KASI-YITP Joint-Workshop:
Cosmology Now and Tomorrow
17 -18 Feb 2012
Cosmology Now and Tomorrow
Misao Sasaki
(YITP, Kyoto University)
Theoretical
KASI-YITP Joint-Workshop:
Cosmology Now and Tomorrow
17 -18 Feb 2012
Cosmology Now and Tomorrow
Misao Sasaki
(YITP, Kyoto University)
Theoretical
KASI-YITP Joint-Workshop:
Cosmology Now and Tomorrow
17 -18 Feb 2012
Cosmology Now and Tomorrow
– personal, biased perspective –
Misao Sasaki
(YITP, Kyoto University)
current status
big bang theory has been firmly established
CMB spectrum at T=2.725K
strong evidence for inflation
only to be confirmed (by tensor modes?)
“standard model”
parameters:
WMAP 7yr
current and future issues
I. GR cosmology
– perturbation theory
– numerical cosmology
I do NOT touch Dark Energy/Modified Gravity
recent developments in MG
→ R Kimura
II. Inflation
– multi-field, non-canonical/minimal
– conformal frame (in-)dependence
III. String Theory Landscape
– observational signatures?
5
I. GR Cosmology
perturbation theory
linear theory has been extremely successful over
the past 20-30 years
• quantization and evolution of perturbations from inflation
single-field slow-roll inflation
R
H
4 k
2
2 &
k /aH
Mukhanov ’85, MS ’86,...
3
( 2 )
3
4 k
3
( 2 )
3
PR ( k )  A k
n S 1
;
nS  1  M
PT ( k )  A k
nT
;
nT  
2
pl
2
 V 
V 
3 2 
2
V 
 V
1 PR ( k )
8 PT ( k )
Lyth-Liddle ’92, Stewart-Lyth ‘93
• CMB anisotropy
Sunyaev & Zeldovich ’70, ....
T
r
r
r r r
r
r
1
( n )   ( x LS S )  n gv ( x LS S )  L ; x LS S  ( 0   LS S ) n
T
3
SW
Doppler
conformal distance to
Last Scattering Surface
WMAP 7yr
T (n1 ) T (n2 )

2 1

C P (cos  ).
4
0
• growth of density perturbations (>~ 10 Mpc)
   i  a ai 
f
;

f   C D M ,  ; 3(1  w D E ) /( 5  6 w D E )
Peebles ’80, ..., Wang & Steinhardt ‘98
 need for NL theory is growing
• Non-gaussianity from inflation
testing/constraining models of inflation
• 2nd and higher order perturbation theory
→ JC Hwang
• higher order effects in CMB spectrum
no systematic studies, need to be developed
Naruko et al. in progress
• (NL) GR effects on cosmological observables
only a few papers, a lot to be done
Meures & Bruni ‘11, Jeong, Schmidt & Hirata ’11,...
E
Numerical GR Cosmology
practically nothing has been done yet
• inhomogeneous universe models
testing TLB (anti-Copernican) model
quantifying GR effects in LSS formation
.......
perturbative? Post Newtonian?
• BH universe
BH dominated (“vacuum”) universe
→ CM Yoo
“vacuum”
(primordial) BH formation
Shibata & MS ’99, ...(but spherically sym)
2D & 3D codes to be developed
II. Inflation
multi-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,...
→ Alabidi, Saito, Stewart, Yamaguchi
any other new signatures?
conformal (in-)dependence of
cosmological perturbations
Makino & MS ‘91, ... ,
Gong, Hwang, Park, MS & Song ‘11
 Linear theory
• tensor-type perturbation
d s   d t  a ( t )   ij  h ij  d x d x
2
2
2
i
j
2
2
i
j
 a ( )   d    ij  h ij  d x d x 


 jh
2
2
d s%   d s
ij
h
j
j
0
2
2

2
2
i
j
  ( x ) a ( )   d    ij  h i j  d x d x 


Definition of hij is apparently -independent.
• vector-type perturbation
2
2
2
j
i
j
ds  a   d  2 B j dx d    ij   i H j   j H i  dx dx 


j
 jB   jH
2
2
d s%   d s
j
0
2
2 2
2
j
i
j
  a   d  2 B j d x d    ij   i H j   j H i  d x d x 


Definitions of Bj and Hj are aslo -independent.
tensor & vector perturbations are
conformal frame-independent
• scalar-type perturbation
d s  a ( )   (1  2 A ) d  2  j B d x d
2
2
2
j
i
j
  (1  2 R ) ij  2  i  j E  d x d x 

2
2
d s%   d s
2
2 2
2
j
  a   (1  2 A ) d  2  j B d x d
i
j
  (1  2 R ) ij  2  i  j E  d x d x 

Definitions of B and E are -independent.
But A and R are -dependent!

 t, x
i
    t   1   ( t , x
0
i
) 
A  A  , R  R 
Nevertheless,...
The important, curvature perturbation Rc , conserved on
superhorizon scales, is defined on comoving hypersurfaces.
R cc  R 
H
1 da
  R 

&
a d

uniform  ( = 0)
frame-independent
if =()
For scalar-tensor theory with
L 
1
2
f ( ) R  K ( X ,  ) , X  
1
2
g

    
we have      
Rc= R=0 is -independent!
generalization to nonlinear case is straightforward
 multi-component case
• general case is discussed in Gong et al. (’11)
• Is distinction between adiabatic and isocurvature
perturbations conformally invariant?

Yes, if we consider trajectories
in field space, because it is
coordinate-independent.
isocurvature
y
But this assumes reduction
of phase space to field space:
& f ( ,y ), y& g ( ,y )
The assumption seems violated in general, eg, when
different comps have different curvature couplings.
→ Minamitsuji & White, in progress
16
III. String theory landscape
Lerche, Lust & Schellekens (’87), Bousso & Pochinski (’00),
Susskind, Douglas, KKLT (’03), ...

There are ~ 10500 vacua in string theory
• vacuum energy rv may be positive or negative
• typical energy scale ~ MP4
• some of them have rv <<MP4
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?
distribution function in flux space
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
19
de Sitter (dS) & Anti-de Sitter (AdS)
2
• dS space: rv>0, O(4,1) symmetry
d s   d t  a (t ) d  ( S 3 ) :
2
2
2
2
a H
1
1
M P  (8 G ) :
rv / 3M P
cosh H t , H 
ae
Ht
P lanck m ass
2
fo r t  
V o lu m e ~ a  e
3
d (S3 )  d 
2
2
 sin   d 
2
2
 sin  d 
2
2
3Ht

• AdS space: rv<0, O(3,2) symmetry
d s   d t  a (t ) d  ( H 3 ) :
2
2
2
2
a H
1
cos H t , H 
| rv | / 3M P
2
collapses within t~1/H
d  ( H 3 )  d   sin h   d   sin  d 
2
2
2
2
2
2

20

A universe jumps around in the landscape by quantum
tunneling
• it can go up to a vacuum with larger rv
( dS space ~ thermal state with T =H/2 )
• if it tunnels to a vacuum with negative rv ,
it collapses within t ~ MP/|rv|1/2.
• so we may focus on vacua with positive rv: dS vacua
rv
0
Sato, MS, Kodama & Maeda (’81)
21
Anthropic landscape
•
Not all of dS vacua are habitable.
“anthropic” landscape Susskind (‘03)
•
A universe jumps around in the landscape and settles
down to a final vacuum with rv,f ~ MP2H02 ~(10-3eV)4.
rv,f must not be larger than this value in order to
account for the formation of stars and galaxies.
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.”
•
rvac → rmatter ~ T4: birth of Hot Bigbang Universe
22
Most plausible state of the universe before inflation is
a dS vacuum with rv ~ MP4. dS = O(4,1) O(5) ~ S4

false vacuum decay via O(4) symmetric (CDL) instanton
O(4)
Coleman & De Luccia (‘80)
O(3,1)
inside bubble is an open universe
bubble wall

2
 x
2
 R
2
false vacuum
t
2
 x
2
 R
2
23
creation of open universe

2
 x
2
 R
2
open (hyperbolic) space
bubble wall
t

2
 x
2
2
 x
2
 co n st .
 co n st .
t
analytic continuation
2
 x
2
 R
2
24

Natural outcome would be a universe with 0 <<1.
• “empty” universe: no matter, no life
Anthropic principle suggests that # of e-folds of inflation
inside the bubble (N=Ht) should be ~ 50 – 60 : just
enough to make the universe habitable.

Garriga, Tanaka & Vilenkin (‘98), Freivogel et al. (‘04)

Observational data excluded open universe with 0 <1.

Nevertheless, the universe may be slightly open:
1  0  10
2
~ 10
3
may be tested by PLANCK+BAO
Colombo et al. (‘09)
25
What if 1-0 is actually confirmed
to be non-zero:~10-2 -10-3?
revisit open inflation!
see if we can say anything about
Landscape
• effect of tunneling on large angular scale CMB
Yamauchi, Linde, Naruko, MS & Tanaka ’11
 other possible signatures
• CMB cold/hot spots = bubble collision?
Aguirre & Johnson ’09, Kleban, Levi & Sigurdson ’11,...
• Non-Gaussianity from bubbles?
Blanco-Pillado & Salem ’10, Sugimura et al. in progress
• Tunneling probability / resonant tunneling?
Tye & Wohns ’09, Brown & Dahlen ‘11
• Measure problem?
Garriga & Vilenkin ‘08, Freivogel ’11, Vilenkin ’11, ....
• any others?
Summary
develop GR cosmology further:
perturbative, non-perturbative, numerical, observational...
(GR can be replace by MG)
propose testable inflation models
non-minimal, non-canonical, multi-field, ....
look for signatures of string theory landscape
................ ! ... ?