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

................ ! ... ?