Academic Training LecturesRocky Kolb
Fermilab, University of Chicago, & CERN
Cosmology and theCosmology and theorigin of structureorigin of structure
Rocky I: The universe observed
Rocky II: The growth of cosmological structure
Rocky III: Inflation and the origin of perturbations
Rocky IV: Dark matter and dark energy
Rocky Rocky II: The universe observed: The universe observedRocky Rocky II: The universe observed: The universe observed• Cosmological parameters:
• Power spectrum of large-scale structure:
• Anisotropy of CMB:
0
0
0
0
0
Hubble's constant
deceleration parameter
the cosmic food chain
, , , , , , .....
age of the universe
temperature of the u
i
M B
H
q
t
T
niverse
( )P k
lC
Theoretical developments (1917-1927)Theoretical developments (1917-1927)• Cosmological principle
• Robertson-Walker metric
• Expansion natural
22 2 2 2 2 2 2 2
2( ) sin
1
0, 1 (flat, positive, negative spatial curvature)
drds dt a t r d r d
kr
k
Observational developments (1912-1929)Observational developments (1912-1929)
“… physically, he is a splendid specimen…”“… magnificent physique ….”“… manly …”“… loveable character …”
University of Chicago 1909 National Champions
Observational developments (1912-1929)Observational developments (1912-1929)
• Cosmological principle (extragalactic astronomy)
• Universe expands
0
-1 -10
recessional velocity
Hubble's constant = 100 km s Mpc
Luminosity distance
R L
R
L
v H d
v c c
H h
d
z
Hubble’s Discovery Paper - 1929Hubble’s Discovery Paper - 1929Hubble’s Discovery Paper - 1929Hubble’s Discovery Paper - 1929s -1 -1
0 500 km s MpcH
constant sHubble'
v
0
0
H
dH
0.72 .03 .07 Freedman et al. (Hubble Key Project)
0.57 .02 Sandage, Tammann, et al.
h
h
Riess et al astro-ph/9410054
Hubble’sdata
Distance-luminosity relationDistance-luminosity relationDistance-luminosity relationDistance-luminosity relation
2
2
2
2(
defines luminosity distance - "know" , measure
Conservation of energy: flux redshifted:
redshift of energy redshift of time interval:
area of
1 )
(1 )
2L
0 1
LF = L F
4 d
=z
z
a t a t
LF = A
A
0
22 2 2 2 2 2 2
0
0
2
2 2 20
centered on sour
(
ce at time of detection,
( ) 4 ( )1
) (1 4 (
)) (1 ) L
S t
drds dt a t r d A a t r
kr
LF =
ad a t r z
t r z
light from comoving coordinate reaches
us now redshifted by an amo ( )unt 1
r
z
Field equationsField equationsField equationsField equations
2
2
2
8 expansion rate
3
4 13 deceleration parameter
3
a k G aH
a a a
a G ap q
a a H
......M R w
3(1 )whatever: 1
w
w w wp w w p z
0vacuum: 1 1p w z
4radiation: 3 1 3 1R R Rp w z
3matter: 0 0 1 M Mp w z
Distance-luminosity relationDistance-luminosity relationDistance-luminosity relationDistance-luminosity relation
0( ) (1 )Ld a t r z 2
2 2 2 2 22
( )1
drds dt a t r d
kr
22 ( ) ( )1
dr dt da
a t H a akr
2 2 2 3 3(1 )0 0(1 )(1 ) (1 ) (1 ) ...w
M wH H z z z
light travels on geodesics2 0ds
20
0 0
3 8
... (1 )
i i
M R w
H G
k
1 1
0 0
2 2 3 3(1 )0 00
( )
1 (1 )(1 ) (1 ) (1 ) ...
r z
wM w
a t H dzdr
kr z z z
Distance-luminosity relationDistance-luminosity relationDistance-luminosity relationDistance-luminosity relation
0( ) (1 )Ld a t r z 1 1
0 0
2 2 3 3(1 )0 00
( )
1 (1 )(1 ) (1 ) (1 ) ...
r z
wM w
a t H dzdr
kr z z z
Program:• measure via
• input and calculate
( )Ld z 2 / 4Ld L F
i 0( )a t r
20 ( )
L
i
H d z O z
Example: matter + lambda 0 M
Lu
min
osi
ty /
So
lar
Lu
min
osi
ty
10
9
9
8
10
4 10
1.6 10
6.4 10
Type Ia Supernovae
-20 0 20 40 60days
Type Ia supernova are standard candlesType Ia supernova are standard candlesType Ia supernova are standard candlesType Ia supernova are standard candles
app
aren
t m
agn
itu
de
[lo
g(d
ista
nce
)]
redshift z
Perlmutter et al. (1998)
Type Ia supernova Hubble diagramType Ia supernova Hubble diagramType Ia supernova Hubble diagramType Ia supernova Hubble diagram
cosmological constant, …some changing non-zero vacuum energy, … or some unknown systematic effect(s)
MATTER
V
AC
UU
M
maximumtheoretical
bliss
scal
e fa
cto
r a
time
normal0a
Newton Ga pGa 3Einstein
3 0p
scal
e fa
cto
r a
time
accelerated
030
p
a
vacuumenergy?
The accelerating universe?The accelerating universe?The accelerating universe?The accelerating universe?• Normal matter slows the expansion of the
universe (deceleration). Gravity is attractive.
• Negative pressure would push apart space.
• “Vacuum energy” (the mass-energy density of
space) is positive, but its pressure is negative.
cosmological constant, …some changing non-zero vacuum energy, … or some unknown systematic effect(s)
MATTER
V
AC
UU
M
The case for :1) acceleration
maximumtheoretical
bliss
2) large-scale structure
0.25 0.05 0.25 1 0.25
0.25 0.35 0.70
M M
M
h h
h
2dF data
cosmological constant, …some changing non-zero vacuum energy, … or some unknown systematic effect(s)
MATTER
V
AC
UU
M
The case for :1) acceleration2) large-scale structure
maximumtheoretical
bliss
3) age of the universe
13.5 2 Gyr
Chaboyer (2001) H0 =70 M t0 (Gyr)
Flat 1.0 0 9.3
Open 0.3 0
12
Open 0.2 0 14
Flat 0.3 0.7 13.5
Flat 0.2 0.8 15
tt00 : age of the universe : age of the universe• white dwarf cooling
• nucleocosmochronology
• globular cluster evolution
Cayrel (2001)
12.6 3 Gyr
First measurement
of stellar uranium
12.6 3 Gyr
13.5 2 Gyr
cosmological constant, …some changing non-zero vacuum energy, … or some unknown systematic effect(s)
MATTER
V
AC
UU
M
The case for :1) acceleration2) large-scale structure3) age of the universemaximum
theoreticalbliss
4) flatness= 1= 0.31 0.3 = 0.7
Flat universeFlat universeFlat universeFlat universe
0 1.03 0.06
Hu
B B hh QSO 1937-1009
Ly
Tytler Tytler
galaxy kinematics
x-ray gas lensing
M M
= 1
= 0.3
1 0.3 = 0.7
Cosmo-illogical constantCosmo-illogical constantCosmo-illogical constantCosmo-illogical constant
Mass density of space:
Who ordered that?
The unbearable lightness of nothing!
30 -310 g cm
Temperature of the universeTemperature of the universeTemperature of the universeTemperature of the universe
The cosmic food chain (The cosmic food chain (ii))The cosmic food chain (The cosmic food chain (ii))
Radiation: 0.02%
Visible matter: 0.1%
Neutrinos: 0.1%
Dark neutrons & protons: 9.78%
Dark matter: 30%
Dark energy: 60%
Observer’s view of the universeObserver’s view of the universe
lumpy (inhomogeneous and anisotropic) full of stars, galaxies, clusters, ….
NGC 6070NGC 6070
Theorist’s view of the universeTheorist’s view of the universe
smooth (homogeneous and isotropic) full of dark matter (and dark energy)
Actual image of dark matterActual image of dark matter
• Assume there is an average density
• Expand density contrast in Fourier modes
• Autocorrelation function defines power spectrum
Power spectrumPower spectrumPower spectrumPower spectrum
3exp k
xx ik x d k
2 3 2
20
( )( ) ( )
2k
kx dkx x
k
x
3 2
2 22
( ) ( )2
k
k
kk P k
• Power spectrum related to rms fluctuations
Power spectrumPower spectrumPower spectrumPower spectrum
1( )( )
R
xk R
sphere of radius R
2 2 N
3 3 N
N
. . . . . . . . . .
trial N
1 1 N
. . . . .
1N N2N N
3N N
2iN N
variance
Power spectrumPower spectrumPower spectrumPower spectrum
3 2
2 1
2k
k
118 Mpch
Observer’s Observer’s
view of the view of the
universeuniverse
(fluctuations)(fluctuations)
Theorist’s Theorist’s
view of the view of the
universeuniverse
(isotropic)(isotropic)
1 2
1/ 22
( , )lm lm
lm l
T T a Y
a C
Angular correlation function, lC
1 1 1 2 2 2( , ) ( , )T T
Angular power spectrumAngular power spectrumAngular power spectrumAngular power spectrum
LAST CENTURY
Angular power spectrumAngular power spectrumAngular power spectrumAngular power spectrum
Angular power spectrumAngular power spectrumAngular power spectrumAngular power spectrum
expected precision
-1 -101 0 50 km s Mpc
0.9 0.1CDM B
n r H
MAP
Rocky Rocky II: The universe observed: The universe observedRocky Rocky II: The universe observed: The universe observed• Cosmological parameters:
• Power spectrum of large-scale structure:
• Anisotropy of CMB:
0
0
0
0
0
Hubble's constant
deceleration parameter
the cosmic food chain
, , , , , , .....
age of the universe
temperature of the u
i
M B
H
q
t
T
niverse
( )P k
lC
Academic Training LecturesRocky Kolb
Fermilab, University of Chicago, & CERN
Cosmology and theCosmology and theorigin of structureorigin of structure
Rocky I: The observed universe
Rocky II: The growth of cosmological structure
Rocky III: Inflation and the origin of perturbations
Rocky IV: Dark matter and dark energy