Cosmology Now and Tomorrow
Misao Sasaki
(YITP, Kyoto University)
KASI-YITP Joint-Workshop:Cosmology Now and Tomorrow
17 -18 Feb 2012
Cosmology Now and Tomorrow
Misao Sasaki
(YITP, Kyoto University)
KASI-YITP Joint-Workshop:Cosmology Now and Tomorrow
17 -18 Feb 2012
Theoretical
Cosmology Now and Tomorrow
Misao Sasaki
(YITP, Kyoto University)
KASI-YITP Joint-Workshop:Cosmology Now and Tomorrow
17 -18 Feb 2012
Theoretical
– personal, biased perspective –
current status
big bang theory has been firmly established
“standard model” parameters:
strong evidence for inflation
CMB spectrum at T=2.725K
only to be confirmed (by tensor modes?)
WMAP 7yr
current and future issues5
I. GR cosmology– perturbation theory– numerical cosmology
II. Inflation– multi-field, non-canonical/minimal– conformal frame (in-)dependence
III. String Theory Landscape– observational signatures?
I do NOT touch Dark Energy/Modified Gravityrecent developments in MG
→ R Kimura
I. GR Cosmologyperturbation theory
linear theory has been extremely successful over the past 20-30 years
• quantization and evolution of perturbations from inflation
31
3
22
21 2 3
4
2( ) ;
( )Sn
S pl
V Vn
kP k M
V VAk
R
3
3
4
2
1
8( ) ;
(( )() )
TT
n
TT
P kn
kP k Ak
P k
R
2
2
/k a H
H
R &
single-field slow-roll inflation Mukhanov ’85, MS ’86,...
Lyth-Liddle ’92, Stewart-Lyth ‘93
• CMB anisotropy
• growth of density perturbations (>~ 10 Mpc)
LSS LSS LSS 0 LSS
1 ;
3( ) ( ) ( ) ( )
Tn x n v x x n
T
r r r r r r r
g L
SW Dopplerconformal distance to
Last Scattering SurfaceWMAP 7yr
1 2
0
( ) ( )2 1
(cos ).4
T
C
T n n
P
CDM DE DE3 1 5 6 ; , ( )/ ( )f
i ia a f w w ;
Peebles ’80, ..., Wang & Steinhardt ‘98
Sunyaev & Zeldovich ’70, ....
need for NL theory is growing
• Non-gaussianity from inflation
• higher order effects in CMB spectrum
• (NL) GR effects on cosmological observables
• 2nd and higher order perturbation theory
testing/constraining models of inflation
→ JC Hwang
no systematic studies, need to be developed
Meures & Bruni ‘11, Jeong, Schmidt & Hirata ’11,...
Naruko et al. in progress
only a few papers, a lot to be done
E
Numerical GR Cosmology
• inhomogeneous universe models
testing TLB (anti-Copernican) model
quantifying GR effects in LSS formation
.......
• BH universe
(primordial) BH formation
BH dominated (“vacuum”) universe
→ CM Yoo
practically nothing has been done yet
2D & 3D codes to be developed
Shibata & MS ’99, ...(but spherically sym)
perturbative? Post Newtonian?
“vacuum”
II. Inflationmulti-field/non-canonical/non-minimal models
• PLANCK will announce the first result by Feb 2013, exactly 1 year from now. So be prepared !
• construct as many models as possible which are compatible with current WMAP data, and which can be tested by PLANCK etc. (not too distant future)
spectral index, tensor perturbation, non-Gaussianity,ad-iso correlation, primordial BH,...
any other new signatures?
→ Alabidi, Saito, Stewart, Yamaguchi
Makino & MS ‘91, ... , Gong, Hwang, Park, MS & Song ‘11
• tensor-type perturbation
Definition of hij is apparently -independent.
0ij jj jh h
2 2 2
2 2
( )
( )
i jij ij
jij ij
i
ds dt a t dx dx
a d x
h
dh dx
2 2 2
2 2 2( ) ( ) ij ii
jj
ds ds
x a d dx dxh
%
conformal (in-)dependence of cosmological perturbations
Linear theory
• vector-type perturbation
2 2 2 2 j i jij ij j j iB Hds a d dx d dx dxH
Definitions of Bj and Hj are aslo -independent.
0j jj jB H
2 2 2
2 2 2 2 j i j jj i j
ij i
ds ds
a d dx d dx dxB H H
%
tensor & vector perturbations are conformal frame-independent
• scalar-type perturbation
2 2 2( ) (1 2 ) 2
(1 2 ) 2
j
i j
j
i jij
ds a d dx d
dx x
A
d
B
E
R
Definitions of B and E are -independent.
0, 1 ( , )i it x t t x
2 2 2
2 2 2(1 2 ) 2
(1 2 ) 2
j
i ji
j
i jj
ds ds
a d dx d
d
A B
E x dx
R
%
,A A R R
But A and are -dependent!
For scalar-tensor theory with1 1
( ) ( , ) ,2 2
f R K X XL g
The important, curvature perturbation c , conserved on superhorizon scales, is defined on comoving hypersurfaces.
c= =0 is -independent!
Nevertheless,...
we have
1c
H daa d
cR R R&
generalization to nonlinear case is straightforward
uniform (= 0)
frame-independentif =()
• Is distinction between adiabatic and isocurvature perturbations conformally invariant?
Yes, if we consider trajectoriesin field space, because it iscoordinate-independent.
isocurvature But this assumes reductionof phase space to field space:
( , ), ( , )f g & &
The assumption seems violated in general, eg, whendifferent comps have different curvature couplings.
multi-component case• general case is discussed in Gong et al. (’11)
→ Minamitsuji & White, in progress
1616
III. String theory landscape
There are ~ 10500 vacua in string theory
• vacuum energy v may be positive or negative
• some of them have v <<P4
• typical energy scale ~ P4
Lerche, Lust & Schellekens (’87), Bousso & Pochinski (’00), Susskind, Douglas, KKLT (’03), ...
which?
17
Is there any way to know what kind of landscape we live in?
Or at least to know what kind of neighborhood we live in?
Vacua with enhanced gauge symmetry
by courtesy of T. Eguchi
may explain the origin of gauge symmetry(SU(3)xSU(2)xU(1)) in our Universe
distribution function in flux space
19
• dS space: v>0, O(4,1) symmetry
3
2 2 2 2 1 2
( )( ) : cosh , / 3v PS
ds dt a t d a H Ht H M
• AdS space: v<0, O(3,2) symmetry
3
2 2 2 2 1 2
( )( ) : cos , | | / 3v PH
ds dt a t d a H Ht H M
collapses within t~1/H
2 1(8 ) : PM G Planck mass
Hta e t for 3 3~Volume Hta e
3
2 2 2 2 2
( )
2sinh sinH
d d d d
3
2 2 2 2 2
( )
2sin sinS
d d d d
de Sitter (dS) & Anti-de Sitter (AdS)
2020 A universe jumps around in the landscape by quantum tunneling• it can go up to a vacuum with larger v
• if it tunnels to a vacuum with negative v , it collapses within t ~ MP/|v|1/2.
• so we may focus on vacua with positive v: dS vacua
0
v
Sato, MS, Kodama & Maeda (’81)
( dS space ~ thermal state with T =H/2)
2121
Susskind (‘03)
• Not all of dS vacua are habitable.
“anthropic” landscape
v,f must not be larger than this value in order to account for the formation of stars and galaxies.
• A universe jumps around in the landscape and settles down to a final vacuum with v,f ~ MP
2H02 ~(10-3eV)4.
• Just before it has arrived the final vacuum (=present universe), it must have gone through an era of (slow-roll) inflation and reheating, to create “matter and radiation.”
vac → matter ~ T4: birth of Hot Bigbang Universe
Anthropic landscape
22
false vacuum decay via O(4) symmetric (CDL) instanton
inside bubble is an open universe
Coleman & De Luccia (‘80)
Most plausible state of the universe before inflation is a dS vacuum with v ~ MP
4. dS = O(4,1) O(5) ~ S4
O(4) O(3,1)
2 2 2x R
2 2 2t x R
bubble wall
false vacuum
creation of open universe23
analytic continuation
open (hyperbolic) space
2 2 2x R
2 2 2t x R
bubble wall
2 2 .x const
2 2 .t x const
2424
Anthropic principle suggests that # of e-folds of inflation inside the bubble (N=Ht) should be ~ 50 – 60 : just enough to make the universe habitable.
Garriga, Tanaka & Vilenkin (‘98), Freivogel et al. (‘04)
Nevertheless, the universe may be slightly open:2 3
01 10 ~10
Natural outcome would be a universe with 0 <<1.
• “empty” universe: no matter, no life
Observational data excluded open universe with 0 <1.
may be tested by PLANCK+BAO
Colombo et al. (‘09)
25
revisit open inflation!
What if 1-0 is actually confirmedto be non-zero:~10-2 -10-3?
see if we can say anything aboutLandscape
Yamauchi, Linde, Naruko, MS & Tanaka ’11
• effect of tunneling on large angular scale CMB
• Tunneling probability / resonant tunneling?
other possible signatures
• CMB cold/hot spots = bubble collision?
• Non-Gaussianity from bubbles?
• Measure problem?
Aguirre & Johnson ’09, Kleban, Levi & Sigurdson ’11,...
Blanco-Pillado & Salem ’10, Sugimura et al. in progress
Tye & Wohns ’09, Brown & Dahlen ‘11
Garriga & Vilenkin ‘08, Freivogel ’11, Vilenkin ’11, ....
• any others?
Summary
develop GR cosmology further:
propose testable inflation models
perturbative, non-perturbative, numerical, observational... (GR can be replace by MG)
non-minimal, non-canonical, multi-field, ....
look for signatures of string theory landscape
................ ! ... ?