Evolutionary effects in one-bubble open inflation for string landscape

16
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

description

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. Spatially quite flat universe. - PowerPoint PPT Presentation

Transcript of Evolutionary effects in one-bubble open inflation for string landscape

Page 1: Evolutionary effects  in one-bubble open inflation  for string landscape

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

Page 2: Evolutionary effects  in one-bubble open inflation  for string landscape

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)]

Page 3: Evolutionary effects  in one-bubble open inflation  for string landscape

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 !

Page 4: Evolutionary effects  in one-bubble open inflation  for string landscape

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”

Page 5: Evolutionary effects  in one-bubble open inflation  for string landscape

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 ??? …

Page 6: Evolutionary effects  in one-bubble open inflation  for string landscape

2009/7/17 MG12@Paris 6

Outline

1. Introduction (finish)

2. One bubble open Inflation and dynamics inside bubble

3. Conclusion and future direction

Page 7: Evolutionary effects  in one-bubble open inflation  for string landscape

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.

Page 8: Evolutionary effects  in one-bubble open inflation  for string landscape

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

Page 9: Evolutionary effects  in one-bubble open inflation  for string landscape

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

Page 10: Evolutionary effects  in one-bubble open inflation  for string landscape

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

Page 11: Evolutionary effects  in one-bubble open inflation  for string landscape

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 opennessρφpot : potential energy density

ρφkin : kinetic energy density

where

Amplitude for tensor-type perturbation

Page 12: Evolutionary effects  in one-bubble open inflation  for string landscape

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 surfaceOpen 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

Page 13: Evolutionary effects  in one-bubble open inflation  for string landscape

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 !!!

Page 14: Evolutionary effects  in one-bubble open inflation  for string landscape

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

Page 15: Evolutionary effects  in one-bubble open inflation  for string landscape

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

Page 16: Evolutionary effects  in one-bubble open inflation  for string landscape

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