Transcript Open Inflation for string landscape

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)
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Spatially quite flat universe
WMAP observational data
indicates that
 Ω0,obs～１
: spatially quite flat
[Dunkley et al. (‘08)]
Completely consistent
Standard inflationary scenario
leads to
 almost flat : Ω0,standard～1
[e.g. Linde (‘08)]
Why should we study
“ openness ” now ???
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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 !
From Linde (‘08)
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.
Inflating regime
End for Inflation
We are here.
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Eternal inflating “megaverse”
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Eternal Inflation and metastable vacua
We should mention that eternal inflation divide whole universe into exponentially
large domains corresponding to different metastable vacuum .
+
 Superstring theory : most promising candidate for theory of everything
The enormous number of metastable vacua appears in LEET of string theory!
We can choose different
metastable vacuum
One can see that the eternal inflation
leads to the exponentially production
of string vacuum.
String Landscape
We are focusing !
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Eternal inflating “megaverse”
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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. ….
These lead to a natural realization of
The inflationary model
with tunneling transition
= Open Inflation
Landscape
Global minimum
tunneling
tunneling
Metastable Vacua
 Can we observe these effects ???
 What’s the observational properties ???
…
Metastable Vacua
Susskind (‘03), Freivogel and Susskind (‘04),Freivogel et al. (‘06),…
Garriga, Tanaka and Vilenkin (‘99) Bousso and Polchinski (‘00),Douglas and Kachru (‘07), …
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Outline
1. Introduction (finish)
2. One bubble open Inflation and dynamics
inside bubble
3. Conclusion and future direction
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Open Inflation
potential
The inflationary model with tunneling transition
1.
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.
2. Bubble nucleation occurs through quantum tunneling.
= Coleman-De Luccia (CDL) instanton
3.
Vfalse
Vtrue
Analytic continuation to Lorentzian regime leads
to O(3,1) open expanding bubble
4. slow-roll inflation and reheating occurs. It solves
entropy problem in this regime.
O(4) sym → O(3,1) sym
scalar field
local minimum
global minimum
Gott
III (‘82), Got III and Statler (‘84), Sasaki,
Tanaka, Yamamoto and Yokoyama (‘93), … 7
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Open Inflation
Open FRW universe
time const surface
 action
 We assume O(4)-symmetric bounce solution :
Euclidean region
Analytic continuation to Lorentz regime
leads to open expanding universe.
Cauchy surface
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Dynamics inside our bubble
We found that in string landscape, “dynamics inside bubble” is most important !
A) The condition for Coleman-De Luccia instanton
[ 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.
The slow-roll inflation can not begin immediately after CDL tunneling.
potential
B) The inflation model with KKLT mechanism
[ Linde(‘08), Kallosh and Linde (‘04), Kachru, Kallosh, Linde and Trivedi (‘03),…]
From standard SUSY phenomena the energy scale of the secondstage of the inflation becomes much lower than the Planck density:
Hfalse >> Htrue
steep
slope
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low
energy
field
There might exist the rolling down phase
with sufficient long period !!!
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Tensor-type perturbation
One can expand metric perturbation by using mode function:
Spatial harmonic function on open universe
Square amplitude is given by
Tunneling effects
[Garriga, Montes, Sasaki
and Tanaka (’98,’99)]
where
: Transfer inside bubble
Log[physical scale]
Transfer includes the information of
the dynamics inside our bubble !
H-1
Large angle
Sasaki, Tanaka and Yakushige (‘97) showed
that the large angle modes gives significant
contribution to spectrum in thin-wall case.
Small angle
High
energy
Log[a]
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present time
Amplitude for tensor-type perturbation
We found that the amplitude can be estimated by using following two time-scale !
tfroze : froze-in time 1/a2=ρφpot+ρφkin
teq : potential-kinetic equality time ρφpot=ρφkin
where
Energy
Log density
1/a2 : energy density for openness
Fluctuations Fluctuations
evolves
floze-in
ρφpot
What’s
happened???
ρφkin
ρφpot : potential energy density
ρφkin : kinetic energy density
?????
?????
H2 =1/a2 + ρφpot + ρφkin
1/a2
attractor
teq
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Nucleation
point
tfroze
Log[scale factor]
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Evolution inside bubble
Just after the tunneling, the dominant
component of the universe is spatial curvature :
Open FRW universe
time const surface
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
Euclidean region
teq : potential-kinetic equality time ρφpot=ρφkin
tfroze : froze-in time 1/a2=ρφpot+ρφkin
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potential
 Very Steep Slope
Large Evolutionary effects : Hfalse >> Htrue
We found that
 tfroze >> teq
 Same as usual thin-wall case !!!
Hfalse2
ρφpot
Htrue 2
ρφpot and ρφkin dramatically
falls down after t=teq !!!
1/a2
low
energy
field
Froze-in
ρφkin
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Very steep
slope
Amplitude is determined by
the Hubble inside the bubble
even in steep slope !
usual scale-invariant spectrum
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 Marginal Steep Slope
potential
Marginal Evolutionary effects : Hfalse > Htrue
We found that
 tfroze ~ teq
 Large enhancement can occur !!!
1/a2
Hfalse2
ρφpot and ρφkin dramatically
falls down after t=teq~tfroze!!!
ρφpot
Htrue 2
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Merginal
steep slope low
energy
field
Amplitude for large angle mode
is determined by
the Hubble outside the bubble.
ρφkin
Amplitude for small angle mode
is determined by
the Hubble inside the bubble.
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 Marginal Steep Slope
 For small mode index = large angle mode
spectrum become enhanced !
Log[power spectrum]
 For large mode index = small angle mode
spectrum is scale-invariant !
Large
evolutionary
effects
Log[mode index]
Potential
inside bubble
Inflation field
Thin-wall
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Conclusion
 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.
After the transition,
 Mild slope
 Very steep slope
 Marginal steep slope
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
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