�|G0/a%�D�uJ.)!EN~/ � Ø� � !E|�[\')u�uJDG*q.HN~/a.�/+%�D�u�.H!EN~/ �tØ � � Ñ��tØ ��Ö � � � !$Nc/+%�D�CE!$[c!{/�w7%�D1(3D� � � £�� Ä %�')(+')#G/+D1(+!$�1D�/a%�Dou�.H!$Ng/�� ')|

� Ñ ��ÆÅ#1.)| ��9Ø �~|3!EN ��mÊ ÆfÛ)È~Ê

`�.@w /a%�D�u�(3.�*�:�#G/".)yZ/�w�.9#1.H[9u�C$D<VNg:�[��JDG(+|

� Ñ �dÆÅ#G.H| � ��Ø �~|3!EN#� �1Ê� Ñ ��Æz#1.H| ��5Ø �~|3!EN ��ÞÊ

!E|� ��Ñ � ��ÆÅ#G.H|�Æ�� ��Ø ���ÊmØ �~|+!ENUÆ � ��Ø ��ÞÊ+Ê�Ï ÆfÛH¡HÊ

|+. ��

Ñ � � ÆÅ#1.)|@Æ �����ÊmØ �~|+!$NmÆ �����Ê3Ê<Ï ÆfÛ)¢~Ê

Page 16: A Map of the Universe - J Richard Gott, M Juric, et al

� �@È �

')N�*Y|+!$N�#1D �MÑ #G.H|�ƳÕZÖHÛHÊUØ �~|+!$N�ÆzÕZÖ)ÛHÊ<0

���

Ñ � Æz#1.H|eÆ

ÕÛ � ��mÊmØ �~|+!$NmÆ Õ Û � ��UÊ+Ê ÆfÛ)É~Ê

')N�*

� � Ñ ���Æz#1.H| �

���Ø �~|+!$N#�

���Ê

Ñ � � ÆÅ#G.H|�Æ

ÕÛ � ��mÊmØ �~|+!ENmÆ Õ Û � ��UÊ+Ê

���Æz#1.H| �

���Ø �~|3!EN#�

���Ê

Ñ ���

� Æz#1.H|eÆ ����

Ø ÕÛ � ��UÊmØ �~|+!$N�Æ �

���Ø ÕÛ � ��UÊ+Ê ÆI�H£~Ê

XL%g:�|10�/a%�D�?HDG#G/+.H(�� � !E|"(+.d/&'d/+D1*Y�gQ8')N-')N�FHC$D�ÕZÖHÛ�� ���'dN�*-[r:�C$/a!$u�CE!$D1*�~Q8'9|3#e')C$DoyÅ'd#G/a.)(.)yL�@Ö% �Z�"B�!EN�#1D�')N~QY/�w�.\?)D1#G/+.H(+|�� � 4 ')N�* � � R 'd/�/+%�DouJ.H!$N~/ � w7!$CECm��D�(3.)/&'W/aD1*8�~Q8/+%�D�|+')[9D')[9.H:�N~/�w7%�D1Nv/a%�D<Q ')(3Dqu�:�/P.)N¦/a%�Dq[c')u�/+%�D}')N�F)CED\��DG/�w�D1DGN /+%�D1[ !E|�u�(+DG|+D1(�?HDG*Ý!ENt/a%�D[c')uU0')N�*Y|+.9/a%�Do[c')u}u�(+.W�3DG#G/+!E.HNY!E|7#1.)N�yz.H(+[c')CI��XL%�D�.HN�C$Qu�CE')#1D�/+%�D ��(+|3/"*�DG(+!{?)'W/a!$?)DcÆI')N�*Y/a%�D�%�!$FH%�DG(*�DG(+!$?d'd/+!$?)D1|&Ê���C$.�w :�u�ÆÅ.)(�FH.o/a.��1D1(3.gÊ�!$|�'W/ � Ñ £�'d/�/a%�DS#1DGN~/aD1(�.)yU/a%�D���')(3/+%q.H(�'d/�/a%�D�uJ.H!$N~/�'W/!EN ��N�!$/�Q� Ñ � ��b�:�/�/a%�DL��')(�/a%U��|�#1DGN~/aD1(�*�.�DG|�N�.)/�')u�uJD1')(�.HNr/+%�D>[c')uP'd/�'dCEC5ÆÅ!$/¸!E|�'W/�Ð�Ñ � � Ê<�XL%�!$|�!E|�'|+D</o.)y�[cD1')|+:�(3DP�1DG(+.��PËm!$])DGw7!$|+Dd0�/+%�DPu�.H!EN~/�'d/�!EN ��N�!$/�Q � Ñ � !E|�N�.)/�u�CE.d/+/aDG*�D1!{/a%�DG(ÆÅ!{/7!E|7'd/7ÐPÑ�Ø � Ê<��B�.P/a%�D�[c')u}u�(+.��3D1#G/+!E.HNY!E|L#G.HN�yz.H(3[\'dCm'd/"')C$CUuJ.)!EN~/a|L!$N}/+%�D�[\'duU��B�%�')u�D1|�')(3Du�(3D1|+DG(3?)D1*�C$.�#1')CEC{QH�

XL%�D�#1.)N�yz.H(+[c')CM[\')u�u�(+.W�3DG#G/a!$.HN�yz.H(�|3%�.@w7!EN�F/a%�DP:�N�!$?)D1(3|+D�u�(+DG|+DGNg/+D1*¦%�D1(+Drw�')|�*�D<?HD1C$.Hu�D1*�~Q\�H L,�!ENY�@É~¡HÛ�0A')N�*\%�D"%�')|�u�(+.A*�:�#GD1*c?d')(3!E.H:�|�|3[\')C$C�?HDG(+|3!E.HN�|�.)ym!{/�.@?)D1(�/+%�D7QHDe'd(+|1��XL%�DG|+D�%�'@?)D��D1D1NP|3%�.@w7N�'d/Z?)'d(+!E.):�|M/+!E[9D1|10WN�.)/a')��C{Qo/+.�/+%�D�?A!E|3!$/a!$N�F"#1.H[9[c!{/+/+D1D�.)y�/+%�DLOS'eQA*�DGN���CE')N�D</&')(3!E:�[ !$N�@ÉHÉ)ÈP')N�*/a.P/a%�Do|�/&'%��.)yM/+%�D�`S'W/a!E.)N�')Cm,�D1.)FH(a')u�%�!E#�BA.�#G!EDG/�Qq!EN��@ÉHÉ)É��� 7D1#1DGN~/S*�!$|+#G.�?)D1(3!ED1|Lw7!{/a%�!$N'�w7!$*�D�(a'dN�FHD�.)y�|3#e')C$D1|�yz(3.H[�/a%�D�|3.HC�'d(�|�Q�|�/aDG[�.H�A�3DG#G/a|G0�/a.r/+%�D�B�=�B�B\F~')C�'�V�!$D1|�')N�*�g:�')|+')(+|L%�'@?)Du�(3.H[cu�/aD1*}:�|7/a.�u�(3.�*�:�#1Do')N�*Yu�:���CE!E|3%/a%�D�[c')u!ENY'�C�')(3FHD�|+#1')CED�yz.H(3[\'W/e�

��:�(�CE')(+FHD�|+#1')CEDr[c')u�!$|S|3%�.@w7N�!$N ��FH:�(+D�¢�Ƴ/a%�D�yz.)CE*�.H:�/�Ê<� �Ô(a')*�!�')C�?HDG#G/a.)( � � ÆÅu�.H!$Ng/+!EN�F'ew>'eQ9yz(+.H[Ô/+%�D���')(�/a%U��|�#GD1N~/aDG(&Ê�'d/�/+%�DSu�.H!$Ng/�� u�.H!EN~/+|�!$Nc/a%�DS*�!$(+D1#</a!$.HN �

���Ñ ��M��XL%�!$|�?HDG#G/+.H(

!ENq/+%�D�[c')uq!E|�(+.)/a'd/aDG*Y�~Qq')N}')N�FHC$DSÕZÖHÛ#� ��-|+.P/a%�'W/#����

Ñ ����

Ø�ÕZÖ)Û � ��}Ñ ÕZÖHÛ�0�|+.P/a%�'d/L!$/u�.H!EN~/a|�!EN\/+%�DS?)D1(3/+!E#1')C5*�!$(+DG#G/a!$.HNU��B�[\'dCEC^(+DGFH!E.HN�|�!ENc/a%�D�:�N�!$?)D1(+|3D�')(+DS(+.)/a'd/aDG*q!EN\/+%�D�[c')u\|3.r/a%�'W//a%�D\(a'd*�!�')C�*�!$(+DG#G/a!$.HNU0¸'@w�'eQ�yz(3.H[�/a%�D\#1D1N~/+D1(r.)yL/+%�Dq��')(�/a%U0�!$|�!$Nt/+%�D\?HDG(3/+!E#e'dC�*�!$(+DG#G/a!$.HN�!$N�/a%�D[c')uU�� "')*�!�'dCMC$!EN�DG|�yz(+.)[ /+%�DP��')(3/+%U��|�#1D1N~/+D1(o')(+D�u�CE.)/3/aDG*�')|S?)D1(3/+!E#1')C�CE!$N�D1|G� Ä !E(3#1CEDG|S.)y�#G.HN�|3/a')N~/(a'd*�!E:�|�yz(+.)[�/a%�Dc#1D1N~/+D1(r.)y�/a%�D\��'d(3/a%¦')(+D9%�.H(3!E�1.)Ng/a')C�CE!$N�D1|G�YXL%�D\CEDGN�F)/+%�.)y>/+%�Dc?)D1#</a.H( � � !$|[r:�C{/a!$u�CE!$D1*��~Q�'}|+#e'dCEDPyÅ')#G/+.H(���Ö% �Z�9XL%g:�|10Z/a%�D9|+#1')CEDPyÅ')#</a.H(�'d/�'}FH!$?)D1N�uJ.)!EN~/o.HN�/+%�D�[\'dut#1')N��Do(3De')*Y.$�Ò'd|"u�(+.Hu�.H(3/+!E.HN�')C�/+.8��.@?HDG("/+%�D�*�!E|�/&')N�#1D�.)yZ/a%�D�u�.H!EN~/>yz(3.H[ /a%�D���')(�/a%U0! M��Æ ���g�3D1#G/+|/a%�'d/>'d(+D�/�w7!$#1DS')|�yÅ'd(�'ew�'@Q\')(3D�|3%�.@w7N}'d/S�@ÖHÛo|3#e')C$DS')N�*q.H�A�3DG#G/a|�/a%�'d/�')(3D��@£�/a!$[cDG|�yz:�(�/a%�DG(>'ew�'@Q')(3Do|3%�.@w7N-'W/��@Ö��@£d/+%q/a%�D�|+#1')CEDd0^')N�*Y|+.�yz.H(3/+%^Ê<�

Page 17: A Map of the Universe - J Richard Gott, M Juric, et al

� ��¡ �

"')*�!�'dC�C$!EN�DG|�|3D1u�')(+'d/aDG*�~Qq')Nq')N�FHC$D��qÆz!ENq(+')*�!E')N�|&Ê�0�F).H!EN�F�.H:�/�w�')(+*qyz(3.H[�/a%�D���'d(3/a%qw7!$CEC^��Du�C$.)/+/+D1*8')|�u�')(a')C$CEDGCU?HD1(�/a!$#e')C�CE!$N�D1|7|3D1u�')(+'d/aDG*��~Q8'9%�.)(+!E�G.HN~/&')C�*�!$|3/a')N�#1Dou�(3.HuJ.)(3/a!$.HN�')CJ/a. �A�>XL%g:�|.H�A�3DG#G/+|�.)y�/a%�Dc|a')[9D9')N�FH:�CE')(�|+!$�1D9!ENÒ/a%�D9|+]~QÌÆI')|�|+DGD1N¦yz(3.H[ /a%�Dc#GD1N~/aDG(r.)y�/+%�Dc��'d(3/a%�Ê�w7!$CEC���Du�C$.)/+/+D1*Y')|L/a%�Do|a'd[cD�|3!E�1Do.HN/a%�D�[c')uU��XL%�D�B�:�N-')N�*-68.A.HNw7%�!E#&%8%�'e?HD�/a%�D�|a'd[cDo')N�F):�C�')(L|3!E�GD!EN¦/+%�D|+]~QÚÆI£  Ç � Ê�w7!$CEC��JDu�C$.)/+/+D1*v')|�#1!E(3#1C$D1|r.)y7/+%�D|a')[9D|+!$�1Dq.)Nv/+%�D[c')u ÆÅ|3!EN�#GDq/a%�DG!E(r#G(+.H|3||+DG#G/+!E.HN�|"')(3D�#1!E(3#1C$D1|7')N�*Y|+%�')uJDG|"')(+D�u�(3D1|+DG(3?)D1*�C$.�#1')CEC{Qc!$NY'�#G.HN�yz.H(3[\'dCU[\'duu�(+.W�3DG#G/+!E.HN^Ê��

XL%�DL[c')uPFH!{?HD1|¸:�|�/a%�'W/���')(3/+%�CE!$N�F���|M?A!ED<wÝ.)y^/+%�DL:�N�!{?HD1(3|+D>/+%�'d/�w�D>w>'dNg/1� ���A�3D1#</a|�')(3DL|+%�.@w7N'd/�'|3!E�1D�!EN�/a%�DP[\')u�u�(+.Hu�.H(3/+!E.HN�')CZ/+.q/a%�DP|3!E�GDr/a%�D<Q�|+:���/aDGN�*t!$N�/a%�DP|3]~QH�rXL%�D9BA:�N�')N�*t68.A.HN')(3DcDG�A:�')CEC{Q�C�')(3FHD�!ENÒ/a%�Dc|+]~Qt')N�*t|+.�'du�uJD1')(o.)y>/a%�Dc|+')[cD9|+!$�1D9!EN�/a%�D9[\'duU�����A�3D1#</a|o/a%�'d/�')(3D#1C$.H|+D�/a.c:�|�'d(+D�[9.H(3D�!$[cu�.H(3/a')N~/L/a.c:�| � ')|S*�DGu�!E#</aDG*�!EN}/a%�'W/�`�D<w ��.H(+]dD1(�#1.@?HDG(1��b�:�!EC$*�!EN�FH|7.HNÉ�� �r'e?)D1Ng:�D�[c'eQ|+:���/aDGN�*�')|"C�')(3FHD�')N8')N�FHC$D�/a.9.H:�(7DGQ)D�')|7/a%�D�*�!$|3/a')N~/�|�/&'d/+D�.dy Ä ')C$!$yz.H(3N�!�'�� ��:�(CE.@?)D1*�.HN�DG| � !$[cu�.H(3/a')N~/�/+.q:�| � 'd(+D�.dy³/aD1N�.)N�C$Q8'cyzD<w¥yzDGDG/�'ew�'eQ�')N�*�|3:���/+D1N�*�'\CE')(+FHD�')N�F):�C�')(|+#1')CEDL/+.o.):�(�DGQHDG|1��� [r:�(3*�D1(�.A#1#G:�(+(3!EN�Fo!EN�.H:�(�N�D1!EF)%A��.H(3%�.�.A*�*�(a'ew7|�[c.)(+DL.)yJ.H:�(�'d/3/aD1N~/+!E.HNP/a%�')N'�[r:�(3*�D1(P.dy7|+.H[9D1.HN�D%�')C$y³w�'eQ¦'d(+.H:�N�*v/+%�DFHC$.H�JDd�Ò��CE.)/3/a!EN�F�.H�A�3DG#G/a|9'd/P'�|+!E�GDqD1�g:�'dC�/a.�/+%�D1!$(')N�F):�C�')("|+#1')CED�[\')]dD1|�u�|3QA#&%�.HC$.HFH!E#1')CZ|+D1N�|+D)� ���A�3DG#G/a|�')(+Dr|3%�.@w7N�/&')]g!EN�F\:�uÒ')N�')(+D1'q.HN-/a%�Dr[\'du/a%�'d/>!$|�u�(3.Hu�.H(3/+!E.HN�'dC�/a.�/+%�D�')(3De'�/+%�DGQc|+:���/aDGN�*!EN\/+%�DS|3]~Q�Æz!$yU/+%�DGQ\')(+DS')u�u�(3.eV�!$[\'W/aD1C{Q�|+u�%�D1(+!$#e')C� ')|7[\'dNgQq')|3/+(+.HN�.H[c!$#e')CJ�J.A*�!$D1|L')(3D@Ê���XL%�Do!$[cu�.H(�/&')N�#GD�.)yZ/a%�D�.H�g�3D1#G/"!$Nq/a%�D�[c')u�Æz/+%�D�yz(a')#</a!E.)N.)y�/a%�D9[c')u�!{/S/&'d])D1|�:�u�ÊS!E|�u�(3.HuJ.)(3/a!$.HN�')C�/a.q/+%�D�#&%�')N�#GDPw�DPw7!EC$CM|3D1DP/a%�DP.H�A�3D1#</o!$y�w�D�C$.�.H]}.H:�/')C$.HN�F}'(a')N�*�.H[ C$!EN�D�.)y�|3!EFH%~/1�r2�N�*�DGD1*U0Z!$y�w�D9C$.�.)]�'d/�/+%�D�[\'duÒyz(3.H[�'#G.HN�|3/a')N~/o*�!E|�/&')N�#GD)0m/a%�D')N�F):�C�')(�|+!E�GD�.)yZ/a%�D�.H�g�3D1#G/+|�!$Nq/a%�D�[c')uqw7!EC$C5��D�u�(+.)uJ.H(�/a!$.HN�')C�/a.P/a%�D�'dN�FH:�CE')(>|+!$�1D�/+%�DGQ|3:���/+D1N�*!ENq/+%�D�|+]~QH��XL%�D�?A!E|3:�')CUu�(3.H[9!EN�DGN�#1D�.)yZ.H�g�3D1#G/+|�!$Nq/a%�D�[c')uqw7!EC$C5��D�u�(+.)uJ.H(�/a!$.HN�')C�/a.r/a%�D1!E(>?A!$|+:�')Cu�(3.H[c!$N�D1N�#1D�!EN/+%�D�|+]~QH�

�Sy�#1.):�(+|3D�/a%�!E|"[cD1')N�|�/+%�'d/"/a%�Dr68.A.HN�')N�*�B�:�N�')N�*-.d/a%�DG(S.H�A�3DG#G/+|�w7!EC$Cm�JD�|+%�.@w7NÒ'd/7/+%�D1!$(/a(3:�D�|3#e')C$D�(3D1CE'd/a!{?HD�/a.c/+%�D1!$(7|+:�(3(+.H:�N�*�!EN�F)|PÆÅ!I�õDd�>/a%�Dr68.A.HN-!$|�|3%�.@w7N�!ENY#1.H(3(+D1#</�|3#e')C$D�(+DGC�'d/+!$?)D�/+./a%�D�#1!E(3#1:�[�yzD1(3D1N�#GD�.)yZ!$/+|>.H(+��!$/�Ê�w7%�!E#&%}!$|>|+[c')CEC���D1#e'd:�|+D�/a%�DGQ}')(3D�|+[c')C$CJ!$Nq/a%�D�|3]gQ)��B�:�u�u�.H|+D�w�D[c')*�D�')N868.HC$C$w�D1!$*�D�D1�g:�'dC�')(+D1'�[c')uu�(3.W�3D1#</a!$.HN}.)y�/a%�D�|+]~QY'd/L'�|3#e')C$D�/a.���/7.HNY'��3.H:�(3N�')CUu�')FHD)·')N¦DGCEC$!Eu�|3D9w7!{/a%¦%�.)(+!E�G.HN~/&')C�w7!$*�/a% È��ðÛ)¢8!EN�#&%�DG|P')N�*t?HD1(�/a!$#e')C�%�D1!$FH%~/r.)y"���$�e×8!EN�#&%�D1|1� �SCE.)N�F-/a%�DD1�g:�'W/a.H(3!�')C�u�CE')N�D�/+%�D�|3#e')C$D�!$|SCE!$N�De'd(�'W/r��!$N�#&%�u�D1(S(+')*�!E')NU�7XL%�Dr*�!E')[9DG/aDG(�.dy�/a%�Dr68.�.)N�.H(SB�:�N!E|S��ÖHÛ � 0�.H(���Ö)¡HÛ)£d/+%q.)y�/a%�D��)ÈH£ � CEDGN�F)/+%}')(+.H:�N�*q/a%�D�DG�g:�'d/a.)(1��XL%g:�|10�.)Nq/a%�!$|>|+]~Q[c')u\/+%�Do68.A.HNw�.H:�CE*�%�'@?)D�'q*�!�'d[cD</aD1(�.)ySÆIÈ  Û)¢�!EN�#&%�D1|aÊ+ÖH¡HÛd£cÑÔ£  £H£)¢~¡c!EN�#&%�D1|G� ��NÒ.H:�(�[\'du�/a%�D�6Y.�.HN�w�.H:�C$*%�'e?HD�'c|+!E[9!ECE')(7*�!�'d[cD</aD1(G0�yz.)(�/a%�Dr|+#1')CEDr.dy�.H:�(S[c')u�!$|�')u�u�(+.eV�!E[c'd/aDGC$Q��r(+')*�!�'dN�Ñ �r!EN�#&%5��XL%�D68.A.HN�')N�*tB�:�Nt')(3DP(a'd/+%�D1(�|+[c')C$CM!$NÒ/+%�D�|+]~QH�rs !{/a%�'u�(+!$N~/aD1(�(3D1|3.HCE:�/+!E.HN�.dy>�H£)£q*�.)/a|�u�D1(�!$N�#&%/a%�DoB�:�NY')N�*Y68.A.HNqw�.H:�C$*q/a%�DGNY��D�')u�u�(+.eV�!E[c'd/aDGC$Qc�r*�.)/+|>!EN*�!E')[9DG/aDG(1��K�.H(�De')|3!EDG(�?A!E|+!$��!EC$!$/�QPw�D%�'e?HD"u�C$.)/+/+D1*�/a%�D�B�:�Nc')N�*\68.A.HNc')|�#1!E(3#1C$D1|�D1N�CE')(+F)D1*��~Q9'�yÅ')#</a.H(�.dy��@¢���B�!E[9!ECE')(¸DGN�C�'d(+FHDG[cDGNg/+|�.)y!EN�*�!$?A!E*�:�')Cm.H�A�3DG#G/+|�CE!$])D�/a%�DrB�:�N�')N�*-/a%�Dr68.A.HN�[9!EFH%~/�')u�u�De')(".HN�|3]~Q-[c')u�|�')u�u�De')(3!EN�Fc.HN�.HN�Du�')F)D)���):�|3/�')|�|�QA[r�J.)CE|¸yz.H(¸#1!$/+!EDG|¸.HNrw�.H(+C$*P[\'du�|�[c'@Q���D>C�')(3FHD1(Z/a%�'dNr/a%�DL#G!$/a!$D1|Z/a%�DG[c|3D1C$?)D1|G��BA/a!$CEC!$/�!E|"!EN~/+D1(+DG|3/+!EN�F9/a.\N�.)/aDow7%�'d/S/+%�D�/+(+:�D�|+!$�1D1|�.HN-/+%�D�[c')u-|3%�.H:�C$*-��D�|3!EN�#GD�!$/�|+%�.�w7|S%�.@w�[r:�#&%

Page 18: A Map of the Universe - J Richard Gott, M Juric, et al

� �@¢ �

D1[9u�/�Qc|+u�'d#1D�!$N\/a%�DS:�N�!$?)D1(3|+DS/+%�D1(3D�!E|1��6-���Syz.H(�D<V�')[9u�CED�|+:���/aD1N�*�|7')N')N�FHCED�.)yZ')��.H:�/7Û � .HNq/a%�D|+]~Qc')N�*9|+.�w�.H:�CE*9��DS')��.H:�/�£��õ£H�~Ç�!$N�#&%�D1|�.HNc'o[c')u�w7!$/+%Y�"!EN�#&%d(a'd*�!�')N�|3#e')C$D)��2ÍyU?)D1(3|+!E.)N�|�.dy5/a%�D[c')uw�DG(+Dou�(+.A*�:�#GD1*8'd/7C�')(3FHD1(L|3#e')C$D�')|Lw�Do|+%�')CECU*�!E|+#G:�|+|7��D1C$.�w�0�!$[\'dFHD1|>.dyM/+%�D�B�:�NU0�68.A.HNU0^'dN�*N�D1')(+�~Q}F~')CE'WV�!EDG|>#1.H:�CE*}�JD�*�!$|+u�CE'eQHD1*8'd/7u�(3.Hu�D1("')N�FH:�C�')(>|3#e')C$Do')N�*}|+!$[cu�C{Qqu�CE')#1DG*}.HN/a%�D�[c')uU�

XL%�Do#1.H[9u�C$DG/aDG*}[\')u!$|7|+%�.@w7NY!EN/a%�D�yz.HC$*�.H:�/�Æ ��FH:�(3D�¢~Ê<�XL%�Dc[\')u�|+%�.�w7|r'8#1.)[cu�C$DG/+D9|+')[9u�CED�.)yL.)�A�3D1#</a|�!$N�/+%�D\#GC�')|3|+DG|�w�Dq')(3Dc!$CECE:�|3/a(+'d/a!$N�Fq!$Nt/a%�D

D1�g:�'W/a.H(3!�')C�|3CE!$#1DoÆ �SÛ ����Û � ʸw7%�!E#&%9!E|�|3%�.@w7N\#1.)N�yz.H(+[c')C$C$Qo#1.H(3(+DG#G/e��XL%�D1|+D".H�A�3DG#G/+|�')(3D7|+%�.@w7N

'd/�/+%�D�#1.H(3(+D1#</o*�!E|�/&')N�#GD1|�')N�*Ò(+!$FH%~/o')|+#GD1N�|3!E.HN�|1�9XL%�!E|�w�Dc|3:�u�u�C$D1[9D1N~/�w7!$/+%t'd*�*�!$/+!E.HN�')CMyÅ')[9.H:�|.H�A�3DG#G/+|".):�/L.)y�/a%�D�u�C�')N�D�w7%�!E#&%Y')(3D�|+%�.@w7N8'd/L/a%�D1!E(�#1.H(3(+D1#</7*�!E|�/&')N�#1D1|7'dN�*}(+!EF)%g/L')|+#GD1N�|3!E.HN�|G��B�./a%�!E|L!E|L��')|+!$#e')C$C$Q\')N8DG�g:�'d/a.)(+!�'dCU|+C$!E#1D�w7!{/a%}|+:�u�u�CEDG[cDGN~/a|1�

�>/o/a%�Dc�J.)/3/a.H[Y0m/a%�Dc[\'dut|�/&')(�/a|�w7!$/a%�')N�DG�g:�'d/a.)(+!�'dC�!EN~/aDG(+!E.)(o#G(+.H|3|�|3D1#G/+!E.HNt.)y�/+%�Dq��')(�/a%U�K¸!$(+|3/�w�D�|+DGD�/a%�D�|3.HCE!$*q!EN�N�D1(>#G.H(+D�.)yZ/a%�D���'d(3/a%w7!{/a%}'P(a')*�!E:�|>.dy ���@Û)£H£r]g[8� ���J.@?)D�/+%�!E|�!E|>/a%�DCE!$�g:�!E*}.H:�/+D1("#1.H(3DqÆÞ��Û)£H£�]g[ � �)×H¢H£9]g[\Ê<0�')N�*8')��.@?HD�/+%�'d/S')(+D�/+%�D�C$.�w�D1(�ÆI�d×~¢H£P]g[ � ÇH¡)£���]g[\Ê')N�*�:�u�u�D1(o[\')N~/+CED-ÆfÇH¡)£��c]g[ � ÈH�d×��\]g[\Ê<�}XL%�Dq��')(�/a%U��|�|3:�(3yÅ'd#1D\%�')|r')N�D1�g:�'d/+.H(+!E')C�(a')*�!E:�|o.)yÈH�~¡d¢S]g[8�MXL%�D1(3D"!$|�'�C$!EN�D�*�D1|3!EFHN�'W/aD1*9��')(�/a%U��|�|+:�(�yÅ')#1DoÆ�' #G(+:�|�/�ÊMw7%�!$#&%P!E|�'�C$!$/3/aCED�/a%�!E#&])DG(�/a%�'dN�')N.H(3*�!EN�'d(3Q}CE!$N�D�/a.cu�(+.Hu�D1(3C$Q}!$N�*�!E#1'd/aD�/+%�D�/+%�!E#&]gN�DG|+|�.)y¸/a%�D�#1(+:�|3/e�7XL%�Dr��'d(3/a%5�õ|�|+:�(�yÅ')#1DqÆ 'Ô#1(3:�|3/&ÊCE!$N�D7!E|�|+%�.@w7N}')|�uJDG(3yzDG#G/aC{Q9|3/a(+')!EF)%g/10���D1#1'):�|3D�.HN\/+%�!E|�|+#1')CED"/a%�DS')C$/+!$/a:�*�DL?)'d(+!�'W/a!E.)N9!$Nc/+%�D���')(�/a%U��||+:�(3yÅ')#GD�!E|\/+.�. |3[\')C$C"/+. �JD�?A!$|+!E��CED)��XL%�DÒ|3#e')C$D�'d/q/+%�DÒ��')(3/+% |3:�(3yÅ'd#1D�CE!$N�D-!$|')u�u�(+.eV�!E[c'd/aDGC$Q��ÖHÛ)Ç)£�Ï&£H£)£�Ï&£H£H£���XL%�D�[c'WV�!E[r:�[ /a%�!E#&]gN�D1|3|�.dy�/+%�D�#1(+:�|3/\ÆI�~¡q]g[\ÊS!E|��3:�|�/���')(+DGC$Q-?A!$|+!E��CEDr.HNÒ/a%�D[c')u 'd/}'¦(3D1|+.)CE:�/+!E.HNÚ.)y��H£)£¦*�.)/a|u�D1(!$N�#&%U0"|+. w�D�%�'e?HDÒ|+%�.@w7N /a%�D�[c'WV�!E[�:�[ #G(+:�|�/}*�D1u�/a%')#G#1.H(3*�!EN�F)C$QH0��gQ\/a%�D�w7!E*�/a%}.)y¸/+%�Do��')(3/+%Y|3:�(3yÅ'd#1D\ÆÅ#1(3:�|3/&Ê>CE!EN�D)�

ÆÅ2ÍyZw�Do%�')*Yw7!$|+%�DG*Yw�D�#1.H:�CE*}%�'e?HD�D<VA/+D1N�*�DG*-/a%�D�[\')u}*�.@w7N~w�')(+*Y/a.�#1.@?HDG(L/a%�D�D1N~/+!E(+D�!$N�N�DG(|+.)CE!E*8#1.H(3D�.)y�/+%�DP��')(�/a%�*�.@w7N�/+.\/a%�D�#1D1N~/+(a')CMN�D1:�/+(+.HN Æz.H("u�(+.)/+.HN^Ê7!EN�')N-!E(+.)N�'d/+.H[ CE.A#e'd/+D1*�'W//a%�D9#GD1N~/aDG(�.dy�/a%�Dc��')(�/a%U�cB�!$N�#1D9'}N�D1:�/a(+.)Nt%�'d|�'(a'd*�!E:�|�.)y�')u�u�(+.eV�!E[c'd/aDGC$Qt� ðÛ � �@£�+�4 _ #1[�.)(� õÉ �\�@£ +AR�R ���0H/a%�D7#G!E(+#G:�[�yzD1(+DGN�#1D7.)y�/a%�!E|�#1DGN~/a(a'dC�N�D1:�/+(+.HN�w�.H:�CE*���D7u�CE.)/3/aDG*c'd|�'�|�/a(+')!EFH%~/�C$!EN�DL'W/Ð�Ñ ��Ç)£  £��MXL%�D�.):�/aDG(¸#1!$(+#G:�[9yzDG(+DGN�#1D�.)y�/a%�D�#1DGN~/a(a'dC�!$(+.HN�'d/a.)[xÆI'd/+.H[c!$#�(a')*�!$:�|Z.)ym� �×~£ ���@£�+ �a#G[80B�CE'd/aDG(oÆ��@ÉHÈd×gÊ+Ê�w�.H:�C$*8��D�u�C$.)/+/+D1*Y')|"'P|3/a(+')!EF)%g/7C$!EN�D�'d/"ÐPÑ ���H¢ õ�HÈ���XL%g:�|G0�!$N�#1C$:�*�!$N�Fr/a%�D�DGNg/+!E(3D!EN�N�D1(�|+.)CE!E*v#G.H(+DY.)yS/+%�D8��'d(3/a%Ü*�.@w7NÜ/+.�/+%�D8#GD1N~/a(+')C"N�D1:�/+(+.HNÜ!EN ')NÜ!E(+.)NÜ'W/a.H[ 'W/c/+%�D8#GD1N~/aDG(.)y�/a%�D9��')(�/a%Òw�.H:�CE*Ò(+DG�A:�!E(+D8ÆÅ'd/���!EN�#&%W(a')*�!E')NÒ|+#1')CEDeÊ�')�J.):�/o')Nt')*�*�!{/a!E.)N�')CZ×~¢!EN�#&%�DG|�.dy�[c')uU0')u�u�(+.eV�!E[c'd/aDGC$Q�*�.H:���CE!$N�F�!{/a|�CED1N�F)/a%U��XL%�D�#1DGNg/+(a')C5'd/a.)[ 'dN�*!$/+|�Ng:�#GCED1:�|>w�.H:�CE*\/+%�D1N.A#1#G:�u~Q\/a%�D��.)/+/+.H[ �)�H� È�!$N�#&%�D1|P.dy�/+%�D[\'duU0�FH!$?A!EN�F�'�N�!E#GD!EC$CE:�|�/a(a'W/a!E.)N�.)y"��.)/a% /a%�DNA:�#1CEDG:�|9')N�* ')C$C�/a%�DD1C$D1#</a(+.)Nt.H(3��!$/a')CE|G�9b�:�/o|+!$N�#1D�w�Dc')(3D9u�(+!E[c')(3!EC$QY!$Ng/+D1(3D1|3/+D1*¦!$N�')|3/+(+.HN�.)[�QH0M')N�*Ò/a%�D9])D<QÒ(+DGFH!E.HN�|.)y�/+%�DP��')(3/+%U��|�!EN~/aDG(+!E.)(S')(3Dr#1.@?)D1(+DG*t!$N-/a%�Dr[\'du�')CE(3De')*�QH0Jw�DP%�'e?HDP|�/a.Hu�uJDG*Ò/+%�Dr[c')u9�3:�|�/�*�DGD1uD1N�.H:�FH%}/a.�|+%�.�w /a%�D�D<VA/+D1N~/S.dyM/+%�D�!EN�N�DG(L|+.HC$!E*}#1.)(+D)� Ê

stD�%�'e?HDÒ|+%�.@w7NÚ/a%�DÒ��'d(3/a%5�õ|}'d/+[c.)|+u�%�DG(+DÒ')��.@?HD�/+%�DÒ��')(3/+%U�õ||3:�(3yÅ'd#1D)�¥XL%�DÒ!E.)N�.H|+u�%�D1(3D

Page 19: A Map of the Universe - J Richard Gott, M Juric, et al

� �@É �

!E|�|3%�.@w7NÝw7%�!E#&%Ü.�#G#1:�u�!ED1|c')NÜ')C$/+!$/+:�*�D(a'dN�FHDY.)y�¡)£ � ÈH£H£Ò]A[Y�Ìb�D1CE.@w�/+%�DY!E.HN�.)|+u�%�DG(+D}!E|�/a%�D|3/+(a'd/+.H|+u�%�D1(3Dtw7%�!$#&% .A#1#G:�u�!EDG|-'dN ')C{/a!{/a:�*�D�(+')N�FHDÒ.)y\��Û � Ç)£ ]g[Y� ��C$/a%�.H:�FH% /a%�DG(+DÒw>'d|8N�.d/D1N�.H:�FH%|3u�')#1D�/a.r!$N�#1C$:�*�D�'�C�')��D1CI0~/a%�D�|�/a(+'d/a.H|3u�%�DG(+D�.HNq/+%�DS[c')uq|3!E[9u�C$Qr.�#G#1:�u�!$D1|�/+%�DS/+!EN~Q9|+u�')#GD��DG/�w�D1D1N}/a%�D�CE.@w�DG(>D1(3(+.H(���')(>!$N�*�!E#1'd/a!$N�F�/+%�D���.)/+/+.H[x.)ym/a%�D�!$.HN�.H|3u�%�DG(+D�')N�*}/+%�D��H|3:�(3yÅ'd#1D�.)y�/a%�D��')(3/+% �9CE!EN�D)��XL%�D�/a(+.)uJ.H|3u�%�DG(+D\ÆI£ � ��ÛP]g[qÊ>!$|L.)y�|3:�#&%�|+[c')C$Cm')C$/+!$/+:�*�DS/+%�'d/"!$/7!$|"|3:���|3:�[cDG*�!EN~/+./a%�Dq��')(3/+%U��|r|+:�(�yÅ')#1D\CE!EN�D9/+%�!E#&]gN�DG|+|1� ���J.@?)D\/a%�Dc!E.HN�.H|+u�%�D1(+Dcw�Dq%�'@?)D\yz.H(3[\')C$C$Q8/a%�DqD�V�.H|+u�%�D1(+Dd0w7%�DG(+D-/+%�D�[9De')NÝyz(3D1D8u�'d/a%Ú!$|c|3: �9#1!$D1N~/aC{QÝC$.HN�Ft/+%�'d/\!EN�*�!{?A!E*�:�'dC�'W/a.H[9|9w7!{/a%ÌDG|+#1')uJD8?HD1C$.�#G!$/�Q#e'dN�')#</a:�')C$C$QDG|+#1')uJDd��B�.c/+%�Do/+.Hu-.dy¸/a%�D�!E.)N�.H|+u�%�D1(3D�D �5DG#G/a!{?HDGC$Q}*�D���N�D1|�/a%�Do.H:�/+D1(SD�VA/aD1N~/S.)y�/a%�D��')(3/+%U��|L'd/a[9.H|3u�%�D1(3D�')N�*q/a%�D�[\')u\|+%�.@w7|Lu�(3.HuJDG(+C{QS�3:�|3/L%�.�w N�'d(+(+.@wÚ/+%�D���')(3/+%U��|L'd/a[9.H|3u�%�D1(3DS!$|(+DGC�'d/+!$?)D�/a.P/a%�D�#G!E(+#G:�[�yzD1(+DGN�#1D�.)yZ/a%�D���')(�/a%U�

`�D�VA/�w�DP%�'@?)DP|+%�.@w7NÒ')C$C¸¢�0õ×gÛd£\')(�/a! ��#1!�'dCM��')(�/a%�|+'d/aDGCEC$!$/aDG|�!$N�.H(3��!$/S')|�.)y���:�F���ÛA0mÛ)£H£)��ÆI'W//a%�D�/+!E[9D�.)yZyz:�CECU68.A.HN8Û)£H£H� d£H¢ ���Û�£)×�·�×~¢ ��X"Ê<��2�N}yÅ')#</"')CECJ.H�A�3D1#</a|"!ENq/+%�D�[\')uY')(3D�|+%�.@w7N-')|L.)y/a%�'d/�/a!E[9D)�9XL%�!$|�!$|�/+%�D9C�')|�/oyz:�CEC�68.A.HNt�JD<yz.H(+DP/a%�Dc#GCE.H|3D1|3/�')u�u�(+.~')#&%t.)y768')(+|�/a.}/a%�Dc��')(3/+%�!$NÛ)£H£)���¸XL%�DL/+!E[9D�w>'d|�#&%�.)|+D1N9yz.H(�!$/+|�u�C�'d#1D1[9D1N~/�.)y�/a%�DSBA:�NU0�68.A.HN9')N�*\6-')(+|G�¸stD"|3%�.@wÚ')C$C���')(3/+%|a'W/aD1C$CE!{/aD1|oÆzN�.)/��3:�|�/"/+%�.H|3D�È~ÛW×c!$N}/+%�DoD1�g:�'d/+.H(+!E')CU|+C$!E#GD@Ê<��XL%�DG|+Dr'd(+Do')#G/+:�')CmN�'d[cDG*8|+'d/aDGCECE!{/aDG|10�N�.d/�3:�|�/r|+u�')#1D��3:�N�]^��BA.H[cD�yÅ')[9.H:�|o|a'd/+D1C$CE!$/+D1|o')(3Dc*�DG|+!$FHN�'d/+D1*¦�~Q�N�')[9D)�}2�B�BÒ!E|�/a%�Dc2�Ng/+D1(3N�'d/a!$.HN�')CB�u�'d#1D�BA/&'W/a!E.)NU��O�B�X !E|>/+%�DoO�:�����CED�B�u�')#GD�XMDGCED1|3#1.Hu�D)��XL%�DG|+D�')(+D���.)/a%}!EN}C$.�w ��')(3/+%8.)(+��!{/e�

T�')N�F):�')(+* �P!$|�|+%�.�w7N50�/+%�DPDe'd(+CE!$D1|�/�C�'d:�N�#&%�DG*�|+'d/aDGCEC$!$/aDo|3/+!EC$CM!$N�.H(+��!{/e��XL%�D Ä %�'dN�*�(a' �"��(a'eQ.H��|3D1(�?)'W/a.H(�QP!E|�')C$|+.�|+%�.�w7N5��XL%�D1(3DS')(3D>/�w�.�[\'d!EN�')C{/a!$/+:�*�D>CE'eQHD1(3|�.)y5C$.@wÌ��')(�/a%9.H(+��!{/a!$N�F�|a'W/aD1C$CE!{/aD1|')N�*8'c|3#e'd/3/aDG(+!EN�Fc.)yM/a%�DG[ ')��.�?)Do/+%�'d/1��XL%�DG(+Do!E|"'9�g:�!{/aD�?A!E|+!$��CED�C$!EN�D�.dy�FHDG.H|3/a'd/a!$.HN�')(�Qq|a'W/aD1C$CE!{/aD1|'d/�')Nc')C$/+!$/a:�*�D7.)y�ÛHÛA0 £H£)£o[9!EC$D1|�')��.@?HD�/+%�D���'d(3/a%5�õ|�|+:�(�yÅ')#1Dd��XL%�D1|3DSFHDG.H|3QAN�#&%�(3.HN�.H:�|L|a'd/+D1CEC$!$/+D1|�')(3DN�D1')(+C{QP')C$C�!$NP.H:�(�D1�g:�'W/a.H(3!�')C�|+CE!$#1Dd� �Ú|+:�(+u�(3!E|+DLw�')|�/a%�D"C$!EN�D�.)y5,o��B}Æf,�CE.)��')C��M.H|3!$/a!$.HN�!$N�F�BAQA|3/+D1[\Ê|a'W/aD1C$CE!{/aD1|�'W/o'Y|3.H[cD<w7%�'d/oCE.@w�D1(o')C{/a!$/+:�*�Dd�9XL%�D1|+D\')(+D9')C$C�!ENÒN�D1')(+C{Q�#1!$(+#G:�C�')(�.)(+��!{/a|�'d/o!E*�D1N~/a!$#e')C')C{/a!$/+:�*�DG|7')N�*Y|+.c')CE|3.9|3%�.@w :�u8')|"'PCE!EN�D�.HNY/+%�D�[\'duU��s�D�%�')*YN�.)/7(3De')C$!E�GD1*/a%�'W/"/+%�D1(3Dow�D1(3D�|3.[c')N~Q}.)y¸/+%�D1|3D�|a'W/aD1C$CE!{/aD1|L.)(7/+%�'d/"/a%�D<Qw�.):�CE*8|+%�.@w�:�u8.HNY/+%�Do[\')uY|+.cu�(+.)[c!$N�D1N~/aC{QH��XL%�D�!$N�N�DG(')N�*Y.H:�/+D1(>T�')N �SC$CEDGN(a')*�!E'd/a!$.HN��D1C$/+|7')(+D�'dCE|+.�|3%�.@w7NU�

b�D<QH.HN�*�/+%�D�')(3/+! ��#G!�')CZ��')(�/a%�|a'W/aD1C$CE!{/aD1|S')N�*�/+%�D�T�')N ��CECEDGN�(a'd*�!�'d/+!E.HN8�JDGC$/+|�CE!$D1|�/+%�D�68.A.HNU0[c')(+]g!EN�Fo/+%�D�D<VA/+D1N~/L.)ym*�!E(+DG#G/�%A:�[\')N\.�#G#1:�u�'W/a!E.)N\.)yU/+%�D�:�N�!$?HDG(+|3D)��XL%�D�6Y.�.HN\!E|�yz:�CEC^.HN ��:�FH:�|�/��Û�0�Û)£H£H���

b�DG%�!EN�*}/a%�D�yz:�CEC�68.A.HNY'd/"')u�u�(+.eV�!E[c'd/aDGC$Q\×�/+!E[9D1|>/+%�D�*�!E|�/&')N�#GD�yz(+.H[ ��'d(3/a%Y!E|>/+%�D�s 6&���|a'W/aD1C$CE!{/aDcw7%�!E#&% %�')|�(+DG#1D1N~/+C$Q [9De')|3:�(+DG* /+%�D}#1.H|3[c!$#[c!$#1(3.�w�'e?HD}��')#&]gFH(3.H:�N�*5� 2Í/�!$|P!EN '�CE.A.Hu��!EN�F-.H(3��!$/�')��.H:�/o/a%�D\ËZÛ8:�N�|�/&')��C$D\Ë�')F)(a')N�F)D\u�.H!EN~/o.HN�/+%�D\.Hu�uJ.H|3!$/+Dc|3!E*�Dc.)y>/a%�DB�:�Ntyz(+.H[ /a%�D��')(3/+%U��XL%�DG(+DGyz.)(+D�!{/>!E|�')u�u�(3.eV�!$[\'W/aD1C{Q��JDG%�!EN�*\/a%�D�yz:�CECJ68.A.HNU�L�@¢)£ � 'ew>'eQ)0�'d/�/+%�D�Ë���Ë�')N�F)(a')N�F)Du�.H!EN~/�!E|7/a%�DrB�.HC�'d(S')N�*�O�DGCE!E.)|+u�%�DG(+!$# ����|3D1(�?)'W/a.H(�Q ÆIB ��O���Ê"|+'d/aDGCECE!{/aDd�7K^(3.H[ Ë��H05B ��O��Ô%�')|S')N:�N�.)��|3/+(+:�#</aD1*-')N�*Y:�N�!$Ng/+D1(3(+:�u�/+D1*}?A!EDGw .)yZ/a%�D�B�:�NY/a%�(3.H:�FH%�.H:�/L/a%�D�Q)De')(G�

Page 20: A Map of the Universe - J Richard Gott, M Juric, et al

� Û)£ �

XZ.r!EC$CE:�|�/a(a'W/aD>/a%�DS*�!$|3/&'dN�#1DG|�yz(+.H[���')(�/a%\/+.�/a%�DSN�D1')(+DG|3/L'd|3/aDG(+.H!$*�|10Aw�D�u�CE.d/�/+%�D���Û�#1C$.H|+DG|3/�/+.��')(3/+%�')|�.)y �S:�FH:�|3/���Û�05Û)£H£H�-ÆÅCE')�JDGCEDG*-`�� ��|��>`�D1')(���')(�/a% ���g�3D1#G/+|&Ê�� �S|�/aDG(+.H!$*ÒÛ)£H£H�\, � w�')|#1C$.H|+DG|3/L/+.���'d(3/a%Y'd/�/a%�'d/L/+!E[9D)� ��N�.)/+%�D1(>/�w�.P/a%�DG[ ')(+DSu�')(3/+!E#G:�C�')(3C$Q9!EN~/+D1(+DG|3/+!EN�F�� �S|3/+D1(3.H!E*8Û)£H£)���`o�@£~¡P!E|"#1:�(3(+DGNg/+C$Q}/a%�D�.HN�C$Q}]gN�.@w7N��g:�')|3!{��|+'d/aDGCEC$!$/aDS.)y�/a%�D���')(�/a% Æ Ä .HN�N�.)(+|PÆIÛ)£H£)×~Ê+Ê<0^'dN�*-|3%�')CEC(+DG[\'d!EN�|+:�#&%¦:�N~/a!$C¸/a%�D�QHD1')(�Û)£H£HÈ�� ��|3/+D1(+.)!E*tÛ)£H£~Û ����Û)É}!E|�.HNt')N�!EN~/aDG(+DG|3/a!$N�F}%�.H(3|+D1|3%�.ADc.H(3��!$/Æ Ä .)N�N�.H(3|�ÆfÛd£H£~ÛHÊ�0�b�D1CE��(+:�N�. '�,�.d/+/SÆfÛ)£)£)×gÊ+ʸ/+%�'d/�#1!E(3#1:�CE'd/aDG|�'d/S��� � ')N�*\%�')|�#1C$.H|+D�')u�u�(3.~')#&%�DG|/a.c��')(3/+%8D<?HDG(3Q8É~Ç�QHD1')(+|G�LB�:�#&%8%�.H(3|+D1|3%�.AD�.H(3��!$/+|"')(+D�/�QAu�!E#1')Cm.)yM.H(+��!$/a|L/+%�'d/"%�'e?HDoD1|3#e')u�D1*Yyz(+.H[/a%�D�XZ(+.W�+'dNqËm×�0AËZÇ�u�.H!EN~/+|�ÆÅb�D1C$��(+:�N�. ' ,�.)/3/�ÆIÛ)£H£)×~Ê+Ê<��B�!EN�#1D7/a%�!$|�'d|3/aDG(+.H!$*c[c'eQ�%�'e?HD�.H(+!$FH!EN�'W/aD1*'d/Ò� � � CE!$])D�/a%�Dt��')(�/a% ')N�*Ú/a%�D�F)(+De'W/}!E[9u�')#G/+.H(\/+%�'d/yz.H(3[cDG* /+%�Dt68.A.HNU0S!{/[9!EFH%~/��D�')N!EN~/+D1(+DG|3/+!EN�F�.H�A�3DG#G/"yz.H(7'P|a')[9u�C$D�(+DG/+:�(+NY[9!E|+|3!E.HN50�')|",�.)/+/"'dN�*-b�D1CE��(+:�N�.�%�'e?)D�N�.d/aD1*5�

6-')(3|�!$|�|3%�.@w7N 'd/�')u�u�(+.eV�!E[c'd/aDGC$QÒÉ�0õ£H£H£Y��')(3/+%�(+')*�!E!I0m.H(o£���×�')|�/a(+.)N�.H[9!E#e'dC�:�N�!{/a|\ÆI')|o|+DGD1N.HN-/+%�D�|3#e')C$D�.HN8/a%�D�(+!EF)%g/&Ê<�S6-')(3|S!E|"N�D1')(S!{/a|Su�.H!$Ng/�.)y�#GCE.H|3D1|�/�')u�u�(+.~')#&% Ƴw7%�!E#&%-!$/S')#&%�!ED<?HDG*�.HN�S:�FH:�|3/�ÛH¡�0gÛ)£)£H��w7%�DGN9!{/Mw�')|�'d/�'�#1DGNg/+D1(Þ�Í/a.W��#1DGN~/aD1(�*�!E|3/a')N�#GD>.)yJÇHÇ�0 ¡HÇ)¢�0 £H£)È�]g[qÊ���K�:�(�/a%�DG(�:�u�')(3D68DG(+#1:�(3QH0A/a%�D�B�:�Nq')N�*9T�D1Ng:�|G��T�D1Ng:�|�!$|�N�De')(�#1.)NW�3:�N�#</a!E.)N9w7!{/a%�/a%�D�B�:�Nc.HN�/a%�D".Hu�u�.H|+!{/aD7|+!$*�D7.)y!$/+|�.H(+��!{/e��XL%�D�B�:�Nq!E|7�@¢H£ � 'ew>'eQ�yz(+.)[Ô/a%�DS68.A.HN\.H(�%�')C{y³w>'eQ9')#G(+.H|3|�/+%�DS[c')u9%�.H(3!E�1.)Ng/a')CEC{QH0~|3!EN�#GD/a%�DS6Y.�.HN�!$|�yz:�CECf�ZXL%�D�B�:�N9!E|L� � � 'ew>'eQPyz(+.)[ /a%�D���')(�/a%U� �>/�*�!E|3/a')N�#GD1|�yz(+.H[���'d(3/a%9.)yJ�JD</�w�DGD1N� £ ð¡P/a. �¥Ç ����')(+Do/a%�Do[\'d!ENY�JDGC$/�')|3/+D1(3.H!E*�|G�7O�DG(+D)0J.H:�/�.)y�/+%�Do/+.)/&'dCZ.dy�Û��@¢�0�×~¢)×c')|�/aD1(3.H!E*�|�!$N/a%�D ��B�X �� �b *�'d/a')��')|3D)0�w�D�%�'e?)D�|3%�.@w7N�.HN�C{Q\/a%�.H|+D9�e×�0{�@¢H��w7%�!$#&%�')(3D�!EN/a%�D�DG�A:�'d/a.H(3!�')C5u�C�')N�DD1�g:�'W/a.H(3!�')CJ|+CE!$#1DrÆ �SÛ �

���Û � Ê���2ÍyZw�D�%�')*}|3%�.@w7N}/+%�D1[ ')CECI0�!{/�w�.H:�C$*Y%�'@?)D��JDGD1N/a.d/&')C$C$Q9��C�'d#&]��

b�Q��3:�|3/�|3%�.@w7!EN�Fq/+%�D�')|3/+D1(3.H!E*�|S!EN�/a%�DPD1�g:�'d/+.H(+!E')C¸|3CE!E#GD�w�D9')(+DP'd��CED�/+.|+DGD9!$N�*�!{?�!$*�:�')C�*�.d/a|1��2�N')*�*�!$/a!$.HNU0g|+.)[cD"yÅ')[c.):�|�[c')!$Nc��D1C{/>')|�/aDG(+.H!$*�|10�CE!E]dD Ä DG(+DG|10���(+.)|10�,�')|3u�(a'�0AT�D1|�/&'�0��):�N�.P')N�*�¸')C$C�')|')(3Dr|+%�.@w7NÝÆÅD<?HD1NÒ!{y�.$��/+%�DPD1�g:�'d/+.H(+!E')CZ|+CE!$#1DeÊS')N�*�!$N�*�!E#1'd/aDG*��~Q�N�'d[cDd�oXL%�Drw7!E*�/+%�.)y�/a%�DP[c')!EN��D1C$/7.dy�')|�/aD1(3.H!E*�|"!$|7|+%�.@w7N�!$NYu�(+.Hu�D1(7|+#1')CED�(3D1C�'W/a!$?)D�/a.9!$/a|L#G!E(3#1:�[�yzD1(3D1N�#GD�!$N}/+%�Do[\')u5��XL%�Do��D1C$/!E|S#1CE.)|+D1(�/a.q/a%�DP��')(3/+%�!$N-/a%�D�')N~/a!{�Í|+.HCE')("*�!E(3D1#G/+!E.HN-|+!EN�#1Dr!{/�!E|�')NÒ')N�Ng:�C$:�|�#1DGNg/+D1(3D1*�.HN�/a%�DPB�:�N')N�*9/a%�DS��')(3/+%\!E|�.$�Y#1DGN~/aD1(G��b�D1#1'):�|+D�/a%�D"[\'d!EN9�JDGC$/�')|3/+D1(3.H!E*�|�CE!$D7')u�u�(3.@V�!$[\'d/+D1C{QP!EN9/a%�D�D1#1C$!Eu�/+!E#u�CE')N�D�w7%�!E#&%�!$|"/+!EC$/+D1*8'd/S')N�')N�F)CEDo.)y�Û)�  Ç � (3D1CE'd/a!{?HD�/a.c/+%�Dr��')(�/a%U��|�DG�A:�'d/a.H(3!�')C�u�CE')N�Dd0�/+%�D1(3Dr')(3D/�w�.r*�D1N�|+D�#GCE:�|�/aD1(3|�w7%�DG(+D"/a%�D�D1#1C$!Eu�/+!E#Lu�CE')N�D"#1:�/+|�/+%�D���')(�/a%U��|�DG�A:�'d/a.H(3!�')C�u�C�')N�D�')N�*9/a%�D�*�D1N�|+!$/�Q.)y¸')|3/+D1(3.H!E*�|7!$|L%�!EFH%�D1|3/1� ��N�D�!EN~/aDG(+|+DG#G/+!E.HNY!E|7'd/"'d�J.H:�/���Ûd%Y')N�*}/a%�D�.)/+%�D1(7!$|7'd/�Ûd×H%U�

�):�u�!{/aDG("!$|L|+%�.@w7N8!EN}#1.HN��3:�N�#G/+!E.HNw7!{/a%}/a%�D�B�:�N8')u�u�(+.eV�!E[c'd/aDGC$QÈ� ��yz(+.)[ /a%�Do��')(�/a%U� ��ND1!{/a%�DG(7|+!E*�D�.)y��):�u�!{/aD1(Lw�D�#1')N-|3D1D�/a%�D�/�w�.\|3w�')(+[9|�.dy�XZ(+.W�+')N-')|3/+D1(3.H!E*�|L/+(a')u�u�D1*8!EN}/a%�D�Ëm×\'dN�*ËZÇ8|3/a')��C$DqË�')FH(+')N�FHDcD1�g:�!EC$!E��(3!E:�[ u�.H!$Ng/+| 5�ÈH£ � 'ew�'@Q�yz(+.)[ �):�u�!$/aDG(r')C$.HN�F8!$/a|�.H(+��!$/e�-K�(+.H[ /a%�D?d')N~/&')F)DruJ.)!EN~/�.)y���')(�/a%U0¸� � �Ô.$�t#1D1N~/+D1(�.Hu�u�.H|3!$/aDr�):�u�!{/aD1(S!EN�!{/a|S.)(+��!{/e0J/+%�DrXZ(+.W�+'dN�|�')(3DP'q��!$/#1C$.H|+DG(�/a.8/a%�D��')(�/a%¦/+%�')N �):�u�!{/aDG(r')N�*v'8��!$/�#1CE.)|+D1(�/a.Ò�):�u�!$/aDG(r!ENt/a%�Dq|3]~Q¦.HN D1')#&% |+!$*�D\/a%�')NÈH£ � �rXL%�D ��C{Q�|3|+DG|�|3u�')#1DG#1(+'dy³/o!E|S?A!E|3!E��C$DrN�D1')(o�):�u�!{/aD1(G�r2Í/o!E|�!$N�')NÒ.H(+��!{/�yÅ')(�.):�/�.)y�/a%�D���')(�/a%U��|D1�g:�'W/a.H(3!�')CZu�C�'dN�D)0J��:�/�w�DP%�'e?HDP!$N�#1C$:�*�D1*�!{/�'dNgQgw�'eQH��b�DGQ).HN�*t�):�u�!{/aD1(�')(+DrB�'d/a:�(+NU0 �"(a')Ng:�|�'dN�*`�DGu�/a:�N�D)�

Page 21: A Map of the Universe - J Richard Gott, M Juric, et al

� �� �

OS'dCECED<Q��õ|�#1.)[cD</�!$|�|+%�.@w7N���DG/�w�D1DGN�/a%�Dc.H(3��!$/+|�.)y �"(a')Ng:�|�')N�*t`�DGu�/a:�N�D)0�'d|�.)y �S:�FH:�|3/c��Û�0Û)£H£)���

`�D�VA/"w�D�|+%�.�w���CE:�/+.�')N�*/a%�D���:�!$uJDG(>��D1C$/>.H�A�3D1#</a|G��stD�')(+D�|3%�.@w7!EN�F9')C$CU¡)¡HÛ�.)y�/a%�D�]gN�.@w7N��:�!Eu�D1(��JDGC$/�.H�A�3D1#</a|YÆz(a'd/+%�D1(�/+%�')N8�3:�|�/P/a%�.)|+Dq!$N�/a%�DDG�g:�'d/a.)(+!�'dC�u�CE')N�DeÊ<��2Í/P!$|�|+:�(+u�(3!E|+!$N�F�%�.@w[c')N~QÒ.)y>/a%�D1[�/a%�D1(+D\')(+Dd�} "DG#1DGNg/+C$Q�*�!$|+#1.@?)D1(+DG* Û)£H£H�T�b���Û�Æ �aB�D1*�N�'$�gÊ�0 ��:�').~'d(�'dN�*tT�')(3:�N�'�0/a%�D>C�')(3FHD1|�/���b ��|�#G:�(+(3D1N~/aC{Q�]gN�.@w7NU0g'd(+D>'dCE|+.�|+%�.@w7N9')N�*�C�')��D1C$D1*U�¸B�D1*�N�'�!E|M#1:�(3(+D1N~/+C$Qo/a%�D>|3D1#G.HN�*C�'d(+FHDG|3/Z]gN�.@w /a(a'dN�|+N�DGu�/a:�N�!�')N�.H�A�3DG#G/e0H'dy³/aDG(M��C$:�/a.�ÆIb�(3.@w7NU0)XZ(+:W�3!$CEC$.�0 'Ú �'d��!EN�.@w7!{/a��ÆfÛ)£)£)×gÊ+Ê���XL%�D��')N�*�.)y���:�!$uJDG(���D1C{/S.H�g�3D1#G/+|S!$|�(3D1C�'W/a!$?)D1C{Q}N�')(+(3.@w��JDG#e'):�|3Dr.)y�/+%�D�|3D1C$D1#G/+!E.HN8D��JD1#</S/a%�'d/�.H�g�3D1#G/+|.)yZ'oFH!$?)D1Nq|3!E�1DS�JDG#1.H[9DS*�!$[c[9D1(�')u�u�(+.eV�!E[c'd/aDGC$Q�'d|�/a%�DSyz.H:�(�/a%qu�.@w�DG(>.)yU/+%�D1!$(�*�!$|3/a')N�#1D�yz(+.H[�/a%�D��')(3/+%Ò')N�*�B�:�NU��XL%�DP��')N�*�.dy���:�!Eu�D1(S��D1C{/�.H�g�3D1#G/+|�%�')|�?)D1(3/+!E#1')C¸*�DGN�|+!{/�Q-|�/a(3!Eu�D1|10U')F~')!$N�*�:�D�/+.')N�F):�C�')("|+DGCEDG#G/a!$.HN�D �5DG#G/a|�*�D1u�D1N�*�!$N�Fq.HN8w7%�D1(3Dr?)'d(+!E.):�|�|3:�(3?)DGQA|�w�DG(+DP#G.HN�*�:�#</aDG*U����|3u�(+!$N�]gCE!EN�F.)y>��:�!Eu�D1(��JDGC$/o.H�A�3DG#G/+|�D<VA/+D1N�* 'dCEC¸/+%�D9w�'eQ�!EN~/a.}/a%�D9|+u�')#1Dc�JD</�w�DGD1N¦/a%�Dc.H(3��!$/�.dy ��(+')Ng:�|r'dN�*B�'d/+:�(+N�Æz/+%�D � Ä D1N~/a'):�(+| ��0�.)yMw7%�!E#&%}w�Dd�õ(3D�.)N�C$Q\u�CE.)/3/a!$N�F�/a%�Do.)N�D1|"!ENq/+%�D�D1�g:�'d/+.H(+!E')CUu�CE')N�D@Ê��

stD�|+%�.@w���!E.)N�D1DG(��@£�0�T�.@QH')FHD1(��o')N�*T�.@Q~'dFHD1("Ûr|+u�')#1DG#1(a'Wy³/a|10^%�D1')*�DG*-'ew�'@Q\yz(+.H[x/a%�D�|3.HC�')(|3QA|�/aD1[Y��XL%�DG|+D�')(+D�.HNP/a%�DG!E(¸w�'eQr/a.�/+%�DL%�D1C$!E.Hu�'):�|+Dd0Hw7%�D1(3D>/a%�DL|3.HC�'d(¸w7!EN�*�[9D1D</a|¸/+%�D7!EN~/aDG(+|3/+D1C$C�')([9D1*�!$:�[8�¸XL%�DGQ}%�'e?)D�N�.d/7(+De'd#&%�D1*8!$/LQHD</e�

�SC$[c.)|3/"'�%A:�N�*�(+DG*-/a!$[cDG|>yz:�(3/+%�D1(�'ew>'eQ/+%�')N}/a%�Do%�D1C$!E.Hu�'):�|+D�!$|7/+%�D��JDGFH!EN�N�!EN�F�.)yM/a%�D ��.H(�/#1C$.H:�*�.dy�#G.H[9DG/a|�w7%�!E#&%�D�V�/+D1N�*�|�yz(3.H[ ')��.H:�/�¢�0õ£H£H£ � � /a.��e£H£�0õ£H£H£ � �o� �Ô#G.H[cD</�D1N~/+D1(+!$N�Fq/a%�D!EN�N�D1(L|3.HC�')(L|�QA|3/aDG[�yz.H(>/a%�D ��(+|3/"/a!$[cDS%�')|"'r/�Q�u�!E#e'dC�')u�%�DGCE!E.)N!EN/a%�!$|L(a')N�FHD)�

b�D<QH.HN�* /a%�D ��.H(�/ Ä CE.H:�*Ü'd(+Dq/a%�DY|�/&')(3|1� XL%�D/+D1Nv��(+!$FH%~/aDG|3/9|3/a')(+|r?A!E|3!E��C$Dq!EN /+%�D|+]~Q ')(3D|+%�.�w7NÒw7!$/+%�C�')(3FHD�|�/&')(�|�QA[r�J.)CE|1��XL%�D�N�D1')(+DG|3/�|�/&')(G0���(3.eV�!$[\' Ä D1N~/&'):�(+!�!$|�|+%�.@w7NÒw7!$/+%Ò'q|+[c')CEC|3/a')(Z|3QA[r��.HCf�M��(+.eV�!E[c' Ä D1N~/a'):�(+!I0H')Nr6�Ç"|�/&')(G0)!$|¸'"[cDG[r�JDG(M.dy�/a%�D � Ä D1N~/&'):�(+!�/+(+!$u�CED�|3/a')(Z|3QA|3/+D1[Y�� Ä DGN~/&'):�(3! ��0�'d/7'�*�!E|�/&')N�#GD�.)yZ'�C$!$/3/aCED7.@?HDG(���u�#PÆÅ|3D1D�|3#e')C$D�.HN\/+%�D�CED<y³/�Ê�0�')N�*}'�|+.HCE')(�/�Q�u�D�|3/a')(10!E|�.HN�Dr.dy�/+%�D�/+D1N���(3!EFH%~/aDG|3/�|�/&')(3|�!EN8/a%�Dr|3]~QH�oXL%�Dq�@£qN�D1')(+DG|3/�|�/&')(S|3QA|3/+D1[9|�')(+DP'dCE|+.\|+%�.@w7NU· �Ä D1N~/a'):�(+!I0�b>'d(+N�')(3*U��|>|3/a')(10As�.HC{y��~Ç)É�0�OS'dC�')N�*�D�Û��H�e¢~Ç�0�B�!E(3!E:�|G0 �7T ')N�*}b�Ë Ä D</a!I0� 7.H|+|��@Çd×�0� ".H|3|Ûd×~¢�0�����(3!E*�')N�!m')N�*8Ë�')#e')!$CEC$D�ÉH�~Ç)Û����SyM/+%�D1|3D)0��"��(3!E*�'dN�!U%�')|"'�#1.HN ��(+[9D1*Yu�C�'dN�DG/7#G!E(+#GCE!$N�Fr!$/1�

BA/a')(+|�w7!$/+%�]AN�.�w7Nc#1.HN ��(+[9D1*9u�C�'dN�DG/+|�#G!E(3#1CE!$N�F�/a%�D1[ Ƴw7!$/a%�� |+!$N ���@£�������� �� . Ê�')(3D7|+%�.@w7N')|q*�.)/a|\w7!{/a%Ì#G!E(3#1CEDG|q')(3.H:�N�*Ü/a%�DG[8� �Sy�/a%�D1|+Dd0SÉHÇ�')(+D8|+.HCE')(c/�QAu�D�|3/a')(+|cw7%�.H|+D�u�C�')N�D</a|\w�D1(3D

*�!$|+#1.@?)D1(+DG* �gQ (+')*�!�'dC7?)D1C$.�#G!$/�Q uJDG(3/+:�(+��'W/a!E.)N�|1� B�.H[9D8.dy�/a%�D-[c.H(3DYyÅ'd[c.H:�|c.HN�D1|qC$!E])D-Ç��-�MD1F�0¡)£8TS!E(G0�')N�*��P��(+!�')(+DcC�')��D1C$D1*U�-XL%�Dq|3/a')(PO�= Û)£HÉ)×gÇd¢8%�')|r'Ò�):�u�!$/+D1(Þ��[c')|+|�u�C�')N�DG/�w7%�!E#&%¦w�')|*�!$|+#1.@?)D1(+DG*Ý�~Q¦(+')*�!E')C�?)D1CE.A#1!{/�Q¦u�D1(�/a:�(3��'d/a!$.HN�|r��:�/Pw>'d|9CE'd/aDG(P')C$|+.�.H��|3D1(�?HD1*Ü!EN¦/+(a')N�|3!$/YÆI6-')�GD1%DG/�')CI��ÆfÛ)£H£)£~Ê<0MO�DGN�(3Q�DG/�')CI��Æ��@ÉHÉ)É~Ê+Ê��qXL%�D���(+|3/�u�CE')N�DG/�*�!$|+#1.@?)D1(+DG* �~Q�/+(a')N�|+!$/�w�')|��,�Ë����ÍX7 L�Ç)È-w7%�!$#&%vCE!EDG|r'd/P'�*�!E|�/&')N�#GD.)y".@?HD1(�]gu�#qyz(+.H[ /a%�Dq��'d(3/a%5��XL%�(3D1D.)/+%�D1( ��,�ËZ��|3/a')(+|rw�D1(3D')C$|+.�yz.H:�N�*}/a.9%�'e?HDo/a(a'dN�|+!{/a!EN�F9u�C�')N�D</a| � X7 >�&�)�H�H0�X7 >�&�H�@��')N�*-X7 >�&�@�~ÛA��XL%�DG|+Dow�DG(+Dr'dCECm!EN}/a%�D|a'd[cD���DGCE*ÚÆÅ o� ��� ���@£���Ç)£���Ê�'d/�')u�u�(3.@V�!$[\'d/+D1C{Q-/a%�Dc|+')[cD�*�!$|3/a')N�#1D-Æ ���  Çd]gu�#@Ê�')N�*�|+.8w�.H:�C$*

Page 22: A Map of the Universe - J Richard Gott, M Juric, et al

� ÛHÛ �

��D8u�C$.)/+/+D1*Ü'd/9uJ.)|+!$/+!E.HN�|P.HNÜ/+%�D8[c')uv/a%�'W/9w�.H:�C$*Ý��D}!EN�*�!$|3/+!EN�FH:�!E|+%�')��CEDd�vXL%�D-u�CE')N�D</cXZ(a��Bg�a�')(3.H:�N�*q,�B Ä £~Û)È~ÇHÛ@�Þ£��@�HÛd×�w>'d|�(+DG#1DGNg/+C$Q�*�!$|+#G.�?)D1(3D1*�~Q�/a(a'dN�|+!{/�'dN�*\#G.HN ��(3[cDG*\�~Q9(a')*�!$.�?HD1C$.�#G!$/�Q[9De')|3:�(+DG[cDGNg/+|9Æ���CE.HN�|3.DG/o')CI��ÆIÛ)£H£)×gÊ3Ê<� ��u�CE')N�DG/�#1!E(3#1C$!EN�F9/a%�DP|�/&')( ��,�ËZ� Û)£H£)�W�Þb>ËZ,S��Û)�HÇ�w�')|*�!$|+#1.@?)D1(+DG*P�~Q�[c!$#1(+.)CED1N�|+!EN�F�ÆÅb�.HN�*�DG/¸')Cf�~ÆfÛ)£H£d×gÊ+Ê��¸��B� Ú��ÛHÇ)¡HØr��Û>!E|Z'�u�:�CE|a'd(�ÆzN�D1:�/a(+.)Nr|3/a')(&Ê5w7!$/+%/a%�(+D1D"/aDG(+(+DG|3/+(+!�'dCJu�CE')N�D</a|�#G!E(3#1CE!$N�F�!$/�w7%�!E#&%cw�DG(+D�*�!$|+#G.�?)D1(3D1*}�~Q\(+')*�!�'dC�?HD1C$.�#G!$/�Q9u�D1(3/+:�(+��'d/a!$.HN�|�.HN/a%�D�u�:�CE|+')(>(3DG?HD1')CEDG*8�~Qq')#1#G:�(a'd/+D�u�:�CE|3D�/a!$[c!$N�FƳs�.HC$|+�G#1�e'dN&'¥K�(a')!$C�ÆÞ�@ÉHÉ~Û)Ê<0�st.HC$|+�1#G�e')NtÆÞ�@ÉHÉ)×gÊ3Ê<�XL%�!$|�w�')|�/a%�D ��(+|�/>|�/&')(�*�!$|+#1.@?)D1(+DG*q/a.o%�'e?HD�u�C�')N�DG/a|G� �SC$|+.�0�B ��£HÛHÇ)�~Ør�@È~Ç)ÛS!E|�|+%�.@w7Nq'dN�*\CE')�JDGCEDG*.HN/a%�Do[c')uU��2Í/"!$|>/a%�D�#1C$.H|+DG|3/"]gN�.@w7N-��(3.@w7N8*�w�')(�y7ÆÅXZD1DGF~')(3*�D1N¦ÆfÛ)£H£)�~Ê+Ê�0�'d/����õ¢~Ûdu�#)�

XL%�D ��(+|�/o(a')*�!$.q/a(+')N�|+[9!E|3|+!$.HNÒ.)y>'dNgQÒ|3!EFHN�! ��#1')N~/�uJ.@w�D1(�/a.YD1|3#e')u�Dc��DGQ).HN�*Ò/a%�D9!E.)N�.H|+u�%�D1(3Dw�')|"/+%�D�X>T���(+.~')*�#e')|�/�.dy¸/a%�Do.)uJDGN�!EN�F�#GD1(+DG[c.)NgQ}.dyM/+%�Dc�eÉH�HÈ�b�D1(3CE!$N ��C{QA[cu�!$#1|L.HN �S:�FH:�|3/���� � 0�@ÉH�)È�0�'-yÅ')#G/rN�.)/aDG*v�gQ Ä ')(+C>B�')F~')Nv!$N¦%�!E|P��.A.H] Ä .)Ng/a')#G/ ��XL%�Dqw�'e?HDyz(+.)Ng/�#G.H(+(3D1|3uJ.HN�*�!EN�F�/+./a%�!E|7/a(a'dN�|+[9!E|3|+!E.)N-!E|�'c#G!E(3#1CEDo%�'e?A!EN�F\'c(+')*�!E:�|S.)y ���@£ 4�4 ��')(�/a%�(+')*�!$!Z.)N �S:�FH:�|3/���Û��SÛ)£H£)×�0J'dN�*!E|�!$N�*�!E#1'd/aDG*Ò�gQ�/+%�D9|3/a(+')!EF)%g/oC$!EN�DrCE')��D1CEDG* �~ �'d*�!E.}|+!$FHN�')C$|�yz(+.H[���'d(3/a%t%�'e?HD9(+D1')#&%�D1*t/a%�!$|�yÅ'd( ��� "')*�!E.P|3!EFHN�')CE|>yz(3.H[���')(�/a%Y%�'e?HDou�')|+|3D1*8|3/&'d(+|7�JDGCE.@w /a%�!$|LCE!EN�D)�

XL%�D�O�!$u�u�')(3#1.H|�|a'W/aD1C$CE!{/aDL%�')|�[9De')|3:�(+DG*q')#G#1:�(+'d/aD"u�')(+')CECE'WV�*�!E|�/&')N�#GD1|�/a.9�H�@¢�0 Û��@¢�|�/&')(3|SÆÅ��B��Æ��eÉHÉ~¡HÊ3Ê<�¸stD�|+%�.@w .HN�C$Q\/+%�Do��0õ�H¢HÈ�O�!$u�u�')(3#1.H|L|�/&')(3|"!$N/a%�D�D1�g:�'W/a.H(3!�')CUu�C�')N�D9Æ ��Û �

���Û � Ê��

�S/a%�DG(�!$N~/aD1(3D1|�/a!EN�Fc(3D1u�(3D1|+DGN~/&'d/+!$?HD�.H�A�3D1#</a|�!EN/a%�D�F~')CE'WVAQ}')(+D�!$CECE:�|3/a(+'d/aDG*U·�/a%�D���CEDG!�')*�DG|10�/a%�DFHC$.H��:�CE')(L#1C$:�|3/+D1(�6��@��0�/a%�D Ä (a')�8N�D1��:�C�'-Æf6t��Ê�0�/+%�D���C�')#&]%�.)CED Ä QAFHNg:�| ���a�H0�/a%�D ��(+!E.)N-`"D1��:�CE'Æf6Y×gÛHÊ<0m/+%�D9=�:�[r����D1C$C¸N�DG��:�C�'}')N�*�/+%�D9 "!$N�FN�D1��:�C�'�0m/+%�D9��'dFHCEDPN�DG��:�CE'�0m/a%�DPT�D1CE'qu�:�C$|a')(G0M'dN�*/a%�D�O�:�C$|+D���XM'@QAC$.H(���!$N�')(�Qcu�:�CE|+')(1� �>/L'�*�!E|�/&')N�#1D�.)yZ¢�]Au�#�!E|�/a%�D�,o')CE')#G/+!E# Ä D1N~/+D1(>w7%�!$#&%%�')(+��.H(3|'qÛA� È9[c!$CECE!$.HN|+.)C�')(7[c')|+|���C�')#&]%�.HCEDd�"XL%�Dr.H:�/+D1(+[9.H|�/SD�V�/+D1N~/�.)y¸/a%�Dr68!EC$]gQs�'eQY.Hu�/a!$#e')C�*�!$|+]!$||+%�.�w7N-')|"'P*�.)/+/+D1*YCE!$N�D)�

b�D<QH.HN�*}/a%�D�6Y!ECE]~Q9s¦'eQ}'d(+D�u�C$.)/+/+D1*YÇHÛr#1:�(+(+DGN~/aC$Q\]gN�.@w7N-[9D1[r��D1(3|>.)yZ/a%�D�Ëm.A#e')C�,�(+.):�u.)yF~')CE'WV�!EDG|1�¸stD�%�'e?HD�!EN�#1CE:�*�D1*}')C$C5.)y�/+%�D1|3D)0�N�.)/¸�3:�|3/L/a%�D�.HN�D1|7!$Nq/a%�D�DG�A:�'d/a.H(3!�')CJu�C�'dN�D)��XL%�D1|+D�')(3D!EN�*�!E#1'd/aDG*8�~Q}*�.)/+|�.)(7/+(+!E')N�FHC$D1|1��6-���)�õ|"#1.H[9u�')N�!E.HN�|�6-�HÛ9')N�*�`�, Ä Û)£~Ç�')(3Do|3%�.@w7N�')|"*�.)/+|���:�/N�.)/7CE')��D1CEDG*}|+!EN�#1D�/a%�D<Q}')(3Do|3.c#GCE.H|3D�/a.c6-���)�

6-¢��)0�!$|L/a%�D ��(+|�/SF~'dC�'WVAQ|3%�.@w7N��JD<QH.HN�*-/a%�D�Ëm.�#1')CM,�(3.H:�u8')N�*8!E|"'c[9D1[r��D1(7.)yM/a%�Dr6-¢�� �6-¢~Û�FH(+.):�uU��2Í/a|�*�!E|�/&')N�#1D�w�')|�*�DG/+D1(+[9!EN�D1*\�~Q Ä D1u�%�D1!E*c?)'d(+!�'d��CEDG|�:�|+!EN�F�/a%�DSO�B�X����S/a%�DG(�yÅ')[9.H:�|F~')CE'WV�!EDG|�CE')�JDGCEDG*c!$N�#1C$:�*�D�6��@£��H0g/a%�D�s %�!E(3CEu�.�.HC�F~')C�'�V�Q-ÆI6�Ç���Ê�0A/+%�D�B�.)[r��(+DG(+.rFH')C�'WVAQ)0�')N�*}6-¢~¡�0!ENr/+%�DL#1DGN~/aD1(�.)y^/+%�DLT�!E(3FH.�#GCE:�|�/aD1(G��2Íy^w�D7|3%�.@w�DG*q')C$C�/a%�D"6 .)�A�3D1#</a|�[\'dNgQow�.H:�CE*�#G(+.@w7*9/+.HFHD</a%�DG(!ENY'S�3:�[r��C$D�'d/L/a%�D�C$.�#1'd/a!$.HNq.)yM/a%�D�T�!$(+FH.�#GCE:�|�/aD1(G�>68¢~¡�%�')(+��.H(+|L!$N8!{/a|L#GD1N~/aDG("/+%�D�CE')(+F)D1|3/7��C�')#&]%�.HC$D�QHD</S*�!$|+#G.�?)D1(3D1*8w7!{/a%Y'P[\'d|+|7.)y¸� �¦�e£ � |+.HCE')(L[\'d|+|+DG|1�

XL%�D�*�.)/a|�')u�u�De')(3!EN�F��JD<QH.HN�*}6-¢���!$N9/+%�DS[c')u\')(+D7/a%�D���Û)È�0 Ç)É)×rB�=�B�B�F~')C�'�V�!$D1|�')N�*\�A:�')|a')(3|Æzw7!{/a%

�ÇHÊo!$N�/a%�DqD1�g:�'d/+.H(+!E')C�u�C�')N�D\D1�g:�'W/a.H(3!�')C�|+C$!E#GD�Æ �SÛ �

���Û � Ê<�-2�Nv')*�*�!{/a!E.)NU0�')C$C����

#1:�(+(+DGN~/aC$Q\]gN�.@w7N-B�=�B�Bc�g:�')|+')(+|>w7!{/a% � �')(3D�u�CE.d/+/aDG*U0�N�.)/Z�3:�|�/L/a%�.)|+D�!$N\/a%�DSD1�g:�'d/+.H(+!E')C5|3CE!E#GD)�

Page 23: A Map of the Universe - J Richard Gott, M Juric, et al

� Û)� �

B�!$N�#1DS/+%�D1|3D�C�')(3FHD"(+D1*�|+%�!{y³/L�g:�')|a'd(+|7')(3DS|+%�.�w7N}yz(+.)[ 'dCEC�.�?)D1(�/+%�D�|3]gQ)0^'�Ng:�[r��D1(>.dyZ/+%�D1[ ')u�u�De'd('d/7(3!EFH%~/"')|3#1D1N�|+!E.)N�|"w7%�!E#&%Y.�#G#1:�(7!EN/+%�D��1.HN�D�.)y¸'e?H.H!$*�')N�#GDoyz.)(>/a%�D�D1�g:�'W/a.H(3!�')CU|3CE!$#1D)��XL%�Do:�u�uJDG(u�')(�/�.dym.H:�(�[\'duc#1')Nq��D�#G.H[cu�')(+DG*\*�!$(+D1#</aC{QPw7!$/a% ��FH:�(3D��S')N�* ��FH:�(+DSÛ���XL%�D�[\'duc|3%�.@w7|>#1C$De')(3C$Q')N�*�w7!{/a%�(3D1#G.HFHN�!$�e')��C$D�|3%�')u�DP')C$CZ/+%�D�|�/a(+:�#G/a:�(+D1|�|3%�.@w7N�!EN-/+%�Dr#1C$.H|+D���:�u-!EN ��F):�(+D�ÛA0Jw7%�!$CEDo|3/a!$CEC|+%�.�w7!$N�F ')C$CL/a%�D�B�=�B�BÜ�g:�')|+')(+|\|+%�.@w7N !EN /a%�DYyz:�CECL?A!ED<w !$N ��F):�(+Dt�H� XL%�D-CE.HF~'d(+!$/+%�[9!E#q|3#e')C$D#e'du�/a:�(3D1|��J.d/a%�|+#1')CEDG|���De'd:�/a!{yz:�CEC{QH� ��N9/+%�D7CEDGy³/10^ÆI'W/�'d�J.H:�/7�H�ðÇW%c'dN�*}��Û)£o68u�#@ʸw�D"#e'dN9|3D1D"#1C$De')(3C$Q/a%�DPC�')(3FHDr#1!$(+#G:�C�')("?H.H!$*�?�!$|+!$��CED�!EN ��FH:�(+DcÛ��oXM./a%�DP(+!EF)%g/10�'d/� #��.)y�É)%��a�e×H%Ò')N�*�'d/�'}*�!E|3/a')N�#GD.)y�Û��@Ç � �~¡)£6YuJ#�w�DP#e'dN�|+D1D�'}BACE.~')N�,�(3De'd/�s¦')C$CM!$N-/a%�D�B�=�B�B-*�'W/&'�0JCE.HN�F)D1(�/+%�')N�/+%�D�,�(+De'W/s�')CEC�.)y¸,�DGCEC$D1(�')N�*}O�:�#&%�(a'YÆz/+%�D Ä y ��Û9,�(+D1'd/�s�')C$C³Ê<�MXL%�D���CE')N�]9(+D1F)!E.HN�|�')(+D�w7%�D1(3D�/+%�D���')(�/a%U��|D1�g:�'W/a.H("#1:�/+|"/+%�DoF~')C�'d#G/a!$#�u�C�'dN�Do')N�*Y!EN~/aDG(+|+DG#G/+|�/a%�D��G.HN�Do.)y�'e?H.)!E*�')N�#1DoN�De')(7/a%�D�F~'dC�')#</a!E#Su�C�')N�DÆzw7%�D1(+Dr/+%�DP!EN~/+D1(+|�/aDGCEC�'d(S*�:�|�/�.H��|3#1:�(3D1|�*�!E|�/&')N~/�FH')C�'WV�!$D1|�'dN�*�w7%�!E#&%�/+%�D9B�CE.H')N�|+:�(3?HD<Q�*�.AD1|�N�.d/#1.@?)D1(&Ê���XL%�D1|3D�')(+DrDG[cu�/�Q8yÅ')NA��|+%�')uJDG*�(+DGFH!E.HN�|�')|�|3%�.@w7NÒ!EN ��FH:�(+D\��')N�* ��FH:�(+D�Û�0J�J.):�N�*�DG*��gQ(a'd*�!�')C�CE!EN�D1|�uJ.)!EN~/a!$N�FÒ'ew>'eQvyz(+.H[ /a%�DY��')(3/+%U0�|3.�.HN .H:�(�[c')uv/a%�DG|+D8')(+D}��.H:�N�*�DG*Ý�~Qv?HDG(3/a!$#e')C|3/+(a')!$FH%~/7CE!$N�D1|G�

XL%�D�,�(3De'd/ �>/3/a(a'd#G/a.)(�Ƴw7%�!E#&%Y!E|LyÅ')(7.$�-/a%�DoD1�g:�'d/+.H(+!E')CUu�CE')N�Do')N�*}/a.@w�')(+*Yw7%�!E#&%Y/a%�D�TS!E(+F).|+:�uJDG("#GCE:�|�/aDG("%�')|"'9[9De')|3:�(a'd��CED�u�D1#G:�CE!E')(>?HDGCE.A#1!{/�Q�Ê�!$|L|+%�.@w7NU�

XL%�D[9.H|3/�u�(3.H[c!$N�D1N~/�yzDe'd/+:�(+Dq.dyL/a%�D}B�=�B�BtC�'d(+FHDc|+#e'dCED\|�/a(3:�#G/+:�(+D|3D1D1Nv!$N ��FH:�(+D¢�!$|�/a%�D�aB�C$.~')Nc,�(+De'W/�s¦')C$C ���ZXL%�!$|�yzD1'd/a:�(+DLw>'d|�N�.d/a!E#GD1*9De')(3C$Q~��.)N9!$NP/a%�DSB�CE.H')N�*�'d/&'�')#G�g:�!E|3!$/a!$.HN�u�(+.A#1DG|+|G0')N�*�%�')|���D1DGN�[9D1N~/a!$.HN�D1*�!ENÒu�'d|+|+!$N�FY!EN�'Y#G.H:�u�C$DP.)y�/+!E[9D1|�!$N�BACE.~')NÒ(3D1u�.H(3/+|10M')#1#G.H[cu�')N�!EDG*Ò�gQu�%�(+')|+DG|�|+:�#&%Ü')| �3CE')(+FHD��vÆIb�C�')N~/a.)N DG/�')CI�LÆIÛ)£H£H�~Ê3Ê<0�')N�* �3|3/+(+!E]g!$N�F ��0 ��w�')C$C{��C$!E]dD ��0¸')N�* �3[c'@Qt��D/a%�DPC�')(3FHD1|�/�#1.H%�D1(+DGN~/�|�/a(3:�#G/+:�(+DPQHD</o.H��|+DG(3?)D1* �¦ÆÅXZD1FH[c')(+]YDG/o'dCf�{0m')|3/+(+.d�Íu�%)£)���@£~¡HÛ)ÇHÊ<��XZ.Y[c')]dD'\�g:�')N~/+!$/&'W/a!$?)D�#G.H[9u�')(+!$|+.HN50�w�Dr%�'e?HDr')CE|3.\|+%�.�w7N�/+%�DP,�(+D1'd/Ss�')C$CZ.dy�,�DGCEC$D1("')N�*�O":�#&%�(+'���XL%�!$|D<VA/+D1N�*�|".@?HDG(�|3DG?HDG(a')C�|3CE!E#GD1|L.)yZ/a%�D Ä y ��Ûr|+:�(�?HDGQ�Ƴyz(+.H[ ×gÛ � /a.���¢ ðÇ � *�DG#1C$!EN�'d/+!E.HN�Ê<�� "'d/a%�D1(>/a%�')Nu�C$.)/+/+!EN�FÒu�.H!EN~/a|Pyz.H(�!{/�%�D1(3D)0>w7%�!$#&%Üw�.H:�CE* ��D8#G.HN�yz:�|3D1*Ýw7!{/a%ÝB�=�B�B |3:�(3?)DGQÜF~')CE'WV�!ED1|rw�D-%�'@?)Du�C$.)/+/+D1*�*�D1N�|3!$/�Qt#1.HN~/a.):�(+|P'e?)D1(a'dFH!EN�F8.@?HD1(r')CEC�/a%�D Ä y ��ÛY|+CE!$#1DG|�yz(+.)[ ×gÛ � /+. ��¢ ðÇ � *�D1#GCE!EN�'d/a!$.HNU�XL%�!$|�?H.HC$:�[9DqD<VA/aDGN�*�|PyÅ')(�')�J.@?)Dq/a%�DDG�A:�'d/a.H(3!�')C�u�CE')N�D)0�'dN�* |+!$N�#1D\w�D}')(3Dqu�CE.d/+/a!$N�F-!{/r!$N (+!EF)%g/')|3#1D1N�|+!E.)N\#1.)(+(+DG#G/+C$QH0A!$/�!$|�N�.)/�u�(+D1|3D1N~/aDG*#1.HN�yz.H(+[c')CEC{QH0H��:�/�!$|��JDG!EN�FoCEDGN�F)/a%�D1N�DG*\!EN�/a%�D�/&'dN�FHD1N~/+!�')C*�!$(+D1#</a!$.HN¦�~Qv'-yÅ')#</a.H(r.dy � �@Ö�#G.H|@ÆIÛ�� � Ê�Ñ �� £~¡A�t`".)/aDq/+%�'d/P|3!EN�#GDq/a%�D Ä y ��ÛÒ,�(3De'd/rs�')C$C�!$|P'yÅ')#</a.H(�.)y"')u�u�(3.eV�!$[\'W/aD1C{Q�Û�� Ç8#1C$.H|+DG(�/+.�:�|�/+%�')N�/+%�D}B�C$.~')N ,�(+D1'd/�s�')C$C�!{/�!$|�*�DGu�!E#</aDG*v'd/r|3#e')C$D/a%�'d/>!$|>Û�� Ço/+!E[9D1|�C�')(3FHD1(G��B�.P'dC$/a%�.H:�FH%9/a%�D Ä y ��Ûr,�(+D1'd/�s�')CEC^|�/a(+D</a#&%�DG|>yz(+.H[xÉ)%c/a.\�eÈ��ð¡W%ÒÆÅ.H(�¡�� ¡%�.H:�(+|>.)y�(3!EFH%~/>')|+#GD1N�|3!E.HN^Ê�0�')|�#1.H[9u�')(3D1*\w7!{/a%\/+%�D�B�=�B�B,�(+D1'd/�s�')C$C^w7%�!E#&%|3/+(+D</a#&%�DG|7yz(3.H[x¢�� ¡d%/a.-�@��� ¡d% ÆÅ.H(�Çc%�.H:�(+|�.)y�(3!EFH%~/�'d|+#1DGN�|+!$.HN^Ê�!{/a|�(+De'dC¸CEDGN�F)/+%�!EN�#G.d��[9.@?A!EN�Fc#1.A.H(+*�!$N�'d/+D1|S(3D1CE'd/a!{?HD�/+./a%�D Ä y ��Û,�(+D1'd/Ss�')CECZ!E|G05�~Q-/+%�!E|�|+!$[cu�C$D�'dN�')C$QA|3!E|10UÛ  Ç �tÇHÖ�Æf¡ ð¡ � �� £~¡)Ê � ��ð¡d×c/a!E[9D1|S')|�C$.HN�F��XL%�!$|"!$|7')u�u�'d(+D1N~/"!ENq/+%�D�#1.H[9u�')(3!E|3.HN���FH:�(3D�|+:�u�u�CE!EDG*}!EN��FH:�(3DoÉ�0�w7%�DG(+Do�J.)/+%Y')(+D�|+%�.�w7N8'd/7/a%�D|a'd[cD9|+#1')CEDc!EN�#1.d�Í[c.@?A!EN�FY#1.A.H(3*�!EN�'W/aD1|G�}XM.8[\')]dDq'}yÅ')!E(�#1.)[cu�'d(+!E|3.HNU0Z|+!$N�#1D�/a%�Dq,�(3De'd/os�')CEC�!$|')C$[c.H|�/>'�yÅ'd#G/a.)(>.)yM�r#1C$.H|+DG(�/a%�'dNq/a%�DoB�C$.~')N},�(+D1'd/>s�')CECI0~w�D�%�'e?)Dou�CE.)/3/aD1*q'q��Û � w7!E*�D�|+CE!$#1D"yz(+.H[/a%�D Ä y ��ÛY|+:�(�?HDGQt/a.�#G.H[9u�')(+D9w7!$/+%�.H:�(�× � w7!$*�D\|3CE!E#GDc!$Nt/+%�D}B�C$.~')NU0Z|+.�/+%�'d/��J.)/+%¦|+C$!E#GD1|�%�'@?)D

Page 24: A Map of the Universe - J Richard Gott, M Juric, et al

� Ûd× �

')u�u�(+.eV�!E[c'd/aDGC$Q9/a%�D�|a'd[cD�w7!E*�/a%Y'd/7De'd#&%8w�')CECI��SyL#1.):�(+|3D)0M/+%�Dcw�')C$CE|o')(+D�N�.d/�u�D1(�yzD1#G/+C$Q�')C$!EFHN�D1*Òw7!$/a%Ò/a%�D9Î 'WV�!$|o.dyL.H:�(o[\'duU0�|+.-.)N�D\%�'d|

/a.�[9De')|3:�(+D}/a%�DG!E(�CEDGN�F)/+%Ý')C$.HN�F�/a%�D8#G:�(3?)D)�ÚXL%�D-B�CE.H')NÜ,�(3De'd/�s�')CECL!$|c'W/\'Ò[9D1*�!E')NÜ*�!E|3/a')N�#GD.)y"���e£�68u�#)��2Í/1�õ|�/a.)/a')C�CED1N�F)/a%¦!$N�#G.d��[9.@?�!$N�F-#G.�.)(+*�!$N�'d/aDG|�!$|�×gÇd£�68u�#q')|r#G.H[9u�')(+DG*�w7!$/+%�/a%�D/a.d/&')C�CEDGN�F)/+%¦.)y>/+%�D},�(+De'W/�s�')CEC�.)y�,�D1C$CEDG(�'dN�* O�:�#&%�(a'-w7%�!$#&%¦!E|rÛd×~£-68uJ#\CE.HN�FY!ENt#1.d�Í[c.@?A!EN�F#1.A.H(3*�!EN�'W/aD1|G��XL%�!$|�!$N�*�!E#1'd/aDG|�/a%�D"|+!$�1D1|�/a%�D�/�w�.�w�')CEC$|�w�.H:�C$*c%�'@?)D�'d/�/a%�D�#G:�(+(3D1N~/>DGuJ.A#&%U��b�:�/�/a%�D,�(+De'W/�s¦')C$C�!$|�'d/�'�[cDG*�!�'dNP(+D1*�|+%�!{y³/�.)y �Ñ £ õ£~Û)É�|3.�!{/e��|¸/a(3:�D7|+!$�1D7'd/�/+%�D7D1u�.�#&%Pw�DS')(3DL.H��|3D1(3?A!$N�F!$/"!$|"|3[\'dCECEDG(L�~QY'9yÅ')#</a.H(7.)y��>Ø \FH!$?A!$N�F�!$/�')NY.H��|+DG(3?)D1*�CEDGN�F)/+%8.)y�Û)�~Û��õÈ)×\68u�#qÆz.H(�¡HÇ)¢�[c!$CECE!$.HNCE!$FH%~/�Q)De')(3|&Ê���XL%�D9BACE.~')N-FH(+D1'd/�w�')CECM!E|�'W/�'q(+DG*�|+%�!{y³/�.)y Ñ £  £H¡)�\|+.!{/e��|S/a(3:�Dr.H��|+D1(�?HDG*tC$D1N�F)/+%!E|�×��@É�68u�#9ÆÅ.H(S�H0 �)È~Ç�[9!ECEC$!E.HN�C$!EFH%~/�Q)De')(3|&Ê���K�.H(�#1.H[9u�')(3!E|+.)NU0�/+%�D Ä 6-bÚ|+u�%�D1(+D�%�'d|7')N.H��|3D1(3?)D1**�!E')[cD</aDG(�.)y7ÆfÛ ��e×�Ï&£H£H£~Ê3Ö��@£HÉ)£rÑ¥ÛHÇ  ¡\68u�#)��XL%�Dr.H��|3D1(�?HD1*ÒC$D1N�F)/+%-.)y¸/a%�D�BACE.~')N-,�(+De'W/Ss�')CECm!$|/a%g:�|�¢H£~¤�FH(+D1'd/aDG(L/a%�')N/+%�D�,�(3De'd/Ls�')CEC5.)y�,�D1C$CEDG(L')N�*YO�:�#&%�(a'��

B�!$N�#1D"w�D�%�'e?HD�Ng:�[9D1(3.H:�|�|�/a:�*�!ED1|�/a%�'W/�|3%�.@w /+%�'d/�/a%�DS�H= /+.Hu�.HCE.HFdQP.)ymCE')(+FHD7|3#e')C$DS|3/+(+:�#</a:�(3D!E|�|3uJ.)N�FHCE!$])DoÆI,�.)/3/e0g=�!$#&]A!$N�|+.)NU0�' 68DGCE.)/3/�Æ��@ÉH¢)È~Ê��)T�.)FHD1C$DGQrD</�')Cf�^ÆÞ�@ÉHÉ)×~Ê��~O"!E]W')FHDLD</�'dCf��ÆIÛ)£H£~Û)Ê+ʸ!$/|+%�.H:�CE*\N�.)/>��D�|3:�(+u�(3!E|3!EN�F�/+%�'d/>')|�w�D�CE.A.H]9'd/�C�')(3FHD1(�|a')[9u�C$D1|�w�D�|3%�.H:�C$* ��N�*D�V�'d[cu�C$D1|�.)y�C�')(3FHD1(#1.)N�N�D1#</aDG*Ú|3/a(3:�#G/+:�(+DG|1� 2�N�*�D1DG*U0Lw�DYw�.):�CE*Ì%�'@?)D-%�'d*Ý/a.t%�'e?HD���D1DGNÌD1|3uJDG#1!�'dCEC$Q¦CE:�#&]~Q /a.�%�'@?)D*�!$|+#1.@?)D1(+DG*�/a%�D9CE')(+F)D1|3/o|�/a(+:�#G/a:�(+D9!EN�/a%�D�.H��|+D1(�?d')��CED9:�N�!{?HDG(+|+D9!EN�/+%�Dc!$N�!$/+!�')C Ä y ��|+:�(�?HD<Q�w7%�!E#&%%�')|�'q[�:�#&%Ò|+[c')CEC$D1(7?H.HC$:�[cD�/a%�')N�/+%�D�B�C$.~')N�|+:�(3?HD<QH��BA!E[r:�CE'd/aDG*�|+C$!E#GD1|�.)y�/+%�D9B�CE.H')N�:�|3!EN�F �^'W/C�'d[r�J*�'S[c.A*�DGCE|LÆÅ')|�|3:�FHFHDG|3/aDG*c�~Q�s 6&����ʸ|+%�.�wÝFH(+D1'd/�w�')CEC$|�')N�*PFH(+D1'd/�w�')CEC�#1.H[9u�CED�V�D1|�/a%�'d/�')(3D�g:�!$/+D�!$[cu�(+D1|3|+!{?HD�Æ Ä .HC$CEDGQrDG/�')Cf��ÆIÛ)£H£H£~Ê3Ê<� Ä .HCEDd0�O�'d/+/+.HNU0~s�DG!ENg��D1(+F�0�' K�(+DGN�]YÆ��eÉHÉH¢~ʸyz.H(�D<V�')[9u�C$D%�')*-'cFH(3De'd/7w�')CEC�!$NY/+%�D1!$( � �ÌÑ £ õ×�Ï ��� Ñ £ õÈqB�C$.~')N}|+!$[r:�C�'W/a!E.)N}w7%�!E#&%-!$|S¢H¤ CE.HN�FHD1(7/a%�'dN8/a%�D,�(+De'W/¸s�')CECg.)yJ,�D1C$CED1(M')N�*rO�:�#&%�(+' �A')N�*r|3.�!$/M#1.H:�CE*r��D�|+')!E*�/+%�'d/M/a%�D>D�V�!E|3/+D1N�#GDL.)y�'�,�(+D1'd/Ms�')C$C�!$N/a%�D�B�C$.~')N�CE.)N�FHD1(�/+%�')N�/a%�DS,�(+De'W/�s¦')C$C�.)ym,�DGCECEDG(�')N�*\O�:�#&%�(a'�w>')|�u�(+DG*�!E#</aDG*c!$N\')*�?)'dN�#1Dd�¸T�!$|+:�')C!EN�|+u�D1#G/+!E.HNc.)y5/+%�D�Û)¡HÇo��XL%�'dCE.H|�|+!E[�:�C�'d/+!E.HN�|�(+DG?)De')C$|�|3!E[9!EC�'d(�|3/+(+:�#</a:�(3D1|�/+.�/+%�D�B�C$.~')N\,�(3De'd/�s�')CEC!EN�[9.H(+D>/+%�')NY�@£~¤ .dy5/a%�D"#1')|+DG|�ÆzXMDGFH[c')(+]rD</�')Cf0g')|�/a(3.d��u�%�)£H���@£H¡HÛHÇHÊ��MXL%g:�|G0�!{/�|+D1DG[c|�(+D1')|+.)N�')��C$D/a%�'d/S/+%�D�B�C$.~')NÒ,�(+D1'd/Ss�')CEC�#1')N��JD�u�(+.A*�:�#GD1*�yz(+.)[ (+')N�*�.)[ u�%�')|+D�,�'):�|3|+!E')N ��:�#</a:�'W/a!E.)N�|�!EN-'|3/a')N�*�'d(+*�^'d/���C�'d[r�J*�'S[c.A*�DGCf0H'�[9.A*�D1CA/a%�'d/�'dCE|+.�u�(+D1*�!E#G/+|�'�|+u�.HN�FHDGCE!$])D>/a.)uJ.HC$.HF)Qo.)y�%�!$FH%P*�D1N�|+!$/�Q(+DGFH!E.)N�|�!EN��H=r�m`".)/&'d��C$Q)0Z.):�(��g:�')N~/a!{/&'d/+!$?HDP/+.HuJ.)CE.HF)Q-')C$FH.H(+!{/a%�[ ')u�u�CE!$D1*�/a./a%�D\Ûd= B�C$.~')NtB�C$!E#1D!E*�D1N~/a! ��D1|�/a%�D\BACE.~')Nt,�(+D1'd/�s¦'dCEC�')|�.HN�D9#G.HN�N�DG#G/+D1*¦|�/a(+:�#G/a:�(+D-ÆIO�.@QACED�D</�'dCf��ÆIÛ)£H£~Û)Ê+Ê<��KM!EFH:�(3D9Û!EN�O".�QAC$DPDG/�')Cf��ÆfÛ)£)£~ÛHÊS#1C$De')(3C$Q8|+%�.@w7|�/a%�!$|�')|�.HN�D�#1.)N�N�D1#</aDG*�|3/+(+:�#</a:�(3D\'W/�/a%�D�[9D1*�!E')N�*�D1N�|+!$/�Q#1.)Ng/+.H:�(¸w7%�D1N�|+[9.�.d/a%�DG*�'d/�Ç�� +�4 68u�#>!$NP'S?H.HC$:�[9D�CE!$[c!{/aDG*�|+')[cu�CED�w7%�D1(+D>/+%�D�?d')(�Q�!$N�FS/+%�!E#&]gN�DG|+|')N�*�?)'d(3QA!EN�FS#1.H[9u�CED</aDGN�D1|3|�.)y�/a%�D>|+:�(�?HD<Qr!EN�*�! �JD1(3D1N~/�*�!$(+DG#G/a!$.HN�|¸')(+D�')#1#G.H:�N~/aDG*ryz.H(1�M2Í/�!E|MuJDG(+%�'du�|N�.Y')#G#1!E*�D1N~/�/+%�'d/���.)/a%�/+%�DcB�CE.~'dN�,�(+D1'd/�s�')CEC¸')N�*Ò/a%�Dc,�(+De'W/�s¦')C$C�.)y>,�DGCEC$D1(�')N�*�O":�#&%�(a'Y')(3D|+DGD1N�(+.H:�FH%�C$Q}/a')N�FHDGNg/+!�')CZ/a.q/+%�DPCE!$N�D�.)y�|3!EFH%~/e��,�(+De'W/Ss�')CEC$|�/&'dN�FHD1N~/+!�')CZ/a.q/a%�DPCE!EN�D�.)y�|+!$FH%~/�')(3D|+!$[cu�C$QÒDe'd|+!EDG(�/a.-|+D1D!$N¦|+C$!E#GD\|+:�(3?HD<QA|10>'d|ruJ.)!EN~/aDG*¦.H:�/P�~Q���(a'd/+.HNU0�68DGCE.)/3/e0 ' 68#e��DGD�Æ��@ÉHÉH¡HÊ<���,�(+D1'd/�s�')CECMuJDG(+u�D1N�*�!$#1:�CE')(�/+.q/a%�DPC$!EN�D�.)y�|+!$FH%~/�w�.):�CE*Ò��Dr[c.)(+Dr*�!��9#1:�C{/S/a.|3D1D���D1#e'd:�|+DP/a%�DN�D1')(LD1N�*}w�.H:�CE*}��D�CE.H|�/7*�:�D�/+.�/+%�!EN�N�D1|3|".dyM/+%�D�|+C$!E#1D�'dN�*/a%�D�yÅ')(LDGN�*w�.):�CE*}��DoC$.H|3/>*�:�D�/a.P/a%�D

Page 25: A Map of the Universe - J Richard Gott, M Juric, et al

� ÛHÇ �

C�'d#&]c.)yZF~'dC�'WV�!EDG|���(3!EFH%~/�D1N�.H:�FH%/a.P��DS?A!E|+!$��CEDS'd/LFH(3De'd/>*�!E|�/&')N�#GD1|G�� 7D1*�|+%�!{y³/L|+u�'d#1D�*�!$|3/a.)(3/a!$.HN�|�.HNC�'d(+FHDo|+#1')CEDG|105!I�õDd��!$N�yÅ')C$Cm.)y�F~')CE'WV�!ED1|7yz(+.)[ ?).H!E*�|S.HN~/a.\*�D1N�|3D1(�(3D1FH!$.HN�|�D1N�%�'dN�#1DG|�#1.HN~/a(+')|3/�yz.H(S(3De')CyzDe'W/a:�(3D1|�/a')N�FHDGNg/+!�')C�/a.8/a%�DqC$!EN�D9.)y7|3!EFH%~/e� �~K¸!EN�FHD1(3|�.)y�,�.A* ��')C$|+.�[c')]dDc/&'dN�FHD1N~/+!�')C�|3/+(+:�#</a:�(3D1|[9.H(+D>N�.)/a!$#e')��C$D��~Q�/+%�!E#&]dD1N�!$N�F�/a%�D1[Y�Ms %�DGN\�M')(+]qÆ��@ÉHÉ)£~Ê ��(3|3/�|3!E[r:�CE'd/aDG*P'S?H.)CE:�[9D�CE')(+FHD�D1N�.H:�FH%/a.8|+!$[r:�C�'W/aDP/a%�D Ä y � |3:�(3?)DGQ)0�'�,�(+De'W/os�')C$C�w�')|�!E[9[cDG*�!�'d/+D1C{Q-|3D1D1N�!ENt/+%�Dq�)= *�'d/a'��qs %�DGN '|+C$!E#GD�/+.8|3!E[r:�C�'d/+D�/+%�D Ä y � |3CE!E#GD�|+D1DGN�yz(+.)[ ��')(3/+% � w7%�!E#&%¦F)DG/a|�w7!E*�D1(o')|o!$/oFHDG/+|oyz:�(3/a%�D1(�yz(+.H[/a%�D���')(�/a% � w�')|�[c')*�Dd0�/a%�D�,�(3De'd/7s�')CEC5!EN}/a%�Do|+!$[r:�C�'W/a!E.)N\w>'d|Su�(3DG/+/�Q}[�:�#&%�'�*�De')*8(+!$N�FHD1(>yz.)(/a%�D},�(3De'd/�s¦'dCEC�.)y�,�DGCEC$D1(�')N�*vO�:�#&%�(a' � DG�g:�')C>!$N¦CEDGN�F)/a%50�|+%�'duJDd0�')N�* *�DGN�|+!{/�QH�ÒXL%�!E|ow>'d|�')N!E[9u�(3D1|+|3!$?)D�|+:�#1#1DG|+|�yz.H(�`7�Í�J.A*�QY|+!$[r:�C�'W/a!E.)N�|1�LXL%�DPB�CE.~'dN�,�(+De'W/Ss�')CECZ')N�*8/a%�D Ä y ��,�(+De'W/Ss�')CEC%�'e?HD���D1DGNyz.H:�N�*!$Nq�g:�!$/+D�|+!$[c!$C�')(�#1!$(+#G:�[c|�/&')N�#1D1|G0�De'd#&%Y!$N'r|+C$!E#GDS.)yZ#1.)[cu�'d(a')��C$D�/+%�!E#&]gN�DG|+|10^'dN�*')|�!ECEC$:�|3/+(a'd/+D1*�!EN ��FH:�(3DqÉ�0M�J.)/+%¦')(3D\�g:�')C$!$/a'd/a!{?HD1C{Q��g:�!$/+Dc|3!E[9!ECE')(�D<V�#1DGu�/r/+%�'d/�/+%�DBACE.~')N�,�(+De'W/s�')CEC�!$|�|3!E[9u�C$Q�C�')(3FHD1(G0g')N�*\')|�w�D"%�'e?HDSN�.)/aDG*U0�.):�(>Ûd= /a.)uJ.HC$.HF)Qr')CEFH.)(+!$/+%�[ ÆIO�.@QACED"DG/�')CI�^ÆfÛ)£)£~ÛHÊ+Ê!E*�D1N~/a! ��D1|�/a%�D�B�CE.~'dN,�(+De'W/�s�')CEC�')|�.HN�DS#G.HN�N�DG#G/+D1*|3/+(+:�#</a:�(3D�!EN\'o?H.)CE:�[9DSC$!E[9!$/aDG*�|+:�(�?HDGQcw7%�D1(3D/a%�D�?d')(3QA!$N�F9/+%�!E#&]gN�DG|+|�')N�*-#1.)[cu�C$DG/+D1N�DG|+|S.dy�/a%�D�|+C$!E#1Do|+:�(3?HD<Q�'d(+D�u�(+.Hu�D1(3C$QY')#G#1.H:�N~/+D1*�yz.H(G�LXL%�DÄ y � ,�(3De'd/Ss¦')C$C¸!$|�')|�C�')(3FHD�'q|3/+(+:�#</a:�(3D\'d|�#1.H:�C$*Ò%�'e?HD ��/�!EN�/+%�D Ä y ��|a')[9u�CEDd0m��:�/�/+%�DcB�CE.~'dN,�(+De'W/�s¦'dCECZ!E|�|3[\')C$CEDG("/+%�')N�/a%�D�|+!E�GDP.)y�/a%�DPB�CE.~'dN�|+:�(�?HDGQ)0�|+%�.@w7!EN�F}/+%�DrD�V�u�D1#</aDG*¦')u�u�(+.~')#&%�/+.%�.H[9.HFHDGN�D1!{/�Qq.HN}/a%�D�?)D1(�Q}C�')(3FHD1|�/L|+#1')CEDG|1�

XL%�D}ÛW*�K |+:�(3?HD<Q Æ Ä .HCEC$D1|+|�DG/�'dCf��ÆfÛ)£)£���Ê+Ê�0¸.)y7|3!E[9!ECE')(�*�D1u�/a%¦/a.8/a%�DqB�CE.~'dNU0�#1.)[cu�C$DG/+D1*t/�w�.|+C$!E#GD1|10^'dN8DG�A:�'d/a.H(3!�')Cm|3CE!$#1D9ÆIÉ���·�Ç)£ �

����e×���·�Ç)£ � Ï��S¡  Ç �

���Û  Ç � Ê�0^')N�*-'�|3.H:�/+%�D1(3N�|+C$!E#1D

ÆfÛA� � ·~×H£ ����£H� � ·~×~£ � Ï����~¡  Ç �

���

�SÛHÛ  Ç � Ê<�MXL%�!E|�|3:�(3?)DGQ�w>'d|�/+%A:�|�N�.d/�'du�u�(+.)u�(+!E'd/aD�yz.)(.H:�("CE.)F~')(+!{/a%�[9!E#�[\'du-.)yM/a%�D�:�N�!$?)D1(3|+D)�"XL%�D�|+.H:�/+%�D1(3N�|+C$!E#GD�w�')|�N�.)/S')CE.HN�F\'9FH(+D1'd/S#G!E(3#1CED�!$N8/a%�D|+]~Q)0�')N�*9/+%�D1(3DGyz.H(3D"w�.H:�C$*c��D7|3/a(3D1#&%�DG*!$y�u�C$.)/+/+D1*9!EN�.H:�(�[c')u�!EN9(+!EF)%g/�'d|+#1DGN�|+!$.HNU��XL%�D"D1�g:�'W/a.H(3!�')C|+C$!E#GD�w�')|L.)yZCEDG|+|L')N�FH:�C�'d(�D<VA/+D1N~/L/a%�'dN}/+%�D�#G.H(+(3D1|+u�.HN�*�!EN�F9B�C$.~')N}BACE!E#GD�')N�*|+.r/a%�DoB�CE.~'dN\w7!$/+%q!$/+|FH(3De'd/+D1("#1.@?HDG(a')FHD�!EN8' �^'W/�DG�g:�'d/a.)(+!�'dCm|+CE!$#1D�w�')|S:�|3D1*-/+.\u�C$.)/7C�'d(+FHD�|+#1')CEDo|3/+(+:�#</a:�(3D�!$N8.H:�(�[c')uU�2�N�*�DGD1*U0~/+%�D7Ûd*�K�|3:�(3?)DGQ)0���D1#1'):�|+DL.dyJ!{/a|M|+[c')CEC$D1(Z#1.@?HDG(a')FHD7!$Nr(+!$FH%~/�')|3#1D1N�|+!E.)NU0g[c!$|+|+DG*�/a%�D>w�DG|3/aDG(+ND1N�* .)yL/a%�DB�CE.~'dN ,�(+De'W/�s�')CEC�')N�* |3.�/a%�D9w>'dCEC�*�!E*¦N�.)/r|3%�.@w :�uv'd|�u�(3.H[c!$N�')N~/aC{QÒ!EN�/+%�DÛW*�K|+:�(3?HD<QP')|M!EN�/+%�DLBACE.~')N5�¸�Z.�w�D1(�|3uJDG#G/+(+:�[ ')N�')C{QA|+!E|Z.)y�/+%�DLÛd*�K�')N�*�/+%�DLBACE.~')N�#1.H[9D�:�u�w7!$/+%r�g:�!$/+D|+!$[c!$C�')(LDG|3/+!E[c'd/aDG|1�"XL%�D1|3Dr/�w�.qF)(+De'W/�|+:�(3?HD<QA|o!$N-[c')N~Q}w>'eQA|�#1.H[9u�C$D1[9D1N~/SD1')#&%�.)/+%�D1(G�S�ZD1(+%�')u�|[9.H|3/�!E[9uJ.H(�/&')N~/+C$QP/a%�DoÛd*�K�u�.@w�DG(L|+u�D1#G/+(+:�[�')N�')C{Q�|3!E|�w7%�!E#&%w�')|7'e?)'d!EC�'d��CED7��DGyz.H(3D�B�CE.H')N}')N�*!$N/a!$[cD�yz.H("s 6&��� ')CEC$.�w�D1*-D1|3/+!E[c'd/aDG|S.)y � � w7%�!$#&%Ò')CEC$.�w�D1*8s 6&��� /a.q(3D ��N�D�/a%�Dr#G.H|+[9.HC$.HFH!E#1')Cu�')(+')[9DG/aDG(+|�:�|+D1*�!$Nr/a%�D>#G.HN�|�/a(+:�#G/a!$.HN�.)y�/a%�!E|�[c')uU�MXL%�D"B�CE.H')N�,�(+De'W/�s¦'dCECA#1.HN~/&'d!EN�|�'�Ng:�[��JDG(�.)y�S��D1C$CU#1C$:�|3/+D1(3|rÆz!EN�#GCE:�*�!$N�F�0Ayz.H(7D<V�')[9u�CEDd0 ����Ûd�H¢�0 ���@È~Ç)£�0!���@ÈHÉ~ÛP')N�*&����¡HÇ)£ryz.H(>w7%�!$#&%-(3D1*�|3%�!$y³/+|')(3Dq]gN�.@w7N^Ê<�ÒXL%�D|3uJ.HN�FHD1C$!E])DcN�'d/+:�(+Dq.dy"�H= /a.Hu�.HC$.HF)QÒ[9De')N�|�/a%�'d/�#1C$:�|3/+D1(+|�'d(+Dq#G.HN�N�DG#G/aDG*v�gQ��CE')[cDGN~/a|>.H(>w�')C$CE|>��:�/7!$yZD<VA/aDGN�*�DG*YyÅ')(LDGN�.H:�F)%U0�w�')CEC$|>|+%�.):�CE*}|+%�.�w %�.HC$D1|L')C$CE.@w7!EN�F�/a%�D�?).H!E*�|L.HNDe'd#&%8|3!E*�D�/a.�#G.H[c[�:�N�!E#1'd/aDd�

2�N�*�DGD1*U0�!ENv.H:�(�[c')u w�DY#e')N |+DGD8|3.H[9D(+D1[9N�')N~/+|c.)y"/a%�D Ä y ��Ût,�(+D1'd/Ps�')CEC�ÆÅ'�#G.H:�u�C$D.)y#1C$:�[9u�|P.H(��HCEDGFH| �~Ê�D<VA/aDGN�*�!EN�Ft!$Ng/+.�/a%�D}D1�g:�'W/a.H(3!�')C>u�C�')N�D}.)y"/a%�D-BACE.~')Nv|+')[cu�CED)� ��|c|3%�.@w7NÝ!$N

Page 26: A Map of the Universe - J Richard Gott, M Juric, et al

� Û)È �

T�.HFHDGCED<QqDG/�')CI�mÆÞ�@ÉHÉ)×gÊ�0�!{yMD�VA/aD1N�*�D1*-/+.P/a%�D�|3.H:�/a%}/a%�D�,�(+D1'd/Ls�')CECJ*�DG?)D1CE.)u�|�%�.HCEDG|>/a%�'d/"'dCECE.@w /a%�Dyz.H(3D1FH(3.H:�N�*�')N�*���')#&]gFH(+.H:�N�*�?H.)!E*�|o/a.Y#1.H[9[r:�N�!$#e'd/+D�CEDe'd*�!EN�F}/a.-'8|3uJ.HN�FHD1C$!E])DP/+.HuJ.)CE.HF)Q�.)y>/a%�D[9D1*�!E')N�*�DGN�|+!{/�Q�#G.HN~/a.H:�(r|+:�(�yÅ')#1Dc!EN �)=r�Z2�Nv�)=r0�/+%�D}B�C$.~')N¦,�(3De'd/os¦'dCEC�[\'eQ���Dq#1.HN�N�D1#</aD1*¦/+./a%�D�|3:�uJDG(+#GCE:�|�/aD1(�.)y ���JDGCECm#GCE:�|�/aD1(3|"yz.):�N�*-�~QYb>'d%�#e')C$C�')N�*-B�.HN�DG!E(+'-ÆÅb>')%�#1')CEC�'�BA.HN�D1!$(a'8Æ��@É)¢)×gÊ+Êw7%�.H|3Do/�w�.9[cDG[r�JDG(+|LC$!ED��3:�|�/"')�J.@?)D�!{/L!EN}*�DG#1CE!$N�'d/+!E.HNU�

2�N�/+%�D�#GD1N~/aDG(¸.)y�/a%�D�,�(+De'W/Ms�')CEC~!$|m/a%�D Ä .H[c' Ä C$:�|3/+D1(10d.HN�D�.)y�/+%�D�CE')(+F)D1|3/Z#GCE:�|�/aD1(3|¸.)y�F~')CE'WV�!ED1|]gN�.@w7NU�

XL%�Do�g:�')|a'd(�� Ä ÛH¡)�P!E|L|3%�.@w7N�')|"'P#1(3.H|+|G�XL%�D�F)(a'e?A!$/&'W/a!E.)N�')C�CEDGN�|>�g:�')|+')(>£)É~ÇH¡�!$|�|3%�.@w7N8'd|�w�D1CEC5')|�/+%�D�C$D1N�|3!EN�F�F~')C�'�V�Q9u�(3.�*�:�#1!$N�F�/a%�D

[r:�C{/a!$u�CED�!E[c')FHD)�PXL%�D9C$D1N�|3!EN�F}F~'dC�'WVAQ�!$|o')CE.HN�Fq/a%�D�|a'd[cD�CE!$N�Dr.)y�|+!$FH%~/o��:�/�'d/o')��.H:�/o.HN�DP/+%�!E(3*/a%�Do#G.d��[9.@?A!EN�FP*�!$|3/a')N�#1Dd�

XL%�D}F~')[9[c'-(a'eQ ��:�(+|3/+D1(c,� �b>É)ÉH£���Û)��!$|P|+%�.@w7N ��yz.H(�'���(+!$DGy"u�D1(+!$.�* /+%�!E|rw�')|P/a%�D}[9.H|3/CE:�[c!$N�.H:�|>.)�A�3D1#</�!$N/a%�D�.H��|3D1(�?HD1*-:�N�!$?)D1(3|+D)�

XL%�D�(+DG*�|+%�!$y³/ rÑ £  ¡)ÈL!E|m|+%�.�w7N�')|Z'LCE!$N�D¸w7%�!$#&%�[c')(+]g|U/+%�D�D1u�.�#&%�/a%�'d/�*�!$?A!$*�D1|U/+%�D�:�N�!$?)D1(3|+D)��|*�DG#1D1C$D1(+'d/a!$N�F\'dN�*�')#G#1D1C$D1(+'d/a!$N�Fcu�%�')|+Dd�����g�3D1#G/+|S#GCE.H|3D1(7/a%�')NY/a%�!$|�C$!EN�Do')(3D�.)��|+DG(3?HDG*Ò'd/�')N-DGuJ.A#&%w7%�DGN�/a%�Do:�N�!{?HD1(3|+Dd�õ|�D�V�u�')N�|+!$.HN�!$|S')#G#1DGCED1(+'d/a!$N�F�0�w7%�!$CED�.H�A�3DG#G/a|�yz:�(3/+%�D1(S'@w�'eQ}/a%�')N8/a%�!$|�C$!EN�Do')(3D.H��|3D1(�?HD1*�'d/"')N}D1u�.�#&%}w7%�DGN8/a%�Do:�N�!$?)D1(+|3D)��|SD�V�u�')N�|+!$.HNY!E|L*�DG#1D1C$D1(+'d/a!$N�F��

XL%�D>:�N�(+D1')#&%�')��C$D>CE!$[c!{/m!E|Z|+%�.�w7N9'd/ rÑ�� õÈHÉ���b�D1#e'd:�|+D>.dy�/a%�D>')#1#GD1CEDG(a'd/+!E.HN�.)y�/+%�D�D�V�u�')N�|+!$.HN.)y�/+%�D�:�N�!{?HDG(+|+Dd0Su�%�.)/a.HN�|q|+DGNg/yz(3.H[ ��')(3/+%ÚN�.@w w7!$CEC7N�D<?HD1(}(3De')#&%Ú.H�g�3D1#G/+|�JD<QH.HN�* /+%�!E|cCE!$N�D)�,�')C�'WV�!$D1|��JD<QH.HN�*�/a%�!$|�C$!EN�DPw7!$CEC�N�D<?HDG(r%�De'd(�.H:�(�#G:�(+(3D1N~/PX>T |+!EF)N�')CE|G�}B�u�'d#1D1|3%�!Eu�|�yz(+.H[ ��')(�/a%U0/a(+'e?HD1C$!EN�F�|3CE.@w�D1(r/a%�')N CE!$FH%~/�w7!EC$C�'dCE|+. ��N�* /a%�Dq/+D1(+(3!$/+.H(3Qt�JD<QH.HN�*v/+%�!E|PC$!EN�Dc:�N�(3De')#&%�'d��CEDd��XL%�!$|(+DG*�|+%�!$y³/7!E|L|3:�(+u�(+!E|3!EN�F)C$QcCE.@w���2Í/7!E|L!$Ng/+D1(3D1|3/+!EN�Fr/+%�'d/Lw�D�#e')NY|+DGDo[c')N~Qq.)�A�3D1#</a|L/a.A*�'eQq/a%�'d/"')(+D�|3.yÅ')(7'ew�'@Q/+%�'d/Lw�D�#1')NYN�DG?)D1("FHDG/L/+.9/+%�D1[Y�

B�=�B�B �g:�')|+')(+|9!EN¦/+%�D8DG�g:�'d/a.)(+!�'dC>u�C�'dN�D�Æ �SÛ ����Û � Êr')(+D}|3%�.@w7NÌ')|�u�.H!EN~/a|P.):�/�/a.�'

(+DG*�|+%�!$y³/o.)y -ÑxÇ õ£Y:�|3!EN�F}(3D1*�|3%�!$y³/+|o*�DG/aDG(+[9!EN�DG*�yz(3.H[ /+%�DcB�=�B�B�|+:�(�?HDGQ�|3uJDG#G/a(+'��cK^.)(��A:�')|a')(3|w7!$/+% �ÚÇ  £Lw�D�%�'e?)D�|3%�.@w7Nr')C$C~�����g:�')|a'd(+|�yz(+.H[ /a%�D�B�=�B�B�w7!$/+% �ÚÇL(+DGF~')(3*�CEDG|+|�.)y�*�D1#GCE!EN�'d/a!$.HNU�XL%�DG(+D�')(3D�N�.@w�'�|+:�(3u�(+!$|+!EN�FHC$Q9C�'d(+FHD�NA:�[r�JDG(>.)yZ�g:�')|+')(+|>w7!{/a% �ÚÇ�]gN�.@w7NU��b�D1#1'):�|3D�'rNg:�[��JDG(.)y�/a%�DG|+Dt')(+D�'d/Y%�!$FH% *�D1#GCE!EN�'d/a!$.HNU0�/+%�DGQ .A#1#G:�(Y'd/Y(+!$FH%~/Y')|+#GD1N�|3!E.HN�|Y/a%�'W/Y')(+D�!ENÚ/a%�Dt�G.HN�DÒ.)y'e?H.H!$*�')N�#GD"yz.)(�/+%�D"D1�g:�'d/+.H(+!E')C�u�C�'dN�D)����')#&%\!E|�|+%�.@w7N'W/�!{/a|�u�(3.HuJDG(�(3!EFH%~/�')|3#1D1N�|+!E.)Nq')N�*c*�!E|�/&')N�#1D)0!EN�#1CE:�*�!EN�F9/a%�DPCE')(+F)D1|3/�(+D1*�|+%�!{y³/�.HN�D�w7!{/a% ÑÔÈ õ×gÛ�w7%�!E#&%Ò!E|SC�')��D1C$D1*vÆI6t�mBA/+(a'):�|+|oÛ)£H£)��0Uu�(3!$?d'd/aD#1.)[c[r:�N�!E#1'd/a!$.HN^Ê<�MXL%�!E|7!$|L#1:�(3(+D1N~/+C$Qq/+%�D�C�')(3FHD1|�/7(+D1*�|+%�!{y³/��g:�'d|a')(7]gN�.@w7NU�

XL%�D�F~')CE'WVAQ}B�=�Kv���e�~Ûd×��@¢�� �~Ø�ÛH¡A�e×gÇHÇow7!{/a%q/+%�D�C�')(3FHD1|�/"')#1#G:�(a'd/+D1C{Qq[9De')|3:�(+DG*8(3D1*�|3%�!$y³/�Æ �ÑÈ  ÇH¡)¢~Ê�!E|L')C$|+.P|3%�.@w7NU��XL%�!E|>w�')|7*�!E|3#1.@?HDG(+DG*8!$Nq/a%�DoB�:���')(+:Y=�DGD1uYK¸!EDGCE*ÒÆÅ��.�*�'d!E(a'�DG/7')CI�mÆIÛ)£H£H�~Ê3Ê<�

Page 27: A Map of the Universe - J Richard Gott, M Juric, et al

� ÛH¡ �

XL%�D8#1.d�Í[c.@?A!EN�F�*�!$|3/&'dN�#1D-'d/cw7%�!E#&%Ý/+%�D ��(+|3/\|3/a')(+|\')(+DYD<V�u�D1#G/+D1*Ì/+.tyz.H(3[ !E|9|+%�.@w7N ')|c'*�')|3%�D1*tCE!$N�D)�9XL%�D�s 6&����|+'d/aDGCECE!{/aDP%�'d|�yz.):�N�*t/+%�'d/�/a%�D ��(+|3/�|3/a')(+|�')u�u�De'd(�'d�J.H:�/rÛd£H£[c!$CECE!$.HNQHD1')(+|r'dy³/aDG(�/a%�Dqb�!$F�b>')N�F�')N�*t/a%�Dq[c')u�/a%�DG(+DGyz.)(+D\!$N�*�!$#e'd/+D1|�/a%�Dq*�!E|3/a')N�#GD\.H:�/�/a.Yw7%�!E#&%¦|�/&')(3|#1.):�CE*}��Do|3D1DGN-!EN}u�(3!EN�#G!Eu�C$D)�

K¸!$N�')CEC{Qc/+%�D1(3D�!$|7/+%�Do#1.H|3[c!$#o[9!E#G(+.@w�'@?)D���')#&]gFH(+.H:�N�*�(a'd*�!�'d/+!E.HN*�!E|+#G.@?HD1(3D1*��~QY�MDGN��1!E')|�'dN�*s !EC$|+.HN8!EN¦�eÉHÈ~Ç�ÆÅ�MD1N��1!�'d| '�s !$CE|3.HNvÆ��eÉHÈ~ÇHÊ3Ê<� Ä 68b�u�%�.)/a.)N�|Syz(+.)[ /+%�!E|S|+:�(�yÅ')#1DP'd(+(+!{?HDr*�!E(+DG#G/+C$Qyz(+.)[�')NYD1u�.�#&%Y.HN�C{Q�H¢)£�0 £)£H£�QHD1')(+|�'dy³/aDG(>/a%�Dob�!$F9b>')N�F��

�ÝC$!EN�D�|+%�.�w7!$N�FS/+%�D>#1.W��[9.�?A!$N�FS(+')*�!E:�|M��'d#&]�/a."/a%�D>b�!EFSb>')N�F�!$|�')C$|+.�|+%�.@w7NU��XL%�!E|¸(3D1u�(3D1|3D1N~/a||+DGD1!$N�F-��'d#&]�/+.Y/+%�D\DGuJ.A#&%Y�3:�|�/r'dy³/+D1(o!EN���'d/a!$.HNU�qXL%�Dc#1.d�Í[c.@?A!EN�FY*�!E|3/a')N�#GD\��DG/�w�D1D1N¦/+%�D\#G.H|+[9!E#[9!E#1(3.@w>'e?HD���')#&]gFH(3.H:�N�*�')N�*�/a%�D�b�!EF�b>')N�F�!E|Z|+%�.@w7NP!$N�#1.)(+(+DG#G/¸u�(+.Hu�.H(�/a!E.)No/+.�/a%�D�#1!$(+#G:�[9yzDG(+DGN�#1Dd�2�NP#1.)[cu�'d(+!EN�F"w7!{/a% ��F):�(+D��)0)w�D�N�.)/aD�/a%�'W/�!ENo/a%�'d/¸[\'du�/a%�D�#1!$(+#1:�[9yzDG(+D1N�#1D>!$|�'�yÅ')#</a.H(M.)y�ÕCE')(+FHDG(1�B�.�!EN.):�(L[\'duU0�w7%�!$#&%8|3%�.@w7|L/a%�Do�HÈH£ � #1!E(3#1:�[�yzD1(3D1N�#GD�.)y�/a%�D�#1.)|+[9!E#�[9!E#G(+.@w>'e?)Do��')#&]gFH(+.H:�N�*-'d|')u�u�(+.eV�!E[c'd/aDGC$Q�/a%�Dq|a')[9D\C$D1N�Fd/a% ')|o/a%�D\*�!�')[9DG/+D1(o.)yL/a%�Dq#1!$(+#1C$D\!$N ��FH:�(+D��H0M/a%�Dq|3#e')C$Dq'd/�/a%�'W/u�.H!EN~/�!E|�')�J.):�/�'9yÅ')#G/+.H(�.dy�Õ¦|+[c')C$CED1(L/+%�')N�!$N ��FH:�(+D\��')N�*-/+%�D�#G.H|+[9!E#o[9!E#1(3.@w>'e?HD���')#&]gFH(+.):�N�*')N�*}/a%�D�b�!EF�b>')N�Fc'd(+D�#1C$.H|+DG(7/+.�De')#&%Y.)/a%�D1(�ÆÅ�~Q}'PyÅ')#G/+.H(L.)yZÕZÊ�/a%�')N8!$N��FH:�(3D9�o')|7D�V�u�D1#</aDG*U�

Ë�')|3/�!E|�|3%�.@w7NÒ/+%�DP#1.W��[9.�?A!$N�F\yz:�/+:�(+D�?A!$|+!E��!ECE!{/�Q}CE!$[c!{/e�"2Íy�w�Drw�')!$/�:�Ng/+!ECZ/a%�Dr!$N ��N�!{/aD�yz:�/a:�(3Dw�DSw7!EC$C�D<?HDGNg/+:�')C$C$Q9�JD�')��CED7/a.�|+D1D�/a%�DSb�!EF�b>')N�FP'W/�/a%�DS#1.W��[9.�?A!$N�F�yz:�/+:�(+D"?A!E|+!$��!EC$!$/�QPC$!E[9!$/1�¸Bg/&')(3|')N�*tF~')CE'WV�!ED1|�/+%�'d/�CE!EDP��DGQ).HN�*�/+%�!E|o#1.W��[9.�?A!$N�Fyz:�/a:�(3Dc?A!E|3!E��!$CE!{/�Q-C$!E[9!$/�'d(+D�yz.H(+D<?HD1(�%�!E*�*�D1N�yz(+.H[.H:�(�?�!$DGw���b�D1#1'):�|+DY.)y7/a%�D*�DYB�!$/3/aDG(rD<V�u�')N�|+!E.)N u�(+.A*�:�#1DG*v�gQ�/a%�D#G.H|+[9.HCE.)FH!E#1')C�#1.HN�|�/&')N~/�/a%�D:�N�!{?HDG(+|+Do%�')|"')N}D<?HD1N~/S%�.H(+!$�1.HNw7%�!$#&%Yw�D�#e')N�N�.)/"|+DGD�.@?HDG(7N�.c[c'd/3/aD1(L%�.�w CE.HN�Frw�D�w>'d!$/e�

2Í/�!E|S(+D1[c')(3]d'd��CEDr%�.�w [c')N~Q�.)y�/a%�DryzDe'd/+:�(+DG|o|3%�.@w7Nt!$N�/a%�!$|�[\'du�%�'e?HD��JDGD1NÒ*�!$|+#1.@?)D1(+DG*�!$N/a%�D\#1:�(+(+DGN~/9')|3/+(+.HN�.)[c!$#e')C�FHDGN�D1(+'d/a!$.HNU�}s %�D1N .)N�D\.)y7:�|Æf�H >,�Ê��JDGF~')N¦|�/a:�*�!$N�F�'d|3/a(3.HN�.H[�Q�'W/')FHD-¢ÚÆÅ!$N �@ÉHÇHÇHÊ<0L.)NÚ')|3/+(+.HN�.H[c!$#e')CL[c')u�|9/a%�DG(+D-w�D1(3D�N�. ')(�/a! ��#1!E')CL|a'd/+D1C$CE!$/+D1|G0>N�. ��:�!$uJDG(\��D1C$/.H�A�3DG#G/+|10ZN�.8.d/a%�DG(�|3/&'d(+|�w7!$/+%�u�C�')N�D</a|G0ZN�.8��(3.@w7Nt*�w�')(�yz|10ZN�.}u�:�CE|+')(+|G0�N�.8��C�')#&]8%�.HCEDG|10�N�.}N�.HNA�|+.)C�')( ����(+'eQq|+.):�(+#GD1|10�N�.9FH')[c[c'�(+'eQq��:�(3|3/+D1(+|G0�N�.PFH(3De'd/>w�')C$CE|10�N�.�FH(+D1'd/7'd/3/a(+')#G/+.H(+|G0�N�.��g:�')|+')(+|G0N�.�FH(+'@?A!{/&'d/+!E.HN�'dC5CEDGN�|+DG|10�')N�*}N�.9.H��|3D1(�?)'W/a!E.)NY.dyM/+%�D�#1.H|3[c!$#�[c!$#1(+.@w�'e?HD���')#&]gFH(3.H:�N�*U�

��º i � ���IÃÅÂ��½�Ãz¿�¼ �XL%�!$|�[\'du-|+%�.�w7|�CE')(+F)D�|3#e')C$D�|3/+(+:�#</a:�(3Drw�DGCECI� �~K¸!$N�FHDG(+|S.dy�,�.A* �'d(+D�?)D1(�/a!E#1')C�w7%�!E#&%�[c')])DG|

(+DG[c.@?A!EN�Fc/a%�D1[ yz.H("C�')(3FHD�|3#e')C$D�|�/a(+:�#G/a:�(+Dru�:�(+u�.H|+DG|�u�')(�/a!E#G:�C�'d(+C$Q\De')|�QH��� /aDG|3/�yz.H(�(3.H:�N�*�N�D1|3|�.)y?H.)!E*�|L'd|>u�(+.)uJ.H|3D1*�~Q\ 7QA*�DGN�ÆÞ�@ÉHÉ~Ç)Ê � /+%�D��SC$#1.A#&]H�Þ�¸'d#1�GQAN�|3]g!m!E|+.d/a(+.)ugQ�/+D1|3/ � #1.H:�C$*q��D�*�.HN�DS.HN/a%�!E|"[\')u8')|"w�DGCECZ')|S.)N8/a%�D�#1.W��[9.�?A!$N�F�[\')u5�LXL%�Dr')��!ECE!{/�Q.)yM/a%�!$|"/+D1|3/�/a.c*�! �JD1(3D1N~/a!E'd/aDo�JD</�w�DGD1N#1.)|+[9.HCE.HF)!E#e'dC~[c.A*�D1C$|M#1')Nr��D�*�DG*�:�#GD1*��~Q�[9De')|3:�(+!$N�F�?).H!E*�!E|+.d/a(+.)ugQ�')|¸'�yz:�N�#</a!$.HNr.)y�#G.H|+[9.HC$.HFH!E#1')C[9.�*�DGC�!ENt/+%�D\u�C�')N�Dc.)yLu�'d(a')[9DG/+D1(+|qÆ � ��0 ��� Ê��-K�.H(�/a%�D\#1.)(+(+DG#G/�#1.H|3[c.HC$.HFH!$#e')C�[9.�*�D1C�/a%�D9?H.H!$*

Page 28: A Map of the Universe - J Richard Gott, M Juric, et al

� Û)¢ �

u�!$#G/a:�(+D1|�w7!EC$C���DS!$|+.)/+(+.Hu�!E#�ÆÅ|3!EN�#GD�/a%�D���')(3/+%q!E|�N�.)/�!ENq'o|+u�D1#G!�')C�uJ.)|+!$/+!E.HN9!EN9/a%�D�:�N�!{?HD1(3|+DeÊ<��XM.�*�./a%�!E|�/aDG|3/�w�D"N�DGD1*q#G.HN�yz.H(3[\')C�[\'du�|�yz.H(�?)'d(+!E.):�|�#1.H|3[c.)CE.HFH!$#e')C�[c.A*�DGCE|10H')N�*\|3.ow�D"N�D1DG*\#1.)N�yz.H(+[c')C[c')u�|qyz.H(/a%�D � Ñ Ør��'dN�* ��Ñ �o�t#1')|+DG|-')|w�D1C$C�')|/a%�D ��Ñ £ #1')|+DÒ|+.v/a%�'d/Y|3/&'W/a!E|�/a!$#e')C#1.)[cu�'d(+!E|3.HN�|L#1')N8��D�[c')*�D)��XL%�D�yz.H(3[r:�CE')|�yz.H(>/+%�D1|3D�u�(3.W�3D1#</a!$.HN�|"')(+D�FH!{?HDGNY!$N/a%�Do')u�u�D1N�*�!{VJ�

�¥K�.H:�(+!$D1(L'dN�')C$QA|3!E|L.)yMC�')(3FHD�|3#e')C$Do|�/a(3:�#G/+:�(+Do[c.A*�DG|L!EN/a%�D�[c')u�Æ����~Ï � � Ê�#1')N8u�(+.@?A!E*�D�!EN�yz.H(��[c'd/a!$.HN8.)N8/a%�D�u�')(+')[9DG/aDG(���Ñ � � � �� Ö ��w7%�D1(3D ��!E|7/a%�D���!�'d|�u�'d(a')[9DG/+D1(1�7K�.H(#��:�#</a:�'W/a!E.)N�|S!$N8/a%�DCE!$N�De'd(M(3D1FH!$[cD�!ENP(+DG*�|+%�!$y³/�|3u�')#1D �AÖ/� )�Æ���Ø����5R&ÊZw7%�DG(+D�8Ñ #G.H| ��w7%�DG(+D#��!E|Z/a%�D7'dN�FHCED��JD</�w�DGD1N/a%�D�N�.H(+[c')C^/a.r/+%�D�w>'e?)D�')N�*q/a%�D�C$!EN�D�.)yZ|+!EF)%g/>!EN}�H=xÆI��')!$|+DG(�Æ��eÉH¢~¡HÊ3Ê<�¸s�'e?HD1|7/&'dN�FHD1N~/+!�')C^/a.P/a%�DCE!$N�D".)ym|+!$FH%~/>%�'e?)D�'�C�'d(+FHDG(�')[9u�C$!$/a:�*�D7!ENq(3D1*�|3%�!$y³/�|+u�')#GDS/a%�')N\w�'@?)D1|Lu�'d(a')C$CED1C�/+.�/a%�D�CE!$N�D�.dym|+!$FH%~/��D1#e'd:�|+D7/a%�D7u�D1#G:�CE!E')(�?HDGCE.A#1!$/+!EDG|�!EN�*�:�#1DG*c�~QP/a%�D7w�'e?HD�D1N�%�'dN�#1D7/a%�D"')[9u�C$!$/a:�*�D>.)y�/a%�DLw�'e?HD�w7%�D1Nu�D1#1:�CE!�'d(L(a')*�!E')CJ?)D1C$.�#G!$/a!$D1|7')(3Do')*�*�DG*8/a.cO�:�����CED�u�.H|+!{/a!$.HN�|7')|7.A#1#1:�(+|7w7%�D1N8F~')C�'�V�!$D1|L'd(+Dou�CE.)/3/aDG*:�|3!EN�F8(+D1*�|+%�!{y³/r'd/�/+%�D\O":�����C$D ��.@w�u�.H|3!$/a!$.HN�|o')|3|+:�[9!EN�FYu�D1#1:�CE!�'d(�?HD1C$.�#G!$/+!ED1|o')(3Dc�GD1(3.��2�[\'dFH!EN�D'\|3D1(+!$D1|�.dy�w>'e?HDG|�!E|3.)/a(3.Hu�!E#o!EN��H=r�^XL%�D1NÒ.HN�D�#e')N�|3%�.@w�/a%�'d/�/a%�Dr'@?)D1(+')FHD�?d')C$:�D�.)y� R !EN��)=�.)y/a%�.H|+D�w�'@?)D1|"w7!$/a%}'dNY.)(+!EDGN~/&'d/+!E.HN�� ��Ñ #1.H|�ÆIÙ5Ê�!$Nq/a%�D�D1�g:�'W/a.H(3!�')CJ|+CE!$#1D�!$|���� R�� Ñ�ÆIÛHÖ)�~Ê�� � R ��XL%g:�|G0w�D�D<V�u�D1#</�')u�u�(+.eV�!E[c'd/aDGC$QH0�yz.H(Lw�'e?HD1|S.H��|+DG(3?)D1*�!EN8.H:�("D1�g:�'d/+.H(+!E')Cm|+C$!E#GD�� �AÖ/� ) ÆÞ�>Ø �õÛHÖd�%����� � R&Ê<�s�'@?)D1|�!EN9.H:�(�[\')u�w7!$/+%c#G.HN�|�/&')N~/�Æ����~Ï�� � Ê�(+D1u�(+D1|3D1N~/LFHC$.H��')C�CE.HF~'d(+!$/+%�[9!E#�|3u�!E(+')C�[9.�*�DG|�w7!{/a%9#1.HNA�|3/a')N~/�!EN�#1CE!$N�'d/+!E.HN}(+DGC�'d/+!$?)Do/+.\/a%�D�CE!EN�D�.)y�|3!EFH%~/1���Sy�#1.H:�(+|+Dr/+%�!E|�!E|�')N�.@?HDG(+|+!$[cu�CE! ��D1*8/+(+D1'd/a[9D1N~/e0|+!$N�#1D�w�D�[r:�|3/7#G.HN�|3!E*�DG(7/+%�D�u�.�w�D1(7|3uJDG#G/a(3:�[ .)y ��:�#</a:�'d/+!E.HN�|>w7%�D1NY(+DGC�'d/+!EN�F�/+%�D�[c.A*�DG|L|+D1DGN-'W/'�u�')(3/+!E#1:�C�')(�w�'@?)D1C$D1N�F)/+%}!EN�/a%�D�u�C�')N�D�')N�*\!ENq�)=�')N�*9/a%�D�� ��N�FHDG(+|�.dyZ,�.A* ��[r:�|3/��JD�D1C$!E[9!EN�'d/+D1*�~Q�|3.H[9Dcyz(+!$D1N�*A��.)y��fyz(+!EDGN�*t')CEFH.)(+!$/+%�[Y�}b�:�/r!$N�FHDGN�D1(+')Cf0Mw�DqD�V�uJDG#G/r/+%�'d/r[9.A*�D1|o/a%�'d/r')(+Dc(a')*�!�')CÆ����SÑ £~Ê�w7!EC$C^%�'e?HD�%�!$FH%�DG(�')[9u�C$!$/a:�*�D1|�/a%�'dNq[c.A*�DG|�/+%�'d/L'd(+D�/a')N�FHDGN~/a!�'dC¸Æ�� � Ñ £~Ê�')N�*\/+%�!E|�D��JD1#</#e'dNq�JD�:�|+DG*D1[9u�!E(3!E#1')CEC{QH0H!$N\#1.)NW�3:�N�#</a!E.)Ncw7!$/+%q`L����.�*�Q9|3!E[r:�CE'd/a!$.HN�|G0H/a.�u�(+.@?A!E*�DS')Nq!EN�*�D1u�D1N�*�D1N~/#&%�DG#&]Ý.HNÝ/+%�D8?d')C$:�D-.dy���� ��N�D�|3!E[9u�C$Q ')*�.Hu�/+|q'�#G.H|+[9.HC$.HFH!E#1')CL[9.�*�DGCf0�#&%�D1#&]g|w7!$/+%Ì`7�Í�J.A*�Q|+!$[r:�CE'd/a!$.HN�|�/+%�D�(+DGC�'d/+!$?)D�')[cu�CE!$/+:�*�D�.)yZ[\')u}[9.�*�D1|L')|"'�yz:�N�#G/a!$.HN}.)y�� � !ENq/+%�D�CE.HFH')(+!{/a%�[9!E#"[\'du')N�*�#1.)[cu�'d(+D1|�w7!{/a%�/a%�D9.)��|+DG(3?d'd/a!$.HN�|o')|3|+:�[9!EN�Fq/+%�D�|a')[9DP#1.)|+[9.HCE.HF)!E#e'dC¸[9.�*�DGCMw7%�DGN�u�C$.)/+/+!EN�F/a%�D\CE.)F~')(+!{/a%�[9!E#�[\')u5·r!$y�/a%�Dc#1.H|3[c.HC$.HFH!$#e')C�[9.A*�D1C�Æ � ��Ï ��� Ê�!E|o#1.)(+(+DG#G/10¸/a%�Dc(+DG|+:�C{/a|�|3%�.H:�C$*¦��D|+!$[c!$C�')(G�

B�!$N�#1D�CE.)F~')(+!{/a%�[9!E#o|+u�!E(a'dCE|�')u�u�De'd(�'d|o|�/a(+')!EFH%~/oCE!$N�D1|�!$NÒ.H:�(�[\'du�u�(+.W�3DG#G/a!$.HNU0�!$/�[c'eQ�u�(3.�?)D:�|3DGyz:�C¸yz.)(�[\'du�u�!EN�F\|+u�!E(a'dC¸F~')CE'WV�!EDG|1��XM')])D�'qu�%�.)/a.HF)(a')u�%�.dy�'\yÅ'd#1D<�Í.HN�|+u�!E(a'dCMF~'dC�'WVAQH05u�C�')#GD�/a%�D.H(3!EFH!$N�.)y�/a%�D>#G.�.)(+*�!$N�'d/aD�|3QA|�/aD1[¥!EN�/a%�D�#1D1N~/+D1(�.)y�/+%�D�FH')C�'WVAQo')N�*�/a%�DGNP#1.HN�|3/a(3:�#G/�.H:�(¸C$.HF~')(3!$/+%�[c!$#[c')uc.dy5/a%�!E|�Û)= u�C�')N�')(�u�%�.)/+.HFH(a'du�%U��XL%�D"|+u�!E(a'dC^')(+[9|�Æzw7%�!$#&%q')u�u�(+.eV�!E[c'd/aDLC$.HF~')(3!$/a%�[c!$#�|+u�!E(a'dCE|&Ê|+%�.H:�CE*/+%�D1N8')u�u�De')("')|L|�/a(+')!EFH%~/7C$!EN�DG|L.HN/a%�D�#1.)N�yz.H(+[c')CJ[\')u5��s�D�%�'e?HD�/a(3!EDG*}/+%�!E|L.)N8'ryÅ')#GD<�Í.HN|+u�!E(a'dC5F~')CE'WVAQqu�%�.)/a.HF)(a')u�%F)!$?HDGN/a.�:�|7�~Q}�H')[9D1|7 7%�.~')*�|7')N�*/a%�D�(3D1|+:�C$/a|>w�D1(3D�?HD1(�Q}|a'd/+!E|�y³Q�!$N�F��XL%�D�|+u�!E(a'dC�')(3[c|�!$N�*�D1DG*�w�DG(+D��JD1'):�/+!$yz:�C�|�/a(+')!EFH%~/�C$!EN�DG|10m'dN�*�yz(+.H[ /a%�DG!E(�|3CE.Hu�DP.HN�DP#G.H:�CE*ÒD1')|+!$C$Q[9De')|3:�(+D\/+%�D1!$(r!EN�#1CE!$N�'d/+!E.HNt')N�FHC$D)�ÒBg/&')(r!$[\'dFHD1|�!EN�/+%�Dqu�!$#G/a:�(+D\w�D1(3DY|�/a!$CEC�#1!$(+#1:�C�')(�!EN�/+%�D[\'du��D1#e'd:�|+D�/a%�D�[c')u}!E|L#G.HN�yz.H(3[\')CI�

Page 29: A Map of the Universe - J Richard Gott, M Juric, et al

� Û)É �

�Uº p ¿�¼M �ÅÁ �eÃÅ¿�¼ �6-')u�|"#1')N}#&%�')N�F)D�/+%�D�w�'@Q\w�D�CE.A.H]c'd/>/+%�D�w�.H(3CE*U��6YD1(+#1'd/a.)(1��|"[c')uu�(3D1|3D1N~/aDG*-!EN��@Ç)ÈHÉ�w�')|

!EN���:�D1N~/+!�')C�N�.)/�.HN�C{Q���D1#e'd:�|+Dq!{/�w>')|�'8u�(3.W�3D1#</a!$.HNt/+%�'d/�|+%�.@w�D1*¦/a%�D\|+%�')uJDG|�.)y�#1.HN~/+!EN�DGNg/+|�w�D1CEC��:�/��JDG#e'):�|+D�yz.)(�/+%�D���(3|3/�/a!$[cDLw�D�%�')*cu�(+D</+/�Qc')#1#G:�(a'W/aDS#G.HN~/a.H:�(+|�yz.)(�`".H(3/+% �S[9D1(3!E#1'�')N�*}B�.H:�/+%�S[9D1(3!E#1'\/a.|+%�.�w���XL%�D Ä .H|+[9!E#�TS!EDGw ')N�*Ò/+%�D��M.@w�D1(3|S.)yMXMDGN ')CEDG(3/aDG*ÒuJDG.Hu�CED�/a.q/a%�D9|3#e')C$D1|�!$N/a%�DP:�N�!$?)D1(3|+DPw�DP%�')*Ò�JDGFH:�N�/a.:�N�*�D1(3|3/&'dN�*U�P=�DPË�')u�u�')(+DGN~/e0Z,�D1CEC$D1(G0U')N�*�O":�#&%�(a'|3%�.@w�DG*t%�.@w'�|+C$!E#1D.dy"/+%�D}:�N�!{?HD1(3|+DY#1.H:�CE*vFH!$?)D:�|9')NvD1N�C$!EFH%~/+D1N�!$N�F�?A!EDGw .)y"/a%�D}:�N�!$?HDG(+|3DY!$Nv*�D1u�/+%U�v`�.@w/a%�'d/�')|3/+(+.HN�.)[cDG(+|7%�'e?HD�')(+(3!$?)D1*8'd/�'�N�DGw :�N�*�D1(3|3/&'dN�*�!EN�F\.)yZ/a%�Do.)yZ/a%�D�:�N�!$?HDG(+|3D�yz(+.)[ /a%�D�|3.HC�')(|3QA|�/aD1[�/+./a%�D�#1.)|+[9!E#r[9!E#G(+.@w>'e?)D9��')#&]gFH(+.H:�N�*U0mw�D9%�.Hu�DP.H:�(�[c')u�w7!$CEC¸u�(+.@?A!E*�D�!EN�|3.H[9DP|+[c')CECw�'@QY'PN�D<w�?A!E|3:�')CUu�D1(3|+u�D1#G/+!$?)D�.HN}/a%�D1|+DoD<V�#G!$/a!$N�FP*�!$|+#1.@?)D1(+!$D1|G�

XL%�D7[c')u�u�(+DG|+D1N~/+D1*q%�DG(+D7!E|�'du�u�(+.)u�(+!E'd/aD>yz.H(¸:�|+D�')|�'�w>')C$C�[c')uU�¸2Í/1�õ|�|3#e')C$DL!E|�')u�u�(+.eV�!E[c'd/aDGC$Q��!EN�#&%�d(a')*�!�')NU� �Ô?HDG(+|+!$.HNt'd/�/�w7!E#GD�/+%�DP|+#1')CEDd0���Û�� Ç)Èq!EN�#&%�D1|��~Q�É~Ç�� Û\!EN�#&%�DG|�/&')C$CMw�.H:�CE*�')C$|+.}��D')u�u�(+.Hu�(3!�'d/+D9yz.)(�'8w�')C$C�#&%�'d(3/P'dN�*�w�.H:�CE*�(+:�N¦N�De')(3C$QÒyz(+.H[ ��.�.H(�/a.-#1D1!$CE!$N�F8!$N¦'-N�.H(+[c')C�(+.A.H[w7!$/+%�'dNt¢Wy³/�#GD1!$CE!EN�F��r2Íy>.)N�DPw>')N~/+D1*�/+.Y|3%�.@w�!EN�*�!$?A!E*�:�')C�.H�g�3D1#G/+|�'W/oÈH£ ��|+#1')CEDd0Z/+%�Dc68.A.HN�'dN�*B�:�Ncw�.H:�CE*\��Do�S!EN�#&%q')#G(+.H|3|10�68����w�.H:�C$*\��D�×�!EN�#&%�DG|>')#G(+.H|3|10�')N�*68')(+|�w�.H:�CE*\��D�£�� £��e×gÇ�!EN�#&%�DG|!EN8*�!�'d[cD</aD1(�')N�*��):�u�!$/+D1(S£�� £HÛH¡HÛ9!$N�#&%�DG|1� ��C$/+D1(+N�'d/aDGC$Q/a%�D�B�:�N�'dN�*Ò68.A.HN�')N�*Ò68D1|3|+!$D1(�.H�g�3D1#G/+|#1.):�CE*o�JD�|+%�.�w7N�'�È)£ ��|+#e'dCED�w7!$/+%o/+%�D�u�C�')N�D</a|Z'd/¸ÈH£H£ ��|3#e')C$D�/a."!ECEC$:�|3/+(a'd/+D¸/a%�D1!E(�:�|3:�')CA')u�u�De'd(a')N�#GD!EN}|3[\')C$CJ/+D1CEDG|+#G.HuJDG|1�

Ä .HN�|3!E*�DG(c|3.H[9D8u�.H|+|3!E��C$D¦ÆÅ')N�*Ü|+.H[9DyÅ')N�#1!{yz:�C³Ê�w�'eQ�|9/a%�!$|c[c')u .)y�/+%�D8:�N�!$?)D1(+|3D-[9!EFH%~/9��Du�(3D1|+DGN~/aD1*8yz.H(LD1*�:�#e'd/+!E.HN�'dCU:�|+Dd�

stD�%�'e?HD�u�(+DG|+D1N~/+D1*�/a%�D�[\')u8.HN8/+%�Dr!$Ng/+D1(3N�DG/S!EN-#G.HCE.)(".)N�')|3/+(+.d�Íu�%U�"2�N�u�(3!EN�#G!Eu�C$Do!{/�w�.H:�C$*��DSDe'd|3Q�/a.�%�'e?HD�|3:�#&%}'�[c')u\.)Nc/a%�DS!EN~/+D1(+N�DG/L'd:�/a.H[c'd/+!E#e'dCEC$Q�#1.)Ng/+!ENg:�.H:�|+C$Q�:�uJ*�'W/aD1*c/a.�/+(a')#&]�/a%�D#1:�(+(+DGN~/7uJ.H|3!$/+!E.HN�|�.)y�/a%�DS|a'd/+D1CEC$!$/+D1|10�68.A.HNU0^BA:�NU0�')|�/aDG(+.H!$*�|10�u�C�')N�DG/a|G0�')N�*8��:�!$uJDG(���D1C{/>.H�A�3DG#G/+|�'d|'�yz:�N�#</a!$.HN.)yZ/a!E[9D)0A!ENqyÅ'd#G/>w�D�%�'e?HD�u�CE.d/+/aDG*q/a%�DG[�')|L.dy¸'Pu�'d(3/a!$#1:�CE')(�*�'d/aD�'dN�*/a!E[9DS:�|+!EN�FP|+:�#&%u�(3.HFH(a'd[c|G�8`"DGwx.H�A�3DG#G/+|r#1.H:�CE*���Dq'd*�*�D1*¦/+.8/+%�D\[c')u¦'d|�/a%�DGQ�w�DG(+Dq*�!$|+#G.�?)D1(3D1*U� Ä C$!E#&]�.HN¦')N.H�A�3DG#G/105')N�*-'9ÈH£WVYDGN�C�')(3FHD1*}?A!ED<w .)y�!{/Lw�.):�CE*8')u�u�De')(G�>X>w�.\#1C$!E#&]g|10�')N�*-'c�HÈH£H£WVD1N�CE')(+FHDG*Y?A!$DGww�.H:�CE*¦')u�u�De')(G0�')N�*¦|3.-yz.H(�/a% � :�N~/a!EC�/a%�D\%�!$FH%�D1|�/r(3D1|+.)CE:�/+!E.HNtu�!E#</a:�(3Dq'e?d')!ECE')��CEDPw�')|ru�(3D1|3D1N~/aDG*U�2�N�*�!{?A!E*�:�'dC�!$[\'dFHD1|�.)yZ')C$C�/a%�D�B�=�B�BcF~')CE'WV�!EDG|�'dN�*q�g:�')|+')(+|>|3%�.@w7N}.HN\/a%�DS[c')u\#G.H:�CE*\�JDS')#1#GD1|+|3D1*!EN/+%�!E|Lw�'@Q)0�')|"w�D1C$C�')|�6 .)�A�3D1#</a|���s %�DGN�')NY!EN�*�!$?A!E*�:�')CU.H�g�3D1#G/"w�')|7|+D1C$D1#</aD1*50J%�DGCEu�yz:�Cm!EN~/aDG(+N�D</CE!$N�]g|>/a.�|+!{/aDG|7/+D1C$CE!EN�Fr[c.)(+D�')��.H:�/7!{/Lw�.H:�CE*Y')u�u�De')(G�

B�!$N�#1D>/+%�D7CEDGy³/�')N�*�(+!$FH%~/�%�')N�*�DG*�FHD1|�.)y^/+%�D7[\')u�'d(+DL!E*�D1N~/a!$#e')CI0d/a%�D"[c')uP#G.H:�CE*P��DLu�(3. ��/&'d��C$Q|+%�.�w7N ')|�'-#GQAC$!EN�*�DG(1�82�N #GQACE!$N�*�(+!$#e')C�yz.)(+[Y0M/a%�Dq[\'du¦'d/�/a%�D'du�u�(+.eV�!E[c'd/+Dc|3#e')C$Dq')N�* *�DG/&'d!EC�.)y��FH:�(+D�¡o!E|�!EN\u�D1(�yzD1#</Lu�(+.)uJ.H(�/a!$.HN9/+.���DS:�|3D1*.HNq'�uJDGN�#1!$C�w7!$/a%c/a%�DS��'d(3/a%5�õ|>|3:�(3yÅ'd#1D�'W/�/a%�DSD1(+')|+DG(D1N�*q')N�*P/+%�DSb�!EF�b>')N�F�'d/�/+%�D"uJ.H!$N~/�D1N�*U���MD1(3%�')u�|�/a%�D7��D1|�/�#<QACE!EN�*�(+!$#e')C�yz.)(+[ yz.)(�/+%�D7[\'du�w�.H:�C$*��D�'�#<Q�C$!EN�*�D1(�.HN�/a%�D7!$Ng/+D1(3!E.H(�.dyU')N9D1C$DG?d'd/+.H(�|+%�'Wy³/�yz.H(�'oF)C�')|3|�D1CED<?d'd/a.H(G����?HDG(3Q��.A.H(�Q).H:cw�D1N~/�:�u

Page 30: A Map of the Universe - J Richard Gott, M Juric, et al

� �H£ �

QH.):cw�.H:�CE*9��D�C$.�.H]g!$N�F�'d/�.H�A�3DG#G/a|�/a%�'d/�w�D1(3D��e£�/+!E[9D1|�yz:�(�/a%�DG(�'ew�'@Q�/+%�')N�/a%�D"u�(+DG#1DG*�!EN�F ��.A.H(1� �/a(3!Eu�:�u9|+:�#&%\')N9D1CED<?d'd/a.H(�|3%�'dy³/�#G.H:�CE*9��D"|3!E[r:�C�'d/+D1*P!EN9'�u�CE')N�DG/a')(+!$:�[�|3%�.@w�0Aw7!{/a%P/a%�D"#<QACE!EN�*�(+!$#e')C[c')u}�JDG!EN�F�u�(3.W�3D1#</aD1*Y.HN~/a.�/a%�Do*�.H[cD�|3%�.@w7!EN�F�/a%�D�?A!$DGw yz(3.H[ /+%�D�D1C$DG?d'd/a.)(7')|7!$/L(3.H|+Dd�

stDY%�'@?)D-u�:�/c.):�(�[\')uv:�u .HNÜ��(+!EN�#1DG/+.HNU��| ��'d/�?�!$*�D1.�w�')CECI�vXL%�!E|Pw�')CECL%�'d|c'Ò%�.H(3!E�G.HN~/&')C(+DG|+.HC$:�/a!$.HN}.)yM×~£HÉHÈPu�! V�DGCE|G��K�(3.H[ /+.HuY/+.��J.)/3/a.H[ .)yM/+%�D�?A!E*�DG.9w�')CEC5!E|"')��.H:�/��@ÈH£)£�u�!{V�D1C$|10�|3.c/a%�D|+#1')CEDc#&%�')N�F)Dq!EN�/+%�Dq[c')utyz(3.H[ /a.Hut/a.���.)/+/+.H[ !E|�')�J.):�/P'8yÅ'd#G/a.)(�.)y��@£��-XL%�!$|�|+%�.�w7|�'8|+[c')CECu�.H(3/+!E.HN}.)yZ/a%�DoD1N~/+!E(+D�[c')uU��s�D�/+%�D1N8|+#e'dN8/a%�!E|L!ENY(+D1')CU/a!$[cD�[9.@?A!EN�F�|3/+De')*�!EC$Q\:�u~w>'d(+*-yz(3.H[ /a%�D��')(3/+%q/a.r/+%�D�#1.)|+[9!E#S[9!E#G(+.@w�'@?)D���')#&]gFH(3.H:�N�*Y')N�*q/+%�D�b�!$FPb>')N�F���XL%�!E|�u�(+.A*�:�#GD1|"'�?A!E(�/a:�')CJ[\'du��¡��õÈPyzD1DG/7w7!$*�Do')N�*��e�)×PyzD1DG/"/&'dCECf��s !{/a%}C�'d|+D1(7��De')[9|7!$/Lw�.H:�C$*8��D�D1')|3Q/+.cu�')!EN~/"'�C�')(3FHD�?HDG(+|+!$.HN.)y7/a%�D[\')u .)Nv/+%�D|+!$*�Dq.)yS'���:�!$CE*�!$N�F�� ��?)D1(3Q¦C�')(3FHD\/aDG[cu�.H(+')(3Q�?HDG(+|+!$.HNv.)y".H:�(P[c')u¦.)y"/a%�D:�N�!{?HDG(+|+D�#G.H:�C$*')CE|3.���D�|+D</L:�u!$N'�u�')(3]�.H(L'd/>'�|3/a')(�u�'d(3/�Qc�gQ\|+!$[cu�C{Q�u�C�'dNg/+!EN�F�[\'d(+])DG(+|�yz.)(�/a%�D|a'dCE!EDGN~/7.H�A�3D1#</a|G�

XL%�Dr[c')u�#G.H:�C$*��JD�u�(+.A*�:�#GD1*�.HNÒ'c#e')(3uJD</�ÈcyzDGDG/�w7!$*�D�×gÇA�ðÇ9yzDGDG/�C$.HN�F9yz.H(�'\%�')CEC{w>'eQ}!EN�')N')|�/a(+.)N�.H[�QY*�DGu�')(3/+[cDGN~/�.H(Su�C�')N�D</&')(3!E:�[Y�7XL%�D1N�D<?HDG(3Q�|�/aD1u�Q).H:�/a.A.H]}*�.@w7N�/a%�D�%�')C$C$w�'eQYw�.H:�C$*/&'d])DcQ).H:¦'d�J.H:�/r'}yÅ')#G/+.H(�.)y7')��.H:�/�/aDGNtyz:�(�/a%�DG(�yz(3.H[ /a%�Dq��')(3/+% � 'YN�!$#1D�w>'eQÒ/a.8%�'e?HD\'Yw�')CE]/a%�(+.H:�F)%Y/+%�D ��N�!{?HD1(3|+Dd�

stD�w�.H:�C$*8C$!E]dD�/a.P/a%�'dN�]}68!$#&%�')D1CZBg/a(a'd:�|+|7yz.H(L|+:�u�u�C$QA!$N�F�:�|Lw7!$/a%}/a%�DoC$!E|�/L.)y�B�=�B�B�A:�')|a')(3|w7!$/+%}(+D1*�|+%�!{y³/�F)(+De'W/aD1(>/+%�')N-Ç��

XL%�!$|7w�.H(3]\w>'d|�|3:�u�u�.H(3/+D1*Y�gQ8�H >,���|"`�B�K FH(+')N~/���B�X7£)×d��£HÈ~¡��e���K�:�N�*�!$N�F8yz.)(�/a%�D\#1(3De'd/+!E.HN¦')N�*¦*�!$|3/+(+!E��:�/a!$.HNt.dyL/a%�DqB�=�B�B ��(+#&%�!{?HDq%�'d|r�JDGD1N u�(3.@?�!$*�D1*��gQ

/a%�D �SC{yz(+DG*Ì�M��B�C$.~')NÜK^.):�N�*�'d/+!E.HN50�/a%�D��¸'d(3/a!$#1!$u�'d/a!$N�F�2�N�|3/+!$/a:�/a!E.)N�|10�/+%�D�`�'d/a!$.HN�')C ��D1(3.HN�'):�/+!E#G|')N�* B�u�')#GD �S*�[9!EN�!E|3/+(a'd/+!E.HN50�/+%�Dq`�'d/a!$.HN�')C�B�#G!EDGN�#1DK�.H:�N�*�'d/+!E.HNU0Z/a%�D ��� BJ��=�DGu�')(�/a[9D1N~/�.dy"��NA�D1(3F)QH0�/a%�D\�H'du�')N�DG|+D\68.HNg��:�]W')F~'d]A:�|+%�.�0¸')N�*Ò/a%�Dc6-'�V���C�')N�#&]�BA.�#G!EDG/�Q)��XL%�DqB�=�B�B-s�DG��|+!{/aDP!$|%~/+/+uU· WwLwLw��õ|3*�|+|G�õ.)(+F ��

XL%�DcB�=�B�B-!$|�[c')N�')FHDG*��~Q-/a%�D�S|3/+(+.Hu�%gQA|3!E#e'dC� "DG|+De'd(+#&% Ä .HN�|+.)(3/a!$:�[ Æ��� Ä Ê�yz.H(S/a%�D��¸')(Þ�/a!$#1!$u�'d/a!$N�F�2�N�|�/a!$/+:�/a!$.HN�|G��XL%�D��¸')(�/a!E#G!Eu�'W/a!EN�F�2�N�|3/+!$/a:�/a!E.)N�|�')(+D"XL%�D���N�!{?HD1(3|+!{/�Q�.)y Ä %�!$#e')F).�0AK^DG(+[9!{�C�'d�U0�/+%�Dr2�N�|�/a!{/a:�/+D�yz.H( ��*�?d')N�#GD1*tBA/a:�*�QH05/+%�D��H')u�')NÒ�¸')(�/a!$#1!Eu�'d/a!$.HN�,�(+.):�uU05XL%�D��).H%�N�|�O".Hu�]g!EN�|��N�!$?HDG(+|3!$/�QH0�/+%�D���.H(3De')N-B�#G!ED1N~/+!E|3/S,�(+.H:�uU0^Ëm.H|���C�')[9.H|L`�'d/a!$.HN�')CUËZ'd�J.H(+'d/a.)(3QH0�/+%�D�6-'WVg�Þ��C�'dN�#&]H�2�N�|�/a!$/+:�/aDcyz.H( �S|�/a(3.HN�.H[�QÌÆf68��2 ��Ê<0¸/+%�D}6-'�VA����C�')N�#&]H�Í2�N�|3/+!$/a:�/aD\yz.H( �S|3/+(+.Hu�%gQA|3!E#1|YÆI6-� ��Ê<0�`"DGw68D�V�!$#1.8BA/a'd/aD��"N�!$?)D1(3|+!$/�Q)0 ��N�!{?HDG(+|+!{/�Q�.)y���!{/+/a|3��:�(3FH%U0���(+!$N�#1D</a.HN �"N�!$?)D1(+|3!$/�Q)0U/a%�D��"N�!$/+D1*�BA/a'd/aDG|`S'e?d')C ����|3D1(3?d'd/+.H(3Q)0^')N�*}/a%�D �"N�!$?)D1(+|3!$/�Q.dyMs�')|+%�!EN�F)/+.HNU�

Page 31: A Map of the Universe - J Richard Gott, M Juric, et al

� ��� �

i º �9Ñ�Ør��� �9Ñ £ �¼ZÀ ��Ñ ��� Â���'���SC{/a%�.):�FH%Ò/a%�Dc.H��|+DG(3?d'd/+!E.HN�|o|+:�FHFHD1|�/�/+%�D��tÑ�£8#1')|+Dc!E|o')u�u�(3.Hu�(3!�'d/+D�yz.)(o/+%�Dc:�N�!$?)D1(+|3D)0¸yz.)(

[c'd/a%�DG[\'W/a!E#1')C�#1.H[9u�CED</aDGN�D1|3|"w�D�#1.HN�|3!E*�DG(L/a%�D�FHDGN�D1(+')C�K�(+!EDG*�[c')N�N[9DG/a(3!E#G|1·

�� R Ñ � �� R Ø�� R Æ � Ê�� �� R Øv|+!$N R � Æ � R Ø |3!EN R �� Ù R Ê �fÏ �9Ñ�Ør�HÏ Æ����@Ê �� R Ñ � �� R Ø�� R Æ � Ê�� �� R Ø � R Æ � R Ø |3!EN R �� Ù R Ê �IÏ �9Ñ £�Ï Æ���Û)Ê �� R Ñ � �� R Ø�� R Æ � Ê�� �� R Øv|+!$N�% R � Æ � R Ø |3!EN R � Ù R Ê �IÏ ��Ñ �o� Æ����HÊ

=�D ��N�D�/a%�D�#1.)N�yz.H(+[c')C5/+!E[9D��~Q�·

05Æ � Ê�Ñ 3 �� ��� Ñ 3 � # �&%

� Æ � ��� R Ø ¢dÕ� � h ' ����Æ ��ÊmØ ���WÆ �AÊ ( Ø � � � h Ê +�4+*ÍR � Æ��S×~Ê

2ÍyZw�D�')(+D�#G:�(+(3D1N~/aC{Q}'d/L/+%�D�D1u�.�#&% � �@0�/a%�D1N}/a%�D�#1:�(+(+DGN~/S#G.HN�yz.H(3[\')C�/a!$[cD�!$| 0UÆ � ��Ê<��s %�D1N8w�D�CE.A.H]��')#&]Y/a.'c(+D1*�|+%�!{y³/ \w�Dr')(+Dr|3D1DG!EN�F}')N-D1u�.�#&%�w7%�DGN ���&Ö2��Æ � Ê7Ñ �LØ �0m')N�*�.H:�/S/a.q'\#1.d�Í[c.@?A!EN�F*�!$|3/&'dN�#1D � FH!{?HDGNY�~Q�·

� Æ ~Ê�Ñ 0UÆ � �<Ê � 05Æ � Ê�Ñ 3 �$# � � %����� ���� �

Æ � ��� R Ø ¢dÕ� � h ' ����Æ �AÊmØ����@Æ �AÊ ( Ø � � � h Ê +�4+*ÍR � Æ���Ç)Ê

�S|9w�D-%�'e?HD-N�.)/aDG*U0L!EN /a%�D �^'d/c#e')|3D � Ñ £�0>w�D�')(3D8yz(+DGDY/+. ')*�.)u�/q'�|+#1')CED}yz.H( �^0L|3.�w�D-|+D</��Æ � �<Ê�Ñ �� � �K�.H(S/+%�D ��Ñ�Ør�P#e')|3D)0Z'q/�w�.}*�!$[cDGN�|+!$.HN�')CM|+CE!$#1D�/+%�(+.):�FH%�/a%�D9:�N�!$?)D1(+|3D�!E|�'|+u�%�D1(3D)��B�.w�D

N�DGD1*v/a.�[\')]dD}'�#1.HN�yz.)(+[c')C>u�(3.W�3D1#</a!E.)N .dy�/+%�D}|+u�%�DG(+DY.HN~/a.�'�u�C�'dN�D)0�')N�* /a%�D1Nvw�DY#e')N ')u�u�C$Q.H:�(�#1.HN�yz.)(+[c')CJC$.HF~')(3!$/+%�[c!$#Lu�(+.��3D1#G/+!E.HN}'d|L�JD<yz.H(+DS/+.Pu�(+.A*�:�#GD�.H:�(�[\')u5��XL%�D�|3/+D1(+DG.HFH(+')u�%�!$#�[\'duu�(3.W�3D1#</a!E.)N�!E|�|3:�#&%v'8#G.HN�yz.H(3[\')C�u�(+.W�3DG#G/a!$.HN�.dyL'8|3u�%�DG(+Dq.HN~/+.�'8u�C�')N�Dd� �S*�.Hu�/�#1.A.H(+*�!$N�'d/+D1|o.HN/a%�Do|3u�%�DG(+Do.)y � 0 �A0�w7%�D1(3D�/+%�D�[cD</a(3!E#�.HN/a%�Do|3u�%�DG(+Do!E|7FH!$?)D1N}�~Q�·

�� R Ñ � R Æ � �<ÊGÆ �� R Øv|+!$N R � � R Ê Æ���ÈHÊ

s %�DG(+D�/+%�D�')N�FHC$D���!E|�N�.@w '�CE.HN�F)!$/a:�*�D�ÆÅXL%g:�|10��o!$|�D1�g:�!$?d')C$D1N~/�/a.PÙq!$N\[9DG/a(3!E# ��Û�')��.@?HD � w7%�D1(3D!EN�[9DG/+(+!$#��Û\w�D9')(3DP#1.HN�|+!E*�D1(+!$N�F/a%�D�DG�A:�'d/a.H(3!�')CM|+C$!E#1Drw7!{/a% �qÑ !$#&% � � UÑ�ÕZÖHÛ���BA.}/+.}FHDG/�/a%�D[9DG/a(3!E#o')��.@?HD�yz(3.H[ [9DG/a(3!E# ��ÛPw�D�|+D</��PÑ !$#&% � � �Ñ ÕZÖHÛ�0�')N�*-(+D1u�C�')#GDrÙ�w7!$/+% �HÊ��7`�.@w�[c')])D�'|3/+D1(3D1.HFH(+')u�%�!$#�#1.HN�yz.)(+[c')C5u�(3.W�3D1#</a!$.HN8.dyM/+%�!E|L|3u�%�D1(3DqÆ � Ï �HÊ�.HN~/+.\'Pu�CE')N�D�w7!$/+%}uJ.HCE')(>#G.�.H(3*�!EN�'d/aDG|Æ� �Ï �)Ê<·

Ñ Û/�JÆ � ��Ê�/&'dN�Æ � Û Ê Æ���¡)Ê� Ñ � Æ���¢HÊ

Page 32: A Map of the Universe - J Richard Gott, M Juric, et al

� �~Û �

XL%�!$|"!$|7'Pu�(+.W�3DG#G/+!E.HN}yz(+.H[x/a%�D�N�.)(3/a%Yu�.HCED�.)Ng/+.\'Pu�CE')N�D�/a')N�FHDGNg/7/+.�/+%�D�|+.H:�/a%-u�.HC$D)��XL%�D���')(3/+%w�.H:�CE*-�JD�'d/�/+%�D�|3.H:�/+%�uJ.HC$D�.)y�/a%�D�|+u�%�D1(+DÆzw7%�DG(+D � Ñ¥£~Ê����¥CE!$N�D�yz(+.H[�/+%�DrN�.H(�/a%8uJ.HC$Do/+.\/a%�Du�CE')N�DL/a%�(3.H:�FH%�/a%�D"u�.H!$Ng/�Æ � Ï �HÊ�.HN�/a%�D7|3u�%�D1(3D�w7!$CEC���D"'d/�')N9')N�FHC$D��ÒÑ � Ö)Û�(3D1CE'd/a!{?HD>/a.�'�N�.H(+[c')C/a.P/+%�D�u�C�')N�D)0^')N�*Y')C$|+.9'd/"')N8')N�F)CED �ÒÑ � ÖHÛr(+DGC�'d/+!$?)D�/a.9'9N�.H(+[c')CJ/+.9/+%�D�|+:�(�yÅ')#1D�.)yZ/a%�Do|3u�%�DG(+D'd/o/a%�D9u�.H!EN~/qÆ � Ï �HÊ�0M/+%A:�|�/a%�D9yz.H(3D1|3%�.H(3/+D1N�!$N�F8/+%�'d/�.�#G#1:�(3|r')C$.HN�F}/a%�Dc(a'eQ�yz(+.)[�/a%�DcN�.H(3/+%�u�.HCED')|�!$/"#1(3.H|+|3D1|S/+%�D�|3:�(3yÅ')#GD�.)y¸/a%�D�|+u�%�DG(+Dr!$|�D�V�')#G/+C$Q}/a%�D�|a')[9D�')|�/+%�D�yz.H(3D1|3%�.H(3/+D1N�!$N�Fc/+%�'d/�.�#G#1:�(3|w7%�DGN !{/r#G(+.H|3|+D1|P/+%�Dq|+:�(3yÅ')#GD.)y7/a%�Dqu�C�')N�Dd�ÒXL%A:�|10�|+%�'duJDG|P!EN¦/a%�Dq|+:�(�yÅ')#1D}'d(+DqC$.�#1')CEC{Q�[\'du�uJDG*w7!$/+%�.H:�/7*�!E|3/+.H(3/+!E.HNC$.�#1')CEC{Q9.HN~/a.P/a%�D�u�CE')N�Dd��XL%�D�[c')u}!E|L#G.HN�yz.H(3[\'dCf��`".@w w�D�%�'e?)D�'P#1.)N�yz.H(+[c')C[c')uÒ.)y�/+%�D9|+u�%�DG(+Dc')N�*Òw�Dc')u�u�C$Q�.):�(�CE.HF~'d(+!$/+%�[9!E#o#1.HN�yz.)(+[c')C�[c')u�/a./a%�D9u�CE')N�')(�[c')u�/a.YFHD</.H:�(L[c')u}.)yZ/a%�D�:�N�!$?HDG(+|3D)·

Î Ñ ��� Æ���ÉHÊÐ Ñ CEN

� Ñ CEN Û2��Æ � �<Ê�/a')NmÆ�� R Ê �� Æ ���@£HÊ

XL%�!$|�u�(+.@?A!E*�D1|�'S#G.HN�yz.H(3[\')CA[c')u�u�!$N�F�yz(3.H[�Æ � Ï �HÊm/a.9ÆzÎ�Ï+Ð�Ê��M2Í/�!$|¸!$N�yÅ')#G/�'�68D1(3#e'd/+.H(�u�(3.W�3D1#</a!E.)Nr.)y/a%�Do|3u�%�DG(+!E#1')CU|3D1#G/+!E.HNY.)y�/a%�Do:�N�!$?)D1(+|3D�w7!$/a%/+%�Do��'d(3/a%}C$.�#1'd/aDG*8'W/>/a%�D�|3.H:�/a%Yu�.HCED�.dyM/+%�D�|+u�%�D1(+D �stDq')(3D\:�|3D1*¦/a.-|+D1DG!EN�F8/a%�Dq68D1(3#e'd/+.H(ru�(3.W�3D1#</a!E.)N�yz.H(�/a%�Dc|+:�(�yÅ')#1Dq.dyL/a%�D\��'d(3/a%�#1:�/�.$�Ì'W/�/a%�D�SN~/a')(+#</a!E#S#1!E(3#1C$D)0�|3.Pw�D�*�.PN�.)/L|+DGD�/a%�'d/>!$y�!$/�w�DG(+D�D<VA/+D1N�*�DG*8[�:�#&%}N�De')(3D1(>/+.r/a%�D�|3.H:�/a%u�.HC$D�ÆÅ!$N/a%�D9C$!E[9!$/�')| � � £~ÊS!$/Sw�.H:�CE*�')u�u�(3.eV�!$[\'W/aDr.H:�(�CE.HF~'d(+!$/+%�[9!E#�[\'du�.)y>'u�CE')N�Dr!$N�/a%�DP(3D1FH!$.HN�.)y/a%�D�|3.H:�/a%8uJ.)CED)��ÆzXL%�!E|"u�(+.��3D1#G/+!E.HN}w�.H:�CE*Y��D�:�|3DGyz:�Cmyz.H(7#G.H|+[9.HCE.)FH!E#1')C5[9.�*�D1CE|>/+%�'d/7w�D1(+D�|+C$!EFH%~/aC{Q#1C$.H|+DG*U� Ê

K�.H(�/a%�D ��Ñ �o��#1')|+Dd0�'�Û)= |+C$!E#1DL.dy5/a%�D":�N�!$?)D1(+|3DS!$|�'oN�DGF~'d/+!$?HDGC$QP#G:�(3?)D1*qu�|+D1:�*�.H|+u�%�D1(3D�w7!$/+%[9DG/a(3!E#d· �� R Ñ4� R Æ � �<ÊGÆ �� R Øv|+!$N�% R � Æ � R Ê3Ê<Ï �9Ñ ��� Æ ���H�@Ês %�DG(+D � !E|>/+%�D�#1.d�Í[c.@?A!EN�FP(a')*�!$:�|10�')N�*Y')|7�JD<yz.H(+D�w�D�%�'e?HDo|+DG/��oÑ4!$# % �'� �Ñ ÕZÖHÛA0�!EN}[9DG/a(3!E#��S�')��.@?HD�/a.YCE.A.H]�'d/�')N�D1�g:�'d/+.H(+!E')C�|+C$!E#GD)0Z')N�*Òw�Dc%�'e?HDc(+D1u�C�')#GD1*�Ù !$Nt[9DG/+(+!$#���w7!$/a% ��0M|+.}/a%�'W/��!E|"N�.@w¥'cCE.)N�FH!$/+:�*�Dd��stD�#e'dN-#1.)N�yz.H(+[c')C$C$Qqu�(+.W�3DG#G/S/+%�D�u�|+D1:�*�.H|+u�%�D1(3Dr.HN~/a.cu�C�')N�Dow7!{/a%�'9[\'duu�(3.W�3D1#</a!E.)N�/a%�'W/r!E|�')N ')N�')CE.HF):�Dc.dyL/a%�Dq|�/aDG(+D1.)FH(a')u�%�!E#cu�(+.W�3DG#G/+!E.HN�yz.)(�/a%�Dq|+u�%�D1(+Dd��XL%�Dq[9DG/+(+!E#')��.@?HD�yz.H(7'�u�|+DG:�*�.H|3u�%�D1(3D�.)yM(a'd*�!E:�| ��Æ � �<Ê�!E|L/a%�D�[9DG/+(+!E#S.HNY/+%�D�%~Q�u�D1(3�J.)CE.H!$*|+:�(�yÅ')#1Dd·

Î R Ø Ð R � � R Ñ � � R Æ � �<Ê Æ ����Û)Êw7%�DG(+D � �Ì£�!EN}'P/a%�(+D1D�*�!$[cDGN�|+!$.HN�')CU68!EN�]).@w7|+]g!Z|+u�')#GD�w7!$/a%}[9DG/+(+!E#d· �� R Ñ � �� R Ø Î R Ø Ð R Æ ���@�HÊ*�D���N�Do#1.A.H(+*�!$N�'d/+D1|L.HN/a%�!E|7|+:�(�yÅ')#1DcÆ � Ï�HÊ��~Q� Ñ ��Æ � ��Ê�#1.H|3% � Æ ���e×~Ê

Ð Ñ ��Æ � ��Ê�|+!$N�% � |+!$N#� Æ ����Ç)ÊÎ Ñ ��Æ � ��Ê�|+!$N�% � #1.)| � Æ ���@ÈHÊ

Page 33: A Map of the Universe - J Richard Gott, M Juric, et al

� �H� �

w7!$/+%�/a%�D�*�D���N�!{/a!E.)N�|m')��.@?HD�!$/U!E|UD1')|3Q�/+.L|+DGD�/+%�'d/mÎ^R<Ø�ÐAR � � RLÑ � �~RdÆ � ��Ê�0W|3!EN�#GD(�~RWÆ � ��Ê�|3!EN�% R � #1.H|3R �)Ø� R Æ � ��Ê�|3!EN�% R � |+!$N R � � � R Æ � �<Ê�#G.H|+% R � Ñ � � R Æ � �<Ê<� Ä .)N�N�D1#</LDe'd#&%uJ.H!$N~/�Æ � Ï�HÊ�.HN\/a%�DS|+:�(3yÅ')#GD�w7!$/+%/a%�Dr.H(+!$FH!ENtƳÎ�ÏaÐJÏ � ÊLÑ ÆÅ£�Ï&£�Ï&£HÊL?A!�'\'c|3/+(a')!$FH%~/Sw�.H(+C$*�CE!$N�D)�"XL%�!$|�w�.H(+C$*�CE!$N�D�%�')|�'c?)D1C$.�#G!$/�QY(+DGC�'d/+!$?HD/a.q/+%�D � 'WV�!E|�.)y �YÑÔ|+!$N�% � Ö�#1.H|3% � Ñ /a')N�% � �rB�.q/+%�!E|�w�.H(3CE*�C$!EN�D�%�')|�'q��.�.H|�/�.)y � (+D1CE'd/a!{?HD�/+./a%�D � 'WV�!E|1�cXL%�!E|�w�.H(+C$*�CE!$N�DP!E|�N�.)(+[c')C¸/a.}/a%�Dc|3:�(3yÅ')#GD\'W/o/+%�D9uJ.H!$N~/cÆ � Ï �HÊ�0M��D1#1'):�|3D9/+%�'d/o�J.A.H|�//&'d])D1|>/+%�D � 'WV�!E|�/a.�/+%�D�w�.)(+CE*�CE!EN�D�!$Nq�g:�D1|�/a!E.)N}')N�*CED1'e?HD1|>/+%�D�%~QAuJDG(+��.HCE!$#�|+:�(3yÅ')#GD�!EN~?d')(+!E')N~/e��ËmD<//a%�Dq!EN~/aDG(+|3D1#G/+!E.HN .dyL/a%�'d/�w�.H(3CE*�C$!EN�D�w7!$/+%¦/a%�Dc/&')N�F)D1N~/Pu�CE')N�D � Ñ ��Æ � �&Ê��JDc/a%�DqF)N�.H[9.HN�!E#c[\'duu�(3.W�3D1#</a!E.)NY.dyM/+%�D�uJ.H!$N~/�Æ � Ï �HÊ>.HN~/+.�/+%�D�u�C�'dN�D�w7!$/+%Yu�.HCE')(>#1.A.H(3*�!EN�'W/aD1|oÆ �Ï �HÊ���XL%�D1N

Ñ ��Æ � �<Ê�/a')N�% � Æ ����¡)Ê� Ñ � Æ ���@¢HÊ

XL%�!$|�FHN�.H[c.)N�!E#Lu�(3.W�3D1#</a!$.HNc[c')u�|�/a%�D�u�|3D1:�*�.H|+u�%�D1(+D�£ � � � � !EN~/a.�'�*�!E|3]P.)yU(+')*�!E:�| oÑ ��Æ � �<Ê<�s %~Q � b�DG#e'):�|+D�!EN�'\/+!E[9D � Ñ ��Æ � �<Ê"/a%�Drw�.H(3CE*�C$!EN�Dow7%�!E#&%Ò%�')|�'\?HD1C$.�#G!$/�Q �}Ñ /&')N�% � /a(+'e?HD1C$|�'*�!$|3/&'dN�#1DP.)y \Ñ � � Ñ ��Æ � �<Ê�/&')N�% � ��XL%�!E|�FHN�.H[c.)N�!E#�u�(+.W�3DG#G/+!E.HNÒ!E|SN�.)/�#1.)N�yz.H(+[c')CI0J��D1#1'):�|+D�/a%�Dw�.H(+C$*�CE!$N�D�!E|"N�.H(+[c')Cm/a.9/a%�D�%~Q�u�D1(3�J.)CE.H!$*-|+:�(3yÅ')#GD���:�/SN�.)/SN�.H(+[c')CU/+.\/a%�D�u�C�'dN�D � Ñ���Æ � �<Ê<�"XL%�!$|FHN�.)[c.HN�!E#�u�(+.W�3DG#G/a!$.HNP[c')u�|�FHDG.�*�D1|+!$#1|�.HNP/+%�DLN�D1FH'd/a!{?HD1C{Q�#G:�(3?)D1*9%~Q�u�D1(3�J.)CE.H!$*P.HN~/a.�|3/+(a')!$FH%~/�CE!$N�D1|.HN�/+%�D\u�C�')N�D � Ñ �JÆ � �<Êo��D1#1'):�|+Dq')N~Qtu�C�')N�Dc!EN�/a%�Dc|+u�')#GDÒÆzÎ�Ï+ÐJÏ � Ê�u�')|3|+!$N�F-/a%�(+.H:�F)%�/a%�Dc.H(+!$FH!EN!EN~/+D1(+|3D1#</a|�/+%�D�|3:�(3yÅ'd#1D�!$N-'9FHD1.A*�DG|+!E#�')N�*Y/a%�!$|7u�C�')N�Dow7!$CECm!EN~/+D1(+|3D1#</S/a%�Do/a')N�FHDGNg/�u�CE')N�D � Ñ���Æ � �<Ê!ENY'P|3/+(a')!$FH%~/7CE!$N�D)�

��#1.)N�yz.H(+[c')CMu�(+.W�3DG#G/+!E.HNU05CE!E]dD�/a%�DP|3/aDG(+DG.HFH(a'du�%�!E#Pu�(+.W�3DG#G/a!$.HNÒ.)y�/a%�DP|3u�%�DG(+D�!E|�u�(+.@?A!E*�DG*Òyz.)(/a%�DYu�|+D1:�*�.H|+u�%�D1(3D-�~Q #1.)N�N�D1#</a!$N�F�w7!$/a% '�w�.H(+C$*�CE!$N�DqDe'd#&%Üu�.H!EN~/�.HN /+%�D}|+:�(�yÅ')#1DtÆ � Ï �)Ê<0�/a.�/a%�Du�.H!EN~/\ÆzÎ�ÏaÐ�Ï � Ê�Ñ�ÆÅ£�Ï&£�Ï � ��Æ � �&Ê+Ê<0M')N�*tCED</+/a!$N�F/a%�!$|�w�.H(3CE*�C$!EN�DP!$N~/aD1(3|+DG#G/�/+%�D9u�C�')N�D � Ñ ��Æ � ��Ê�'d/�'u�.H!EN~/rÆ� �Ï �HÊ���`�.@w�/a%�'d/Sw�.H(+C$*�CE!$N�Do%�')|�'c?)D1C$.�#G!$/�Q��Ñ�|+!EN�% � Ö�Æz#1.H|3% � Ø ��ÊLÑ�/a')N�%ZÆ � ÖHÛ)Ê�Æz:�|+!$N�F'\%�'dC$y�')N�F)CED�/+(+!$FH.HN�.H[9DG/+(+!$#o!$*�D1N~/+!$/�Q�Ê<��XL%g:�|G0U/a%�!$|Sw�.)(+CE*�CE!EN�D�%�'d|�'\��.�.H|�/�(+DGC�'d/+!$?)D�/a.c/a%�D � 'WV�!$|.)y � ÖHÛc')N�*-/+%�D1(3DGyz.H(3Dr'c��.A.H|3/S.)y � ÖHÛ9(3D1CE'd/a!{?HD�/a.\/+%�D�N�.)(+[c')Cm/a.c/+%�D�u�C�')N�D � Ñ ��Æ � ��Ê��"s %�D1N�!$/!EN~/+D1(+|3D1#</a|L/a%�D�%~QAu�D1(+��.HC$!E#�|3:�(3yÅ')#GD�'d/L/a%�D�uJ.H!$N~/�Æ � Ï �)Ê<0�/+%�D�N�.H(3[\'dCJ/a.r/+%�D�%~QAuJDG(+��.HCE!$#�|+:�(�yÅ')#1D�'W//a%�'d/Lu�.H!EN~/L%�'d|7'r�J.A.H|3/>.)y � (3D1C�'W/a!$?)DS/a.r/+%�D � 'WV�!E|>!$Nq/a%�D�|+')[9D�u�C�')N�D)��XL%g:�|G0^/+%�D�w�.H(+C$*�CE!$N�DS%�'d|'\��.�.)|3/�.)y � ÖHÛ9(3D1C�'W/a!$?)Do/+.\/a%�D�N�.H(3[\'dCZ.dy�/a%�Do/&')N�F)D1N~/�u�CE')N�D�')N�*�')C$|+.\'c��.�.H|�/�.)y � Ö)Ûc(+DGC�'d/+!$?HD/a.�/a%�DS%~QAuJDG(+��.HCE!$#"|3:�(3yÅ'd#1D)0A|+.�!$/�%�')|�')N9D1�g:�')C���.�.H|�/SÆI')N�*c.H��|3D1(3?)D1|>DG�g:�')CJË�.)(+D1N~/+��#G.HN~/a(a'd#G/a!$.HN�|aÊ(+DGC�'d/+!$?)Dc/a.���.)/+% ÆÅFH!{?A!EN�F8!E*�DGNg/+!E#1')C�yz.)(+D1|3%�.H(�/aD1N�!EN�FH|r')|r!ENt/a%�D|�/aD1(3D1.HF)(a')u�%�!E#qu�(3.W�3D1#</a!$.HN¦.)y7/a%�D|+u�%�D1(3D@Ê7')N�*}/a%�DG(+DGyz.)(+D�/a%�D�[c')u}u�(+.��3D1#G/+!E.HNY!E|L#G.HN�yz.H(3[\'dCf��XL%�!$|Lw�.H(3CE*�C$!EN�DS#1.HN�N�D1#G/+!EN�F�/a%�Dou�.H!$Ng/ÆzÎ�Ï+ÐJÏ � Ê7Ñ ÆÅ£�Ï&£�Ï�� ��Æ � ��Ê3Ê�/a.q/+%�DPuJ.)!EN~/�Æ � Ï�HÊ�.HN�/+%�Dr|+:�(3yÅ')#GD�/+%g:�|�!EN~/aDG(+|3D1#G/+|�/a%�Dr/a')N�FHDGNg/�u�C�')N�D� Ñ ��Æ � �<ÊL'd/L/a%�Dou�.H!$Ng/�Æ �Ï �HÊ�FH!{?HDGN8�~Q

Ñ Û2��Æ � �<Ê�/a')N�%�Æ � Û Ê Æ ���@ÉHÊ� Ñ � Æ ��Û)£HÊ

XL%�!$|r[\'du�|�/+%�Du�|+DG:�*�.H|3u�%�DG(+DY£ � �� � !EN~/a.�'�*�!E|3]�.dy�(+')*�!$:�| �Ñ Û2��Æ � �&Ê<�Ò`�.@wxw�D%�'@?)D

Page 34: A Map of the Universe - J Richard Gott, M Juric, et al

� �)× �

'8#G.HN�yz.H(3[\'dC�[\'du�u�(3.W�3D1#</a!E.)Nt.)y�/a%�D9N�D1FH'd/a!{?HD1C{QÒ#1:�(�?HDG*���Ñ �o�\:�N�!$?)D1(+|3D\.HN~/+.�'8u�C�')N�Dd�qXL%�!$|#1.)N�yz.H(+[c')C>[c')u !E|r/+%�D8.)N�D8!$CEC$:�|3/+(a'd/+D1* !EN ��|+#&%�D1(1��|\yÅ')[9.H:�|9')N�FHD1C$|c'dN�*Ü*�DG?A!EC$|9u�(+!EN~/�w7%�!$#&%Ü!$|.)y³/+D1N9:�|+DG*9/+.�!$CECE:�|3/a(+'d/aD�/a%�!$|�#1.H|3[c.HC$.HF)QqÆÅ#<yÞ��,�.d/+/�ÆfÛd£H£���Ê3Ê<�M`�D<VA/�w�D7/&'d])DL/a%�!$|�#1.HN�yz.H(+[c')C�u�CE')N�')([c')u�Æ WÏ�HÊ�'dN�*}')u�u�C{Q�.H:�(�#1.HN�yz.)(+[c')C^CE.HF~'d(+!$/+%�[9!E#L[c')u�u�!$N�Foyz:�N�#G/+!E.HN\/+.�!{/e��XL%g:�|G0�w�DSu�(+.A*�:�#GD�'#1.)N�yz.H(+[c')CU[c')u.)yZ/a%�Do:�N�!$?)D1(+|3Dow7!{/a%Y#1.A.H(+*�!EN�'d/+D1|G·

Î Ñ � � Æ ��Û��@ÊÐ Ñ CEN Û2��Æ � �<Ê�/&')N�%UÆ � ÖHÛHÊ �� Æ ��ÛHÛ)Ê

`�.d/aD�/a%�D9|+!$[c!$C�')(3!$/�Q}w7!$/+%�/+%�D9yz.)(+[r:�CE'qyz.H(o'Y|3u�%�D1(3!E#1')C �tÑ�Ør�9:�N�!{?HD1(3|+D ��!ENÒ/a%�D �tÑ ���c#e')|3D��/a')N�% ��|+!$[cu�C$Qc(+D1u�C�')#GD1| ��/&'dN ���

stDr#e')N�[c')]dDr[\'du�|Syz.H(S')CEC�/a%�(3D1Dr#1')|+DG|1��XL%�DG|+D9')(+D�:�|+D<yz:�C¸yz.H(�#1.H[9u�')(3!E|+.)N-u�:�(3uJ.)|+D1|G��K�.H(D<V�')[9u�C$D�|+:�u�uJ.H|3Dow�D�*�DG?)D1C$.HuY')N}!E|+.d/a(+.)ugQ\[cD1')|+:�(+D�yz.H(�?).H!E*�|7')|L|+:�F)FHD1|�/aD1*8�~Q}b>')(3��')(a'P LQA*�D1N5�stDc#G.H:�CE*�')u�u�C$Q�/+%�!E|�/+.Y/+%�DP?H.H!$*�|�.HNt.):�(�#1.HN�yz.)(+[c')C�:�N�!{?HDG(+|+Dc[\'du�|3!EN�#GDc!{/�u�(+DG|+DG(3?HDG|r|+%�')uJDG|CE.A#e'dCEC$Qo'dN�*P/a%�DL?H.)!E*�|�')(3DL|+[c')CECI�MXL%�D"|3%�')u�D1|�.)y^/a%�D7?).H!E*�|�*�D1u�D1N�*9.HNP/a%�D�'d|+|+:�[cDG*9#G.H|+[9.HC$.HFH!E#1')C[9.�*�DGCf�MXL%�!E|�!E|�/a%�D �SC$#1.A#&] � �¸')#G�GQAN�|3]A!J/aD1|�/e��2ÍyUw�DS%�'@?)D�/+%�DS(3!EFH%~/�#1.H|3[c.)CE.HFH!$#e')C�[c.A*�D1C�/+%�D�?).H!E*�|w7!EC$C��JD\')u�u�(3.eV�!$[\'W/aD1C{Q�(+.):�N�* ')|�|+:�F)FHD1|�/aD1* �~Qt LQ�*�D1NU0�'dN�*�/a%�!E|o#e')N¦��Dc/+D1|�/aD1*5��B�:�u�uJ.)|+D)0�'d|s 6&�S��|3:�FHFHDG|3/+|10M/+%�D��^'d/ �tÑ £}#e'd|+D9!E|o#1.H(3(+D1#</�w7!{/a% � �vØ ��� Ñ �H0MXL%�D1Ntw�D\#1')N�u�CE.)/�/a%�D|a'd[cD�(+D1*�|+%�!{y³/�*�'d/a'\��:�/�#G.HN�yz.H(3[\'dCEC$Q')|+|3:�[c!$N�Fq|3CE!EF)%g/+C$Q}#GCE.H|3D1* � ��Ø ��� �Ô�H0 �YÑÔØr�r[9.�*�D1CE|.H(7|+C$!EFH%~/+C$Qq.)uJDGN � ��Ø ���

��H0 �qÑ"�o��[9.A*�D1C$|�'dN�*8#&%�D1#&]Y!E|+.d/a(+.)ugQq.)y¸/+%�Do?).H!E*�|�!$N8D1')#&%-#1')|+Dd�

stD�#e')N/a%g:�|7#&%�DG#&]q%�.@w�|3D1N�|3!$/+!$?HD�/+%�D�!E|3.)/a(3.Hu~Q\/+D1|3/7!$|>!ENC$!E[9!$/+!EN�F�/a%�D�CE.A#e'd/+!E.HNq.dyZ/+%�D�[9.�*�DGC5!$N/a%�D\Æ � �SÏ ��� Ê>u�')(+')[cD</aDG(Lu�C�')N�D)�

j º k ¿�Á�¾WÂ� �2�NY')u�u�C{QA!EN�F�/+%�D�CE.)F~')(+!{/a%�[9!E#L[c')uq/+.r/a%�D�u�(3.H��C$D1[x.)y�|+%�.@w7!$N�FP/a%�D �"N�!$?)D1(+|3D)0�w�D�%�'e?HD�:�|3D1*

'r[r:�C{/a!{/a:�*�D".)y���.)/a%.)N�CE!$N�D�|3.H:�(3#1D1|G0�uJDG(+|3.HN�')CJ#1.H[9[r:�N�!$#e'd/+!E.HN\')N�*q*�'d/&'ru�:���CE!$|+%�DG*!ENo�3.H:�(+N�')C$|1�XZ.9!$CEC$:�|3/+(a'd/+DS/a%�D�w�De'dC$/a%8')N�*?d')(3!EDG/�Qq.)yZ*�'d/&'P*�DGu�!E#</aDG*8!$N}/+%�D�6-')uU0�w�D�%�'e?HDo#&%�.H|3D1N8/+.�CE!E|�/>/a%�D|+.):�(+#GD1|"!EN/a%�!$|L|+DG#G/a!$.HNU�

�68.A.HN}u�%�'d|+D�"N�!$/+D1*8BA/&'W/aD1|"`�'@?d')C ����|3D1(�?)'W/a.H(�Q �S|�/a(+.)N�.H[9!E#e'dC �SC$[\')N�')#)0UÆ���B�`�� ��CE[c')N�')#�ÆIÛ)£H£H�HÊ+ÊƸ%~/+/+uU· )'H'���:�|3N�.���N�'e?AQ)�õ[9!EC d*�'d/a' d*�.A#1| H68.A.HN���%�')|3D)��%~/a[9CZÊ

���')(�/a%YFHD1.HC$.HFH!$#e')C�*�'d/a'��CECEDGNU��| �S|3/+(+.Hu�%gQA|3!E#e'dC ��:�'dNg/+!$/+!ED1|�Æ Ä .eV�ÆfÛ)£)£H£~Ê+Ê

Page 35: A Map of the Universe - J Richard Gott, M Juric, et al

� �~Ç �

���(3/a! ��#1!E')C5|+'d/aDGCEC$!$/aDG|68!$])Dr68# Ä ')N~/+|1��B�'W/aD1C$CE!{/aD�XM(+')#&]g!EN�Fcw�DG��u�')FHD1|rÆI')C$CE*�'W/e� /aCED ��CED@Ê��SXL%�D���CEDo!EN�#GCE:�*�D1|S.)(+��!{/&')CDGCED1[9D1N~/+|\|+:�u�u�CE!$D1*Ì�~Q ��2�, ÆÅ`���B � H,oB�K Ä ��(3��!$/a')C72�N�yz.H(3[\'d/+!E.HNÝ,�(+.H:�u�Êc')N�*Ý*�'d/&'t.HN.)/+%�D1(7|+'d/aDGCECE!{/aDG|>.H��/a')!EN�DG*}u�(+!$[\')(3!EC{Q��gQY'd[\'d/+D1:�(�?�!$|+:�'dCm.H��|+DG(3?d'd/+!E.HN�|G�Ƹ%~/+/+uU· d.H!$F��H��FH|3yz#d�õN�'d|a'���FH.@? 9ÊƸ%~/+/+uU· d:�|3D1(+|aÛ���DG?��H��N�DG/ ��e[9[c#G#e')N~/a| W/aC$D1| d!EN�*�D<VJ�õ%~/+[cC¸Ê

�O":�����C$D�BAu�')#1D�XZD1C$D1|+#G.Hu�DoC$.�#1'd/a!$.HN��C�')N �¸'W/+/aDG(+|3.HN '�=�'e?A!ENvst.H(+]g[c')N�ÆIB�#1!$D1N�#GD-'dN�*Ì6Y!E|+|3!E.HNÝB�#&%�DG*�:�C$!EN�Ftb�(a'dN�#&%U0 ��u�D1(Þ�'d/+!E.HN�|q')N�* =�'d/a' 6-')N�')FHD1[9D1N~/Y=�!{?�!$|+!$.HNU0"B�u�'d#1D�XZD1CEDG|+#G.HuJD�BA#1!EDGN�#1D�2�N�|3/a!{/a:�/+D@Ê�0Su�(3!$?d'd/aD#G.H[c[�:�N�!E#1'd/a!$.HN

�Ä %�'dN�*�(a' ���Í(a'eQ ����|3D1(3?d'd/+.H(3QqCE.A#e'd/+!E.HN 7.H� Ä ')[9D1(+.)N�Æ Ä ����B�#1!$D1N�#GD ��u�D1(+'d/a!$.HN�|LXZDe')[\Ê<0�u�(+!{?)'W/aD�#1.)[c[r:�N�!E#1'd/a!$.HN

���|3/aDG(+.H!$*}#e'd/a')CE.HFËm.@w�DGCEC�����|3D1(�?)'W/a.H(�Q��S|�/aDG(+.H!$*�=�'W/&')��'d|+D7Æ ��B�X �� "bLÊ<0WÛ)£)£H� )£)× ��@É�|3N�')u�|3%�.)/10Ww7!{/a%�D1u�%�D1[9D1(3!E|#1')CE#G:�C�'d/+D1*yz.H( ��:�F}��Û�0^Û)£)£H�y³/+uU· Wy³/auU��CE.@w�D1C$Cf��D1*�:Wu�:��dDGCEFH��)')|3/+.H(+�5�õ%~/a[9C

�68!$N�.H(L��.�*�!ED1|G��D1u�%�D1[9D1(3!E|��u�%�DG[cDG(+!$|"#G.H[9u�:�/aDG*}:�|+!$N�F\'dN8'd*�')u�/+D1*}?HD1(3|+!$.HN8.dyM/+%�D ��(3��K¸!{/7|+.)y³/�w�')(+D�u�'d#&]d'dFHD)���(+��K¸!$/�!E|�w7(3!$/3/aD1N��gQt/a%�D ��(3��K¸!{/r#1.)N�|+.H(�/a!$:�[8·9=�DGu�/e��.)y�68'd/a%�DG[\'W/a!E#G|10 �"N�!$?���.)y"��!E|+'Æ �SN�*�(3De'�68!$C�')N�!f0~Bg/aDG?)D1Nc o� Ä %�D1|3CED<Q�Ê�0 �S|�/a(+.)N�.H[9!E#e'dC ����|3D1(3?d'd/+.H(3Q�.)yJb�(+DG(a'�0~68!ECE')N}Æf68')(+!$.Ä ')(3u�!EN�.gÊ<0 ��|3/a(3.HN�.H[9!E#1')C�����|+D1(�?d'd/a.H(�QH0�b�D1C$FH(a'd*�DÒÆ��5.)(a')N ��N�D���1D<?�!<;#@Ê�0 Ä `� 2�N�|3/+!$/+:�/aD\yz.)(B�u�')#1D �S|�/a(3.Hu�%~QA|+!E#G|10J ".)[cD�ÆI,�!$.@?)'dN�N�!mbS��T�'dCE|+DG#1#&%�!�Ê<�Ƹ%~/+/+uU· dN�D<wL/a.HNU��*�[Y�õ:�N�!Eu�!I�õ!{/ ��1N�D1.A*�QA| )'d|3/a!$N�yz. d.)(+� ��/ PÊ

���:�').H')(7')N�*8B�DG*�N�'c!$N�yz.H(3[\'d/+!E.HNƸ%~/+/+uU· WwLwLw���FHu�|1��#e'dC$/aDG#&%U��D1*�:��e#&%�')*tÊ

�Ä .H[9DG/10^B�:�N50�68.�.)N-')N�*8u�CE')N�D</7D1u�%�DG[cDG(+!$|,�D1N�DG(a'd/+D1*:�|3!EN�FP�H��Ë�O��� 72�����`�B ��N��ÍCE!EN�D�B�.)C�')(�BAQA|3/+D1[ =�'d/a'�')N�*}��u�%�D1[9D1(3!E| Ä .H[9u�:��/a'd/a!$.HNYB�D1(�?A!E#1Dd�Ƹ%~/+/+uU· d|+|3*U� �3u�Cf��N�')|+'��õF).�? d%�.H(+!$�1.HN�|G�õ%~/+[cCMÊ

�B�u�')#1D�u�(3.H�JDG|T�.@Q~'dFHD1(}�H0�T�.@Q~')F)D1(cÛ�0���!$.HN�DGD1(�@£�0 �"C$QA|+|3D1|9uJ.H|3!$/+!E.HN�|�.H��/&'d!EN�DG*¦yz(+.H[ `���B � O"D1C$.)s�DG�w�D1��u�')FHD�'d/"`�B�B�= Ä ÆI`�'d/a!$.HN�')CUB�u�')#GDrBA#1!EDGN�#1Do=�'d/a' Ä D1N~/aDG(&ÊƸ%~/+/+uU· dN�|3|+*�#d�õFH|�yz#)��N�')|+'��õF).�? d|3u�')#GD d%�DGCE!$.H| d%�D1CE!I�õ%~/+[cCMÊ

Page 36: A Map of the Universe - J Richard Gott, M Juric, et al

� �HÈ �

�O"D1CE!$.Hu�'):�|+D=�!$|3/&'dN�#1DL/&'d])D1N9/a.o�JD"')u�u�(+.eV�!E[c'd/aDGC$Q\�H�@£ � � !$N9/+%�D7*�!E(3D1#</a!E.)N9.dym')u�u�(+.eV�!E[c'd/aDGC$Qq�e¢)%\ #���

���.H(�/ Ä CE.H:�*XM')])DGN8/+.9D�VA/aD1N�*8yz(+.)[�¢�0õ£H£H£� ��/a.}�@£H£�0 £H£)£�� �

��@£P��(3!EFH%~/+D1|3/"|�/&')(3|B�.):�(+#GD�yz.H(>u�.H|+!{/a!E.)N�|�'dN�*}u�')(a'dCEC�'�V�DG|1·�B�2�6-b��S= 7DGyzDG(+D1N�#1D�*�'d/a')��')|3D)0 Ä DGNg/+(+D�*�D�=�.)N�N�D1DG|')|�/a(3.HN�.H[9!E�g:�DG|L*�D�BA/a(+')|+��.H:�(3FƸ%~/+/+uU· d|+!$[r��')*5�õ:��Í|3/+(a')|3��F�� yz( d|3!E[P� ��*U��u�C�Ê

��@£PN�D1')(+DG|3/"|3/a')(+|B�.):�(+#GD�yz.H(Su�.H|3!$/a!$.HN�|S')N�*�u�')(+')CECE'WV�D1|G·7 "DG|+De'd(+#&% Ä .HN�|3.H(3/+!E:�[ .HNÒ`�D1')(+�~Q�BA/&'d(+|105CE!E|�/�')|�.)y�):�C{Q��H0�Ûd£H£)×Ƹ%~/+/+uU· WwLwLw���#&%�')(a'��õFH|3:U��D1*�:d �� Ä ��`�B WX ���L�@£)£��õ%~/+[ Ê

��¸VA/a(+'W��|3.HC�')(�u�C�')N�DG/a|2 � � ��st.H(3]A!$N�F},�(+.H:�u�.HN���VA/+(a')|3.HC�')(���CE')N�D</a| �C$!E|�/�.)y�u�CE')N�DG/+|105/+%�D�~�¸VA/a(+')|+.HCE')(���C�'dN�DG/+|Ä 'd/a')CE.)F �q.)y�/a%�D��~�¸VA/a(+')|+.)C�')(���CE')N�DG/+|���N�#GQA#1C$.Hu�D1*�!E'$�}[\')!$N~/&')!$N�D1*��~Q��)D1')N�B�#&%�N�DG!E*�DG(�'W/Ä `� SB � �¸')(3!E|�����|+DG(3?d'd/a.)(3QƸ%~/+/+uU· WwLwLw���#1!$w���*�DG:d2 � � W*�!$?�� Ww7F)D1|+u�du�C�'dN�DG/+|1��|+%~/a[9C�ÊƸ%~/+/+uU· WwLwLw���.H��|+u�[8� yz( dDGN�#GQA#GC dDGN�#GQA#1CI�õ%~/+[cC¸ÊƸ%~/+/+uU· d#GyÅ'��ÍwLwLw���%�')(3?d')(3*U��D1*�:Wu�C�')N�DG/a| ��,oË��¸��X7 >��ÇdÈ��õ%~/+[cCZÊ

�O"!Eu�u�'d(+#1.)|L|3/&'d(+|��B���0m�@ÉHÉ~¡�0�XL%�DoO�!Eu�u�')(+#G.H|"')N�*YX�QA#&%�. Ä 'd/&'dCE.HFH:�D1|10���B ��B����a��Û)£H£Æ¸%~/+/+uU· W/a*�#<�ÍwLwLw���%�')(�?d')(+*U��D1*�:d|+.dy³/�w>')(3D d#1'd/&'dCE.HFH| d%�!$u�u�')(3#1.H|G�õ%~/a[9C¸Ê

�B�DGCEDG#G/aDG*�6YD1|+|3!EDG(�.H�g�3D1#G/+|=�!$|3/&'dN�#1DG|�')N�*\#1.)[c[9.HN9N�')[9D1|�/&')]dD1Nqyz(+.)[Ô/a%�DSBA/a:�*�D1N~/a|�yz.H(�/+%�D���V�u�C$.H(a'W/a!E.)N\')N�*q=�DG?)D1C �.Hu�[cDGNg/o.)y>B�u�'d#1D8ÆfB���=�B�Ê�68DG|+|3!ED1( Ä 'd/a')CE.HFu�')FHD1|G�\�Z.H|+!{/a!$.HN�|�/&'d])D1N�yz(+.H[ /a%�D\B�2�6-b ��=(3DGyzD1(3D1N�#GD�*�'d/&')��')|+DƸ%~/+/+uU· WwLwLw���|+D1*�|1��.H(+F W[cDG|+|+!$D1( qÊ

�68!$CE]~Q\s�'eQ=�!$|+]\(+')*�!$:�|>/&')]dD1NY/a.��JD���ÇW]Au�#)��=�!$|3/a')N�#1D�/+.9FH')C�')#</a!$#�#1DGNg/+D1(7/&')]dD1N}/a.���D�¢d]Au�#)�

�Ëm.A#e')C�,�(+.):�u=�'d/a'�/&')]dD1NYyz(+.H[ '9C$!E|3/>.)y�Ëm.A#e')Cm,�(3.H:�u868D1[��JDG(S,�')CE'WV�!ED1|�[\')!$N~/&')!$N�D1*�~QYB���=�BƸ%~/+/+uU· WwLwLw���|+D1*�|1��.H(+F ��e|+u�!$*�D1( d|+u�!E*�DG( )ËZ, dCEF���%~/a[9CZÊ

Page 37: A Map of the Universe - J Richard Gott, M Juric, et al

� �~¡ �

�,�(+D1'd/#�>/+/+(a')#</a.H(Ëm.A#e'd/+!E.HN*�'W/&'ryz(+.H[�B�2�6-b��S=r0^(+D1*�|+%�!{y³/7*�!E|�/&')N�#GD)· !��Ñ ×�Ï&�~Ç)£�]g[Ì| +�4

�,�(+D1'd/Ls¦'dCECÄ .HN~/+.H:�(+|���')|+DG* .HN Ä y ��Û8(+DG*�|+%�!{y³/ Ä 'd/a')CE.)F�0M|3:���|3DG/ Ä y ��ÛA�8XL%�D\#1.HN~/a.):�(+|P'd(+D\��')|+DG* .HNF~'dC�'WV�!EDG|L|a'd/+!E|�y³Q�!$N�F �S¢  Ç �

���×gÛ  Ç � 0���Û)£ �

���Û)ÇHÇ � 0�')N�*-£ õ£��

��£ õ£~ÇP#1.H[9u�(3!E|��

!$N�Fr/a%�D Ä y ��Û��õ| ��(3|3/�ÈP|+CE!$#1DG|oÆf,�D1CEC$D1(L'dN�*-O":�#&%�(+'-ÆÞ�@ÉH¢HÉ~Ê3Ê<�Ƹ%~/+/+uU· d#GyÅ'��ÍwLwLw���%�')(3?d')(3*U��D1*�:��e%g:�#&%�(a'qÊ

�B�=�B�B*�'d/&'��CE.d/+/aDG*cyz(3.H[�(a'ew B�=�B�Bc|3uJDG#G/a(3.H|+#G.Hu~Qq*�'W/&'�.H��/&')!$N�D1*c:�|+!$N�FP=�'e?A!E*BA#&%�CEDGFHD1CI�õ|>B���� Ä X7 �u�!$uJDGCE!$N�D � |+u �SË�Ë���*�'d/ ��C$D � *�'d/aDG*�Û)£)£H� )£�� ���Çow7!{/a%Y' � ÇP!EN�#1CE:�|+!E.)N#1:�/�')u�u�CE!EDG*U�B�=�B�B�g:�'d|a')("*�'d/a'Pw7!{/a% � Çru�(+.@?A!E*�DG*8�~Q868!$#&%�')DGCZBA/a(+'):�|+|G0�u�(+!{?d'd/aD�#G.H[c[�:�N�!E#1'd/a!$.HNU�Ƹ%~/+/+uU· d|+u�D1#</a(3.��õu�(+!EN�#1DG/+.HNU��D1*�:�qÊ

���CE.d/+/a!$N�F��CE.d/+/aDG*}:�|+!$N�FcB�6 |3.)y³/�w�')(+Do�~QY ".H��D1(�/"O���Ëm:�u�/a.HNU�Ƹ%~/+/+uU· )')|�/a(+.��õu�(3!EN�#GDG/+.HNU��D1*�:��e(+%�C d|+[ Ê

�2�N�*�!$?A!E*�:�')CU�g:�')|+')(7*�'d/&'B�2�68b���=¥*�'d/&'d��')|+D

�Ä .H|3[c.)CE.HFH!$#e')C�*�'d/a's 6&�S� Ä .HCECE')��.H(a'd/+!E.HNcu�:���C$!E#1'd/a!$.HN�|�Æ�b�DGN�N�D</+/�DG/"')CI��ÆfÛ)£)£H�~Ê>Ê

�s 6&�S�ÌCE.A#e'd/+!E.HN\!EN}|+u�'d#1Do'd/L/a%�D�/+!E[9D�.)yZ/a%�D�[c')u=�')C$D�K¸!$N�]^0^,o'd(3QO"!EN�|3%�'ew�0�O�!E(+')N~Q~'��MDG!E(3!E|oÆfÛd£H£H�~Ê�0�uJDG(+|3.HN�')Cm#G.H[c[�:�N�!E#1'd/a!$.HN

n�������n�����p��ok

�P� �S��')�e'��3!E')NU0!����0�!EN}u�(3D1|+|G0�')|3/+(+.d�Íu�%)£H�)£~Çd×~É~ÛÆIÛ)£H£H�HÊ

�SC$#1.A#&] Ä �{0^�¸')#G�GQAN�|+]g!MbS�{0m�@É~¡)É�0�`S'd/+:�(+Dd0�Û)¢��H0��HÇ)¢

�SC$.HN�|3.�0� ��$0�D</"')Cf�^Ûd£H£)×�0 ��u^��0^È��@��0�Ë���Ç)�

b>')%�#e')C$Cf0�`o�!���!'ÔB�.HN�DG!E(a'�0� o��6t�m�@ÉH¢)×�0 �Su^��0�Û)¡H¡�0^ÛH¡

b�DGCE��(3:�N�.�0��L�{0 'Ô,�.)/+/10^���� ��$0^')|�/a(3.d��u�%�)£)×~£~Çd�~¡HÛqÆIÛ)£H£)×gÊ

b�DGN�N�DG/3/e0 Ä �^Ë���DG/�')CI�^Û)£H£)��0���u^�~BJ0��e×~¢�0J�

Page 38: A Map of the Universe - J Richard Gott, M Juric, et al

� �H¢ �

b�CE')N~/a.HNU0�6t�^ o��DG/�')Cf��Û)£H£H��0��Su^��0�ÇdÉ~Û�0�¢��eÉ

b�CE')N~/a.HNU0�6t�õ ��$0�Ëm:�u�/a.)NU0� �� Oo�$0�6-')C$DGQ)0�K��ð6t�{0 ��.):�N�F�0A`��{0 �5DG%�'e?A!f0g2&�$0�')N�*qË�.@?)D1*�'eQH0�����Ûd£H£H��0�����0�@ÛHÇ�0^ÛHÛ)¡)È

b�.AD1]dD)0^�P�$0 Ä .H|+[9!E#�T�!ED<w�·�XL%�D ��N�!{?HDG(+|+D�!$N×~£��):�[9u�|10��).H%�NY=�'eQ Ä .H[9u�')N~Q)0�`�D<w ��.H(3]�ÆÞ�@É~ÇH¡HÊ

b�.HN�*U0�2&�!���{0�DG/"')CI�^Û)£H£d×�0 �Su���0^ÈH£HÈ�0�Ë��@ÇHÇ

b�(3.�w7N50�6t�^�L�$0�XZ(+:W�3!$CEC$.�0 Ä �!���$0 '� �')��!EN�.@w7!$/+�)0�=r��Ë���Û)£H£)×�0�2 � � Ä !$(+#d�$0�¢)�H£)×�0U�

68!$#&%�')D1C�X��¸b�:�|+%�'�0�K^(3D1* Ä � �S*�'d[c|G0� 7!E|a'-O���s�DG#&%�|+C$D1(10�'dN�* �S:�FH:�|3/P�7�¸��?�(+')(+*50�Û)£H£H��0 �Su���0ÇdÉHÈ�0^¡��e�

Ä .HC$D)0^BJ�{0^OS'W/+/a.)NU0�BJ�{0�s�DG!ENg��D1(+F�0^=r��O��{0 '�K�(+DGN�]^0 Ä ��BJ�U�@ÉHÉ)¢�0^6-`� ��BJ0^�H£H£�0�É)×gÇ

Ä .HC$CED1|3|10^6���DG/�')Cf��Û)£H£��H0�6-`S #��B�0J�HÛ)¢�0U�@£)�HÉ

Ä .HC$CEDGQ)0�s��J`��{0m,�.)/3/e05���U ���2&�{05stD1!$NA��D1(3F�0J=r�5Oo�$05�¸')(3]�0 Ä �$0 'xb�D1(+C$!EN�*50 ��� ���UÛ)£)£H£�0 �Su^��0UÇHÛ)É�0¡dÉ~Ç

Ä .HN�N�.H(+|G0�6t�$0^D</"')Cf�^Ûd£H£~Û�0^6&'o��BJ0^�H¡�0U�e×~�HÇYÆIÛ)£H£~Û)Ê

Ä .HN�N�.H(+|G0o6t�$0SDG/8')Cf�{0��HÇW/a% Ëm:�N�')(Y')N�* ��C�'dN�DG/a')(3Q BA#1!EDGN�#1D Ä .HN�yzDG(+DGN�#1Dd0�68')(+#&%¥��Ç��a�@É�0�Ûd£H£)×�0ËmD1')FH:�D Ä !$/�Q)0�XZD<V�')|10�')��|3/a(+')#G/"N�.��$��ÇdÈ~Ç

Ä .eVJ0 ����`��{0!�SC$CEDGNU�õ| ��|3/+(+.Hu�%~QA|+!$#e')C ��:�')N~/+!$/a!$D1|G0�×)/a%}DG*�!$/+!E.HNU0��S2Þ�Ìu�(3D1|3|10JB�u�(3!EN�FHDG(oÆfÛ)£)£H£~Ê

Ä (+.dy³/e0U �� ��� Ä �{05stD1!$NA��D1(3F�0U=r�JO��{0mb�.)C$/aDd0U6��$0mb�:�(+C$D1|10mBJ�$05O�DG(+N��g:�!$|3/e0UË��{0m��'d/+�)0U`o�$05��!E(+]g[c')NU0=r�{0!'¥X�Qg/aC$D1(G0^=r��Û)£H£~Û�0��Su^��0�Çd¢��H0^Û)£

*�DoË�')u�u�'d(+D1N~/10�Tr�{0�,�DGCECEDG(10�6t�����$0 ' O�:�#&%�(a'�0J���^�M�5�@ÉH¢HÈ�0��Su^��0^�H£HÛ�0�Ë��

=�D��MD<QAN�F�0� o�{0!�S[9.A#1.c6-')u}.)y�B�u�')#GDr6}Q�|�/aDG(+!EDG|rÆÞ�@É~Ç)¢HÊ

��')[9D1|10 Ä ��')N�* ��')[9D1|G0� ��$0õ�M.@w�D1(3|S.)yMXMDGN ÆI68.@?A!ED � É��ðÇ�[9!ENg:�/+D1|&Ê�0 � �9#GDY.dy Ä %�'d(+CEDG|�')N�*Ü �'eQ��')[9D1|>yz.)(L2ÞbL6 ÆÞ�@É~¡H¡HÊ

��!E|3D1N�|�/aD1!$NU0^=r�^����D</S'dCf��Ûd£H£��H0 ����0m��ÛHÛ�0�ÛHÛ)È~¡

��B���0m�eÉHÉ~¡�0�XL%�D�O"!Eu�u�'d(+#1.)|7')N�*YX�QA#&%�. Ä 'd/&')C$.HFH:�DG|10���B�� B��¸�a��Û)£H£

K�(+DGD1*�[c')NU0�s��^Ë���D</"')Cf�^Ûd£H£��H0 ��u^��0�ÇHÇ)��0�×g¡

K�:�]g:�FH!{/&'�0U6t�$0m2�#&%�!E]W'ew>'�0mX��{0Z,�:�N�NU0Z���5�7�{0�=�.H!I0m6t�{0ZB�%�!$[\')|+')]g:U0m�P�{0�' BA#&%�N�D1!$*�D1(G0Z=r�U�M�{0�����0�)�H�H0U��¡W×~¢}Æ��@É)ÉHÈ~Ê

Page 39: A Map of the Universe - J Richard Gott, M Juric, et al

� �HÉ �

,�')(+N�'e?A!E#&%50^�M�^6t��D</�')Cf�U�eÉHÉH¢�0��Su^��0�Ç)£)É�0^¡d×

����,�')(+(3!EF~'r'dN�*&����T�!$CEDGN�]g!ENU0���%~QA|1�� 7DG?��^=�Ç)¡�0�ÛHÛ)�H£}ÆÞ�@ÉHÉH¢HÊ

,�D1CEC$D1(G0�6t�^')N�*-O":�#&%�(a'�0����$0�B�#G!EDGN�#1Dd05ÛW×~È�0�¢)É~¡}Æ��@ÉH¢)É~Ê

,�N�D1*�!$NU0�`o� �P� '�O�')[9!EC$/+.HNU0 �������^B���Û)£H£~Û�0�6-`S #��BJ0^�)�)×�0U�@£H¡

��(+�<Q�|3�G/+.)y�6t��,�;.H(3|+]g!f0���(3!E#oO�!{?H.HNU0�b�D1NW�+'d[c!$N8=r��s¦')N�*�D1C{/e0�')|�/a(3.d��u�%�)ÉH¢���Ûd�~Ç)£ÆÞ�@ÉHÉH¢~Ê

,�.)/+/10^���  ��{0�XL!E[9D�XM(+'e?HD1C�!$N8��!$N�|3/+D1!EN5�õ| ��N�!$?HDG(+|3D)0^ut�@¡HÇ�0�O".H:�FH%~/a.)N-6Y!��9!ENU0�`�DGw ��.H(+]^0�Û)£)£��H�

,�.)/+/10^���^ o�{0�=�!$#&]A!$N�|+.)NU0^6t�{0 '�68DGCE.)/3/e0 ����Ë��m�@ÉH¢HÈ�0��Su^��0^�H£)È�0��)×��

,�:�N�NU0������L�{0^DG/"')CI�$0 ����0m�H�@È�0��H£)×~£}ÆÞ�@ÉHÉH¢~Ê

O�DGN�(3Q8,P�{0^6-')(3#GQY,P�$0^b�:�/aC$D1(7�M� '�T�.HF)/�BJ�{0�2 � ��/aDGCED1F)(a')[�¡)�H£~¡�0mÆ��@ÉHÉ)É~Ê

O�!$]W')FHD)0 Ä ��DG/�')Cf��Û)£H£~ÛA0�� ��B���0�Çd×�0^¡d£~¡

O�.)FHF�0�=r��s��{0^')|�/a(+.W��u�%dÉHÉH£~Ç��)�@È}Æ��@É)ÉHÉ~Ê

O�.)FHF�0�=r� s��$0^KM!EN�]g��D1!EN�D1(10�=r� �Z�$0�BA#&%�CEDGFHD1CI0�=r�ð���{0^')N�*8,�:�N�NU0����õ�L��Û)£H£��)0 ����0m��Û)Û�0^Û���ÛdÉ

O�.@QACEDd0^K���D</S'dCf��Ûd£H£~Û�0 ��u^��0�Ç)¢H£�0�ÈHÈH�

��')!E|3D1(G0�`��m�@É)¢~¡�0^6-`� ��BJ0�ÛHÛH¡A0U�

��.�*�')!E(+'�0��P��D</S'dCf��Ûd£H£H��0�� ��B���0�Ç)Ç�0^Ë���¡

��(a'):�|+|10^Ë���6t� '�BA/&'d(+]g[\'dNU0^,P�^=r�^Û)£H£H£�0��Su���0�Ç)���H0^Û)Û

��:�N�*�!$#)0�X��{0^DG/"')CI�U�@ÉHÉH¡�0 �Su���0�×~¢~Û�0^¡)Ç

���dËm!EN�*�D)0H�ZD1(�/a!E#GCED���%~QA|+!$#1|�'dN�*r2�N��^'W/a!E.)N�')(3Q Ä .)|+[9.HCE.HFdQcÆIOS'd(3w�.�.A*r')#1')*�DG[c!$#���:���C$!E|3%�D1(3|10 Ä %g:�(G0Bgw7!$/a�GD1(3C�')N�*�Ê�Æ��@ÉHÉ)£~Ê

6-')�GD1%U0^X��{0�DG/�')CI��Û)£H£)£�0 �Su���0�Ç)�~Û�0�ËZÇHÇ

68.H(3(+!$|+.HNU0Z�Z�$0¸68.H(3(+!E|3.HNU0Z')N�*Ò/a%�D ���9#1D9.)y Ä %�')(3CED1| '� "'eQÒ��')[9D1|10M�M.@w�D1(3|�.)y�XMDGNU0�BA#1!EDGN~/a! ��#��[cDG(+!$#e')N}Ëm!E��(a')(�QH0�`"DGw���.H(3]^�U�@ÉH¢~Û

�¸'d(+]^0 Ä ���@ÉHÉH£�0�6-`S #��B�0�Ûd×gÛ�0^ÇdÉH�

�MDGN��1!E')|10 ��� ��� '�s !ECE|3.HNU0� ���s��m�@É)È~Ç�0 ��u^��0m�e×gÛ�0�×��@É

�MDG(+#G!$?d')Cf0�s�������DG/"')CI�^Û)£H£��)0^6-`S #��B�0^�~ÛH¡�0U�@Û)É~¡

Page 40: A Map of the Universe - J Richard Gott, M Juric, et al

� ×~£ �

�MDG(+C$[r:�/+/+D1(G0�BJ��DG/�')CI�U�@ÉHÉ)É�0���u^��0�Ç���¡�0�Ç)È~Ç

��!EDG(10Z���m ��$0m68:�N�NU0M��� ���$0�O"!EN�*�|+CED<QH0� ��mbS�{0�O�DGN�N�D1|3|3Q)0�,P�mBJ�{0���D1N~/e0MBJ�m6t�$0�Ëm:�u�/a.HNU0� ��mOo�$0�'2Í?)D1�G!<;#)0 ��¸��Ûd£H£H��0�����0m��ÛHÇA0U��ÇHÇ)É

��(a'd/+.HNU0^�L�!���{0^68DGCE.)/3/e0!����Ë��$0 '�68#e��D1Dd0J6t� �r�m�@ÉHÉ~¡�0��Su^��0�×~¡)É�0�Ë���Ç

7!E#&%�')(3*�|10�,P��X���D</S'dCf��Ûd£H£~Û�0 ����0m��Û)��0�Û)É)×gÇ

7!ED1|3|10!����,���D</�')Cf��Û)£H£��H0��Su^��0�Ç)È)£�0�×~É

LQ�*�D1NU0�bS�^B��m�@ÉHÉ~Ç�0��Su^��0�×gÇ)Û�0^ÛHÇ

LQ�*�D1NU0�bS�^B�� '�68D1C$.)/+/10 ����Ë��m�eÉHÉHÈ�0 ��u^��0�×g¡)£�0U�@ÈH£

B�#&%�[9!E*�/�6t�$0m�eÉHÈH��0�`�'d/a:�(+D)0m�eÉ~¡�0U�@£d×~£

��� Ä ��B�C�'d/+D1(G0^��� Ä %�D1[Y�^��%~Q�|G���HÉ�0����eÉHÉYÆ��@ÉHÈd×gÊ

B�C$.~')NU0 Ä �{0�K¸!EDG(+|�/aD1!$NU0�=r�{0�,�.)/3/e0����¸ o�{0�OS'eQHDG|10>���$0 ��|+|3D1(3[\')N50� ��{0�stD1DG]g|10����$0�XL%�D?A!ED<w�yz(+.H[��')(�/a%tÆf68')u^Ê<0^`�'d/a!$.HN�')Cm,�DG.HFH(a'du�%�!E#d0!��#G/+.H��D1(�Æ��@É)ÉHÉ~Ê

B�[9!$/+%U0���� ���{0�DG/�')CZÛ)£)£~Û�0�����0m��Û)��0�Û���Û��

B�[9.�.d/e0�,P��K���D</�')Cf�J�@ÉHÉ~Û�0��Su^��0^�HÉ)È�0�Ë��

B�N~QA*�D1(G0J���^�M�{0^K¸C�'d/3/aDGN�!EN�F�/a%�Do��')(3/+%U0 ��N�!$?HDG(+|3!$/�Q}.)y Ä %�!E#1')FH.9��(+DG|+|10 Ä %�!$#e')F).-ÆÞ�@ÉHÉH�HÊ

B�u�D1(3FHD1CI0�=r��`���D</�')Cf��Û)£H£H��0��Su^�~BJ0m�1×~¢�0U��¡)Ç

BA/+D1!ENg��D1(3F�0�BJ�{0 ��T�!$DGw .)yM/+%�D�s�.)(+CE*yz(3.H[�Éd/+%���?HDGNg:�D ��0J`�D<w ��.H(3])DG( Ä .@?HDG(10J6-'eQYÛ)É�0m�@É~¡)È

BA/+.H:�FH%~/a.)NU0 Ä �$0�D</�')C�Û)£H£HÛ�0 ����0m�@Û)��0�×~¢HÇ

BA/+(a'):�|3|10J6t�!����DG/�')CI�^Û)£H£~ÛA0�����0m�@Ûd×�0U�@¢��@£

XZD1D1FH')(+*�DGNU0�bS�����{0�DG/�')CI�^Û)£H£H��0��Su���0�Ç)¢HÉ�0�ËZÇ��

XZ:�(+N�DG(10��L�^Ë���')N�*-,�.d/+/e0����� o�{0!�Su5�ð����B�:�u�u�CEDG[cDGN~/e0^�~Û�0�×~£HÉYÆ��@ÉH¡)È~Ê

��N�!$/aDG*8BA/&'d/+D1|�`S'e?d')C�����|3D1(3?d'd/+.H(3Q���|3/+(+.HN�.)[c!$#e')C �SCE[c')N�'d#)0�Ûd£H£H�

T�D1(3*�D)0^Ë���D</S'dCf��Ûd£H£~Û�0^68`S #��BJ0^�H�HÇ�0�×~�~Û

T�.HFHDGCED<QH0A6t�ABJ�{0A�¸')(3]^0 Ä �{0�,�DGCECEDG(10g6��A���$0AO�:�#&%�(a'�0����g�Z�$0A')N�*\,�.)/+/10A���~ o�{0��SuU� ���{0A×~Û)£�0AÇHÛHÇ�ÆÞ�@ÉHÉ)×gÊ

st.HCE|3�1#1�1')NU0!���m�@ÉHÉ)×�0�B�#1!$D1N�#GD)0�Û)È)×�0^Ç)�H¢

Page 41: A Map of the Universe - J Richard Gott, M Juric, et al

� �� �

st.HCE|3�1#1�1')NU0!��� '�K�(a')!$Cf0�=r� ���m�eÉHÉ~Û�0�`�'d/a:�(+D)0^�HÇHÇ�0U�e×~Ç

��.H(3]�0^=r��,��{0�DG/�')CI�$0�����0U��Ûd£�0U��ÇH¡dÉ8ÆIÛ)£H£H£HÊ

� ì�îðëmâ�äfá�â�äfîõç1å��Uã<ëUâ�äfá�âWã<äIá ���mîõåIìSåIìWá�êZêMò���� ��� æLãGïÞäfèGë5÷�ü � � �

Page 42: A Map of the Universe - J Richard Gott, M Juric, et al

� ×gÛ �

X¸'d��CEDP�H� Ä .W��[9.�?A!$N�FP(a')*�!E!5yz.H(L*�! �JD1(+DGN~/7(+D1*�|+%�!{y³/a|

�Æ�~Ê�ÆI68uJ#eÊ `".)/aD

� �e×�0 Û)¢H� b�!EF�b>'dN�F�ÆzD1N�*Y.)yM!EN���'d/a!$.HN�')(�Q\u�D1(3!E.A*^Ê�~Û)�)� �e×�0{�@È~Ç ���g:�'dCm[\'d/3/aDG(7')N�*Y(a')*�!E'd/a!$.HNq*�DGN�|+!{/�Q}D1u�.�#&%�@£H¢)É �e×�0õ£H£H£ "DG#1.H[r��!EN�'d/+!E.HN

È ¢�0�×gÛHÛÇ ¡�0õÉH�H�× ¡�0õ�H£~Ç� È�0�×~È��Û Ç�0 Ûd×gÇ� ��0õ����¡

£  Ç �H0õ¢H¢~Û£  Û ¢H£HÉ£ {� ×��@�

Page 43: A Map of the Universe - J Richard Gott, M Juric, et al

� ×~� �

K¸!$F����H��� ,�')CE'WV�!ED1|S')N�*Ò�g:�')|+')(+|�!$N�/a%�DPDG�A:�'d/a.H(3!�')C¸|+CE!$#1D}Æ ��Û ����Û � ÊS.)y�/a%�D9B�C$.~')NÒ=�!$FH!$/a')C

B�]~QqB�:�(3?)DGQc*�!E|3u�C�'eQ)D1*q!$N\#1.W��[9.�?A!$N�F�#G.�.)(+*�!$N�'d/aDG|�.):�/�/+.�/a%�DS%�.H(3!E�G.HNU��XL%�D�#1.d�Í[c.@?A!EN�F�*�!$|3/a')N�#1DG|/a.}F~'dC�'WV�!EDG|�')(+D�#1')CE#G:�C�'d/+D1*�yz(+.)[ [9De')|3:�(+DG*�(+DG*�|+%�!$y³/e0Z')|3|+:�[9!EN�F8O":�����C$D��.@w�')N�*Òs 6&�S��#1.H|Þ�[9.HCE.HF)!E#e'dCmu�')(a'd[cD</aD1(3|1�oXL%�!E|S!E|�'q#G.HN�yz.H(3[\')CZ[c')u � !$/Su�(+DG|+D1(�?HDG|�|3%�')u�D1|1�os %�!EC$D�/+%�!E|�[c')u�#1')N#1.)N�yz.H(+[c')C$C$Qo|+%�.@wÌ/+%�D7#1.H[9u�C$DG/aD"BACE.~')NP|3:�(3?)DGQ)0�/a%�D"[c'��3.H(3!$/�Q�.)yJ!EN~/aDG(+D1|�/a!$N�F�CE')(+F)D>|+#1')CED7|3/+(+:�#</a:�(3D!E|�#G(a')[9[9D1*�!EN~/+.8'��C$.H��!EN�/+%�D�#1DGNg/+D1(G�9XL%�D9*�')|+%�DG*�#G!E(+#GCEDr[c')(3]A|�/+%�D�.H:�/+D1(�CE!$[c!{/S.dy ��FH:�(+DcÛ��XL%�Do#1!$(+#1C$D�C�')��D1C$D1*Ò� ��N�(3De')#&%�'d��CEDd��[\')(3]g|7/+%�D�*�!E|�/&')N�#1Do�JD<QH.HN�*Yw7%�!E#&%}w�D�#1')N�N�.)/"(3De')#&%¦ÆÅ!f��D)��w�D#e'dN�N�.)/7(3De')#&%w7!$/+%CE!$FH%~/>|+!$FHN�')C$|>')N~Q.)�A�3D1#</L/a%�'d/>!E|�yz:�(�/a%�DG(7'ew>'eQ�Ê<��XL%�!E|�(a')*�!$:�|>#G.H(+(3D1|+u�.HN�*�|7/+.'r(+DG*�|+%�!$y³/7.)y �Ñ � õÈHÉ�� ��|�� K�:�/+:�(+D�#G.H[c.@?A!EN�Fr?�!$|+!$��!EC$!$/�QPC$!E[9!$/e�Hw�D�C�')��D1C�/a%�D�#G.d��[9.@?A!EN�Fr*�!E|3/a')N�#GD/a.cw7%�!E#&%�'cu�%�.)/+.HN-w�.H:�CE*�/+(a'e?HDGCMyz(3.H[ /a%�D�!EN��^'W/a!E.)N�')(3QYb�!EFqb�')N�F\/+.\/a%�D�!EN ��N�!$/+Doyz:�/+:�(+Dd��XL%�!$|!E|�/a%�D\[c'WV�!E[r:�[ (a')*�!$:�|�.):�/�/+.8w7%�!$#&% .H��|3D1(3?d'd/+!E.HN�|ow7!$CEC�DG?)D1(r��D\u�.H|3|+!E��CED)���>/�× ðÇd£���� � 0�!$/o!$||+:�u�(+!$|+!EN�FHC$Q\#1CE.)|+D)�

Page 44: A Map of the Universe - J Richard Gott, M Juric, et al

� ×H× �

K¸!$F��LÛ�� � �5.�.)[�!ENY.)y�/+%�D�(3D1FH!$.HNY[\')(3])DG*-�~Q}/a%�Do*�')|3%�D1*�#G!E(3#1CED�!$N ��FH:�(+D9�H0^.H:�/"/a.c£�� £)È ��� . � � � �ÆfÑ�¢~Ç)¢c68u�#@Ê���XL%�D�uJ.)!EN~/a|"|+%�.@w7NÒ')(3D�FH')C�'WV�!$D1|7yz(+.H[�/+%�D�[c')!ENY')N�*���(+!$FH%~/S(3D1*�FH')C�'WVAQ|+')[9u�CEDG|.)ym/+%�D�B�=�B�BJ� Ä .H[9u�')(3D1*\/+. ��FH:�(+Dr�H0gw�D�#e')NN�.�w |3D1D�'�C$.)/�.)y�!EN~/aDG(+DG|3/a!$N�Fr|�/a(+:�#G/a:�(+D)��XL%�D�B�CE.~'dN,�(+De'W/Ss�')CEC�#e'dN��JDr|3D1DGN�|3/a(3DG/+#&%�!EN�Fqyz(3.H[ ¢ ð¡W%-/a.��1×H%�!EN� o� ���J'd/�'c[cDG*�!�')N-*�!E|�/&')N�#GD�.)y�'d�J.H:�/���@£}6YuJ#d��SC$/+%�.H:�F)%Ò/+%�D�C�')(3FHDr|3#e')C$DP|3/a(3:�#G/+:�(+D�!$|�De')|3!ED1(�/+.}|+D1Dd0¸' �H�G.�.)[ !$N �}CE!E]dD�/a%�!E|�yÅ')!$CE|�/+.#e'du�/a:�(3Do')N�*Y*�!E|3u�C�'eQH0�!EN}.HN�D�[c')uU0�/+%�D�|+!E�GD1|7.)yM[c.A*�DG(+N}(+DG*�|+%�!{y³/7|+:�(�?HD<Q�|G�

Page 45: A Map of the Universe - J Richard Gott, M Juric, et al

� ×gÇ �

K¸!$F����� � ,�')CE'WV�!ED1|o')N�*��g:�')|+')(+|r!$N�/+%�D\DG�g:�'d/a.)(+!�'dC�|3CE!$#1D9.)y�/+%�DB�=�B�BJ0M*�!E|+u�C�'eQHDG*�!ENtCE.A.H]g��')#&]/a!$[cDc#1.A.H(+*�!EN�'d/+D1|G��XL%�D(a')*�!E')C�*�!E|�/&')N�#GD!EN¦/+%�D ��FH:�(+D#1.)(+(+DG|+u�.HN�*�|P/+.�CE.A.H]g��')#&]Ò/a!E[9D)��s %�!ECED/a%�D,�')C�'WV�!$D1|�'d/o/a%�Dc#1DGNg/+D1(r.A#1#G:�u~Qt'8C�'d(+FHDG(�'d(+De'�0M/a%�!E|o[\')u�!E|�'8[9!E|3CED1')*�!EN�FYu�.H(�/a(a'eQH')C�')|oyÅ'd(')|7|+%�')uJDG|�')N�*Y/+%�D�F)D1.H[9DG/+(3Q.)y¸|+u�'d#1D�')(+Do#1.HN�#1D1(3N�D1*5�>2Í/"!E|7N�.)/"#1.)N�yz.H(+[c')C � !$/"#G.H[cu�(+D1|3|+DG|�/a%�D')(3De'q#1C$.H|+D�/a.\/+%�DP%�.H(3!E�1.)NvÆz/+%�!E|�#G.H[9u�(+DG|+|+!$.HN�!E|�[c.)(+DrD�V�u�CE!E#G!$/+C$Q}|+%�.�w7NÒ!$N ��FH:�(3D9ÇHÊ<����CE|3.�05/a%�DF~')CE'WV�!EDG|7')(+D�|3/+!EC$C5/a.A.�#1(+.@w7*�DG*�!EN/+%�D�#1D1N~/+D1(S.dyM/+%�D�[c')u/a.9|+%�.�w ')CECU.dy¸/a%�Do!$N~/a(+!$#e'd/+D�*�DG/a')!EC$|L.)y/a%�D1!E(L#GCE:�|�/aDG(+!EN�F���K¸!EF):�(+D�×9|+%�.�w7|�'P�1.A.H[�!$N.)y¸/+%�D�(+D1F)!E.HN!$N�|+!$*�D�/a%�D�*�'d|+%�DG*-#1!$(+#GCED)�

Page 46: A Map of the Universe - J Richard Gott, M Juric, et al

� ×~È �

K¸!$F��Ý×�� � �5.�.H[ !EN .)y�/a%�D8(3D1FH!$.HNÜ[c')(3])D1*Ü�~Q /+%�D-*�.)/+/+D1*Ý#G!E(3#1CED}!$N ��FH:�(+D8��0>|+%�.�w7!$N�F B�=�B�BF~')CE'WV�!EDG|�.H:�/�/+.£�� Û � � � . � � � � ��XL%�D�*�DG/a')!EC$|".dy�F~')C�'�V�Q}#GCE:�|�/aDG(+!EN�Fq')(3D�N�.@w�*�!$|+u�CE'@Q)D1*�[�:�#&%���DG/+/+D1(G�O�.@w�DG?)D1(10�CE!$])D ��FH:�(+D�Û�0~!$/�|�/a!$CEC�yÅ'd!ECE|M/a.�#e')u�/a:�(3D"/+%�DLw7%�.HCEDL|3:�(3?)DGQ9!EN�.HN�D)0g(+D1')|+.HN�')��C$Qr|+!E�GD1*U0g[c')uU�

Page 47: A Map of the Universe - J Richard Gott, M Juric, et al

� ×g¡ �

K¸!$F�� Ç�� � B��g:�'d(+D #1.)[c.@?A!EN�FÜFH(+!$*�|+%�.�w7N�!$N�CE.A.H]g��')#&] /a!$[cDt#1.A.H(+*�!$N�'d/+D1|1� ,�(3!E*�|3u�')#1!$N�FÌ!$|£ {� ��� � Ñ ×gÛHÛ  Ûdצ68uJ#d����')#&%ÚFH(+!$*Ì|+�g:�'d(+D-w�.H:�C$*Ú#1.HN~/&'d!ENÚ')NÝD1�g:�')C�Ng:�[��JDG(\.)y�F~'dC�'WV�!EDG|\!$N'�^'d/�|+CE!$#1D�.)y¸#1.HN�|3/&'dNg/�?HDG(3/a!$#e')CU/+%�!E#&]gN�DG|+|G�LXL%�D�*�!$|3/+.H(3/+!E.HN}.)y¸|+u�')#GDo/+%�'d/�!E|7u�(3.�*�:�#1D1*8�~Q}:�|+!$N�F/a%�D"C$.�.)]A��')#&]�/a!$[cDL!$|�.H�~?A!E.H:�|�')|�/a%�D"|3�g:�')(+DG|���D1#G.H[cDL[9.H(3D�'dN�*c[9.H(3DL*�!E|�/a.H(�/aD1*9!EN�|3%�')u�DS')|�.HN�D')u�u�(+.~')#&%�D1|7/a%�D�%�.H(3!E�G.HNU�

Page 48: A Map of the Universe - J Richard Gott, M Juric, et al

� ×~¢ �

K¸!$F���È�� � Ëm.HF~')(3!$/a%�[c!$#o[c')u�.)y�/+%�Dr#1.)[cu�C$D<V-u�C�'dN�D)��T�D1(�/a!E#1')CM'WV�!E|�!E|"/a%�DPN�'d/a:�(+')C¸C$.HF~')(3!$/+%�[ .)y/a%�D7')��|+.)CE:�/+D�?d')CE:�D�.)yJ'�#G.H[9u�CED�VrNg:�[r��D1(G0Hw7%�!EC$D�!{/a|�u�%�')|+D7!E|¸u�CE.)/3/aDG*P.HNr/a%�DL%�.H(+!$�1.HN~/&'dC�'WV�!E|G�¸stDu�C$.)/S× � �@£ �v�e£\Ng:�[r��D1(+|�uJDG(S*�DG#e')*�D)05yz(3.H[�/a%�D ��(+|�/�/a%�(+D1D�*�D1#1')*�DG|1��XL%�!$|S[c')u-!$|�#G.HN�yz.H(3[\'dCf0��:�/"#G.�?)D1(3|S'Pw7!E*�D�(+')N�FHD�.)yM|+#1')CEDG|1�

Page 49: A Map of the Universe - J Richard Gott, M Juric, et al

� ×~É �

K¸!$F���¡�� � �M.A#&])D</S[c')u}.)y�/a%�Do:�N�!$?)D1(+|3D)����|+[c')CEC$D1(�?HD1(3|+!$.HN}.)yM/+%�D�[9.H(+D�*�D</&')!$CEDG*[\')u|3%�.@w7N-!$N/a%�D�yz.)CE*�.H:�/ ��FH:�(3Do¢

Page 50: A Map of the Universe - J Richard Gott, M Juric, et al

� Ç)£ �

K¸!$F���¢�� � 6-')uY.)yZ/a%�D ��N�!$?HDG(+|3D

Page 51: A Map of the Universe - J Richard Gott, M Juric, et al

� �� �

K¸!$F��rÉ�� � B�C$.~')Nt,�(+De'W/�s¦'dCEC¸#G.H[9u�')(+DG*�/a. Ä y ��ÛY,�(3De'd/Ss¦')C$C�'d/�/+%�D�|a')[9DP|+#1')CEDP!$N�#1.d�Í[c.@?A!EN�F#1.A.H(3*�!EN�'W/aD1|G�����g:�!$?d')C$D1N~/�(3D1*�|3%�!$y³/S*�!E|�/&')N�#GD1| !�}')(+D�!EN�*�!E#e'W/aD1*5�SXL%�D9B�C$.~')N8|+CE!$#1D�!E|S× � w7!E*�Dd05/a%�DÄ y ��Û�|+C$!E#1D7!$|"�@Û � w7!$*�D"/+.�[c')]dD���.)/a%c|+C$!E#1DG|�')u�u�(3.@V�!$[\'d/+D1C{Qr/a%�D"|a'd[cD7u�%~QA|+!$#e')C^w7!E*�/+%q'd/�/+%�D"/�w�.w�')CEC$|1��XL%�DcB�C$.~')NÒ,�(+D1'd/Ss�')CECMD<VA/aDGN�*�|�yz(+.)[ �e×)%-/a.}É)%5�o2Í/�#G.HN�|3!E|3/+|�.)y�.HN�DP|�/a(+')N�*Ò'd/�/+%�DPCED<y³/e0w7%�!$#&%c*�!{?A!E*�DG|�/+.oyz.)(+[�/�w�.�|�/a(+')N�*�|��JD</�w�DGD1N��)�H� �d%\')N�*\É��õ¢)%U0Hw7%�!E#&%\#G.H[9DL��')#&]r/a.)FHDG/+%�D1(�/a.�yz.H[.HN�DS|3/a(+')N�*}')FH')!ENÒÆzCE!$])D�'r(+.~')*c/a%�'d/>�JDG#1.H[9D1|L'�*�!$?A!E*�D1*%�!$FH%~w>'eQ9yz.H(>'�w7%�!$CEDeÊ<��XL%�D Ä y ��Ûr,�(+De'W/s�')CEC�Ƴw7%�!E#&%8!EN�#GCE:�*�DG|"/+%�D Ä .H[\'�#1C$:�|3/+D1("!ENY/a%�Do#1DGNg/+D1(aÊ<0�%�')|S��D1DGN-u�C$.)/+/+D1*8.HN-'9#1.HN�D�')N�*8/a%�D1N�^'d/3/aDGN�D1*Y.HN~/a.c'Pu�C�')N�D)��XZ.)/&')CmNg:�[��JDG(+|7.)yMF~')C�'�V�!$D1|L|3%�.@w7N-!END1')#&%-|3CE!$#1D�')(3D�')CE|3.9!$N�*�!$#e'd/+D1*U�


Recommended