Open Inflation Reviving
- a signature of string theory landscape?Misao Sasaki
(YITP, Kyoto University)
CosKASI Symposium
16 April 2014
2
1. Era of precision cosmology
Big Bang theory has been firmly established
wavelength[mm]
COBE/FIRAS
CMB spectrum at T=2.725K
200 sigma
error-bars
frequency[GHz]
3
Strong evidence for Inflation
Planck 2013
T (n1 )T (n2 )

2 1

C P (cos  ).
 0 4
• almost scale-invariant spectrum: nS  0.960  0.0073 (68% CL)
• highly Gaussian fluctuations:
local
f NL
 2.7  5.8 (68% CL)
only to be confirmed (by tensor modes?!)
4
Discovery(?) of primordial GWs
BICEP2 (2014)
spacetime vacuum fluctuations from inflation
B-mode polarization in CMB anisotropy
• E-mode (even parity)
• B-mode (odd parity)
= cannot be produced from
density fluctuations
55
BICEP2 result
sky map
B-mode spectrum
If confirmed, it “proves” primordial inflation
& quantum gravity!
6
What’s next?
7
2. 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
?
8
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?
9

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 et al. (’81)
10
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  R2
false vacuum
t 2  x 2  R 2
11
creation of open universe
ds vacuum :O(4,1)
Euclidean bubble: O(4)
open universe
nucleated bubble: O(3,1)
=open universe
dS vacuum
bubble wall
12
3. Open inflation in the landscape
universe is inside nucleated bubble = open universe
• observational data imply 1-W < 10-2 : almost flat
•

two possibilities
1. inflation after tunneling was long enough (N>>60)
1  W0 = 1
“flat universe”
signatures from bubble collisions?
Sugimura, Yamuchi & MS (2012)
last scattering surface
us
colliding bubbles
13
2. inflation after tunneling was short enough (N = 50 ~ 60)
1  W  102 ~ 103 “open universe”
0
any signatures in large angle CMB anisotropies?
Here we argue that we are already
seeing a couple of such signatures
on large angle CMB
 dipolar statistical anisotropy
 tensor-scalar ratio: Planck vs BICEP2
4. Dipolar statistical anisotropy
T
 T 
 1  A cos   
T
 T 0
l l  1Cl
l
14
15
dipole asymmetry observed by WMAP/Planck
asymmetry of Cl in the direction of ell=1
dipole asymmetry of Cl in the direction
maximizing the asymmetry
16
Planck XXIII
T
 T 
 1  A cos   
T
 T iso
A  0.07
creation of open universe &
supercurvature mode
wavelength > curvature radius
“supercurvature” mode
open universe
dS vacuum
bubble wall
17
18
Gradient of a field over the horizon scale
= Super-curvature mode in open inflation
observable
universe
may modulate the amplitude of
perturbation depending on the direction.
19
a viable model
Kanno, MS & Tanaka (2013)
L
1
1
1 2
1 2 2
2
2
2
2 2

f

V
(
f
)


s

m
s

f
s

c

mc c
 
 
  
s
2
2
2
2
(s, c )-sector ~ "axion"-like
f : inflaton
s : isocurvature mode with super-curvature perturbation s
c : curvaton
HF : Hubble at
false vacuum
H F2
ms2  H 2
 curvature perturbation is almost Gaussian
f 2  H 2 ,
c 2
H2
 2
f (s  s )
V (f )
mc2
20
2
 2 2

H
2
PS (k )   Nf H  N c 2

f (s  s )  k / a  H

dipolar modulation through f (s )
c-field is a “free” field (no direct coupling to inflaton)
no significant non-Gaussianity, nor quadrupole
s-field eventually dies out ( because ms ~ H )
modulation is larger on larger scales
= consistent with Planck 2013
21
5. r-controversy?:Planck vs BICEP2
r < 0.1 if ns=const.
r ~ 0.2
resolved if dns /dlnk<0 (running spectral index)
broken spectrum is more favored than running
Abazajian et al. (2014)
22
observational indication
running spectrum
broken spectrum
break
H0-1
curvature
radius?
broken spectrum is favored
Bayesian evidence
Abazajian et al.,
arXiv:1403.5922 [astro-ph.CO]
23
fast-roll phase in open inflation

curvature dominant phase
right after tunneling, H is
dominated by curvature:
a  t, f  

V  f 
4
V (f )
r
1
H 
 2
2
3M P a
2
t
fast-roll phase
fast-roll phase
kinetic energy grows until
slow-roll phase
f
H *1
f2
 V at t*  2.3
2
2
V
M P2  V  
V 
: “slow-roll” parameter


2 V 
for V ~ 0.01, there is N =Ht ~ 20 e-folds of fast-roll phase
24
theoretical (qualitative) predictions
• suppression of curvature perturbation during first
  V1/2 e-folds (↔large scales) of open inflation
N ~
H2
PS ( k ) 
:
2
2
2 (2 ) M pl
H
  2
H
~  
V
• no suppresion in tensor perturbation
8H 2
PT (k ) =
(2 )2 M pl2
PT
 16 V
r
 16 ~
PS
• curvature scale at the end of fast-roll phase
Rcurv
t*
1/2


2.3

 ~ 20 if V  0.01
V
1
1
H
H*
WK 
~ 0.01
25
scalar & tensor spectrum in open inflation
Linde, MS & Tanaka (1999)
scalar
tensor
(no suppression)
scalar suppression begins
indeed at smaller scales
curvature
radius
H0-1 if WK ≈ 0.003
26
6. Summary
1. Dipolar statistical anisotropy requires a
non-standard inflation scenario
Modulation of the fluctuation amplitude by
supercurvatue mode in open inflation
2. Tension between Planck & BICEP2 may be
resolved if Ps(k) is suppressed on large scales
Suppression due to fast-roll phase at the
beginning of in open inflation
These may be signatures from string landscape
27
• embedding models in string theory?
• any other testable predictions?
• other features in CMB? LSS? ...?
We are beginning to test
string landscape!