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2009/7/17 MG12@Paris 1
Evolutionary effects in one-bubble open inflation
for string landscape
Daisuke YAMAUCHI Yukawa Institute for Theoretical Physics,
Kyoto University
Collaborators :: A. Linde (Stanford), M. Sasaki, T. Tanaka, A. Naruko (YITP)
MG12@Paris, SQG1
2009/7/17 MG12@Paris 2
Spatially quite flat universe
Ω0,obs~1: spatially quite flat
WMAP observational data indicates that
Completely consistent
Why should we study“ openness ” now ???
[Dunkley et al. (‘08)]
almost flat : Ω0,standard~ 1
Standard inflationary scenario leads to
[e.g. Linde (‘08)]
2009/7/17 MG12@Paris 3
Eternal Inflation
From Linde (‘08)
Eternal inflating “megaverse”
We are here.End for Inflation
Inflating regime
There will be a end for inflation at a particular point.BUT, there will be no end for the evolution of the universe as a whole in eternal inflation.
Large quantum fluctuations produced during inflation leads to production of new inflationary domains, which is eternal process of self-production of the universe !
2009/7/17 MG12@Paris 4
We should mention that eternal inflation divide whole universe into exponentially large domains corresponding to different metastable vacuum .
Eternal Inflation and metastable vacua
The enormous number of metastable vacua appears in LEET of string theory!
Superstring theory : most promising candidate for theory of everything
We can choose different metastable vacuum
+
One can see that the eternal inflation leads to the exponentially production of string vacuum.
String LandscapeWe are focusing !
Eternal inflating “megaverse”
2009/7/17 MG12@Paris 5
Susskind (‘03), Freivogel and Susskind (‘04),Freivogel et al. (‘06),…
Properties of “String Landscape”• There exists enormous number of metastable de Sitter vacuum .
• The global universe is an eternal inflating “megaverse” that is continually producing small “pocket universe”.
• The tunneling transition to other metastable vacuum always occurs. ….
Garriga, Tanaka and Vilenkin (‘99) Bousso and Polchinski (‘00),Douglas and Kachru (‘07), …
These lead to a natural realization of
The inflationary model with tunneling transition
= Open Inflation
Landscape
Global minimum
Metastable Vacua
Metastable Vacuatunneling
tunneling
Can we observe these effects ??? What’s the observational properties ??? …
2009/7/17 MG12@Paris 6
Outline
1. Introduction (finish)
2. One bubble open Inflation and dynamics inside bubble
3. Conclusion and future direction
potential
scalar field
local minimum global minimum
Vfalse
Vtrue
2009/7/17 MG12@Paris 7
The scalar field is trapped in the false vacuum during sufficiently long period. It solves homogeneity problem in this regime and universe is well approximated by a dS.
1.
Bubble nucleation occurs through quantum tunneling.2.= Coleman-De Luccia (CDL) instanton
Analytic continuation to Lorentzian regime leads to O(3,1) open expanding bubble
3.
O(4) sym → O(3,1) sym
Gott III (‘82), Got III and Statler (‘84), Sasaki, Tanaka, Yamamoto and Yokoyama (‘93), …
Open Inflation The inflationary model with tunneling transition
slow-roll inflation and reheating occurs. It solves entropy problem in this regime.
4.
2009/7/17 MG12@Paris 8
Euclidean region
time const surfaceOpen FRW universe
Open Inflation
We assume O(4)-symmetric bounce solution :
Analytic continuation to Lorentz regime leads to open expanding universe.
Cauchy surface
action
2009/7/17 MG12@Paris 9
We found that in string landscape, “dynamics inside bubble” is most important !
B) The inflation model with KKLT mechanism
From standard SUSY phenomena the energy scale of the second-stage of the inflation becomes much lower than the Planck density:
[ Linde(‘08), Kallosh and Linde (‘04), Kachru, Kallosh, Linde and Trivedi (‘03),…]
Hfalse >> Htrue
Dynamics inside our bubble
A) The condition for Coleman-De Luccia instanton
The slow-roll inflation can not begin immediately after CDL tunneling.
[ Jensen and Steinhardt (‘84), Linde (‘99), Linde, Sasaki and Tanaka (‘98), … ]
If this condition is broken, HM instanton, which leads to the huge density perturbation and inhomogeneous domains, appears.
There might exist the rolling down phase with sufficient long period !!!
potential
steep slope
field
low energy
2009/7/17 MG12@Paris 10
Tensor-type perturbation One can expand metric perturbation by using mode function:
Square amplitude is given by
where
[Garriga, Montes, Sasaki and Tanaka (’98,’99)]
Spatial harmonic function on open universe
Transfer includes the information of the dynamics inside our bubble !
Tunneling effects
Sasaki, Tanaka and Yakushige (‘97) showed that the large angle modes gives significant contribution to spectrum in thin-wall case.
present time
Large angle
Small angle
Log[physical scale]
Log[a]
H-1
High energy
: Transfer inside bubble
2009/7/17 MG12@Paris 11
tfroze : froze-in time 1/a2=ρφpot+ρφkin
teq : potential-kinetic equality time ρφpot=ρφkin
We found that the amplitude can be estimated by using following two time-scale !
Log[scale factor]
EnergydensityLog
teq tfroze
What’s happened???
ρφpot
ρφkin1/a2
Fluctuations evolves
Fluctuations floze-in
attractor
Nucleation point
?????????? H2 =1/a2 + ρφpot + ρφkin
1/a2 : energy density for openness
ρφpot : potential energy density
ρφkin : kinetic energy density
where
Amplitude for tensor-type perturbation
2009/7/17 MG12@Paris 12
Evolution inside bubbleJust after the tunneling, the dominant component of the universe is spatial curvature :
Euclidean region
time const surface
Open FRW universe
Curvature dominant phase
From b.c. at the nucleation point, the potential can be well approximated as constant. Thus, one can solve EOM as a attractor solution:
Attractor solution
tfroze : froze-in time 1/a2=ρφpot+ρφkin
teq : potential-kinetic equality time ρφpot=ρφkin
2009/7/17 MG12@Paris 13
Very Steep SlopeLarge Evolutionary effects : Hfalse >> Htrue
potential
Very steep slope
field
low energy
Froze-in
1/a2
ρφkin
ρφpotHfalse2
Htrue 2
Same as usual thin-wall case !!!
tfroze >> teq We found that
Amplitude is determined by the Hubble inside the bubble
even in steep slope !
usual scale-invariant spectrum
ρφpot and ρφkin dramatically
falls down after t=teq !!!
2009/7/17 MG12@Paris 14
Marginal Steep Slope
1/a2
ρφpotHfalse2
Htrue 2
ρφkin
Marginal Evolutionary effects : Hfalse > Htrue
Large enhancement can occur !!!
tfroze ~ teq We found that
Amplitude for large angle mode is determined by the Hubble outside the bubble.
Amplitude for small angle mode is determined by the Hubble inside the bubble.
ρφpot and ρφkin dramatically
falls down after t=teq~tfroze!!!
potential
Merginal steep slope
field
low energy
2009/7/17 MG12@Paris 15
Log[power spectrum]
Log[mode index]
Marginal Steep Slope
Potential inside bubble
Inflation field
For small mode index = large angle mode spectrum become enhanced ! For large mode index = small angle mode spectrum is scale-invariant !
Thin-wall
Large evolutionary
effects
2009/7/17 MG12@Paris 16
We considered the possibility that “one-bubble open inflation scenario” can realize in “string landscape”. Especially, we presented power spectrum under the conditions that one expects in string landscape. we found that the amplitude of the fluctuation is determined not by Hubble outside bubble but by the one inside bubble even if the potential tilt is large.
Conclusion
Mild slope Very steep slope Marginal steep slope
After the transition,
Same as usual thin-wall case
Large enhancement can occur if one chooses specific parameters.
Future direction Scalar-type perturbations leads to supercurvature mode. Multi-field extension leads to classical anisotropy. Non-Gaussianity due to the vacuum choice