2009/7/17 - PowerPoint Presentation

Slide1

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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, SQG1Slide2

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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 : Ω

0,standard

～

1

Standard inflationary

s

cenario

leads to

[e.g.

Linde

(‘08)]Slide3

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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 !Slide4

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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 Landscape

We are focusing !

Eternal inflating

“

megaverse

”Slide5

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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

Vacua

tunneling

tunneling

Can we observe these effects ???

What’s the observational properties ???

…Slide6

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Outline

Introduction (finish)One bubble open Inflation and dynamics inside bubble

Conclusion and future directionSlide7

potential

s

calar field

local minimum

global minimum

V

false

V

true

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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) sy

m

→

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

.Slide8

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Euclidean region

time const surface

Open FRW universe

Open Inflation

We assume O(4)-symmetric bounce solution :

Analytic continuation to Lorentz regime

leads to

open

expanding universe.

Cauchy surface

actionSlide9

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We found that in string landscape, “dynamics inside bubble” is most important !

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),…]

H

false

>>

H

true

Dynamics inside our bubble

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

s

teep slope

field

l

ow energySlide10

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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 bubbleSlide11

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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]

Energy

density

Log

t

eq

t

froze

What’s happened???

ρ

φpot

ρ

φkin

1/a

2

Fluctuations evolves

Fluctuations

floze

-in

a

ttractor

Nucleation point

?????

?????

H

2

=

1/a

2

+

ρ

φpot

+

ρ

φkin

1/a

2

: energy density for openness

ρ

φpot

: potential energy density

ρ

φkin

: kinetic energy density

where

Amplitude for tensor-type perturbationSlide12

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Evolution inside bubble

Just 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

t

froze

:

froze-in

time

1/a

2

=

ρ

φpot

+

ρ

φkin

t

eq

:

potential

-kinetic

equality time

ρ

φpot

=

ρ

φkinSlide13

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Very Steep Slope

Large Evolutionary effects : Hfalse

>> Htrue

potential

Very s

teep slope

field

l

ow energy

Froze-in

1/a

2

ρ

φkin

ρ

φpot

H

false

2

H

true

2

S

ame

as

usual

thin-wall

case !!!

t

froze

>>

t

eq

We found that

Amplitude is determined by

the Hubble

inside

the bubble

even in steep slope !

usual scale-invariant spectrum

ρ

φpot

a

nd

ρ

φkin

dramatically

falls down

after

t=

t

eq

!!!Slide14

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Marginal Steep Slope

1/a

2

ρ

φpot

H

false

2

H

true

2

ρ

φkin

Marginal Evolutionary effects :

H

false

>

H

true

Large enhancement

can occur !!!

t

froze

~

t

eq

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

in

side

the bubble.

ρ

φpot

a

nd

ρ

φkin

dramatically

falls down

after

t=

t

eq

~t

froze

!!!

potential

Merginal

s

teep slope

field

l

ow energySlide15

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Log[power spectrum]

Log[mode index]

Marginal Steep Slope

Potential

inside bubble

Inflation field

For s

mall mode index =

l

arge angle

mode

spectrum become

enhanced

!

For large mode index = small angle mode

spectrum is

scale-invariant

!

Thin-wall Large evolutionary effectsSlide16

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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