Evolutionary effects in one-bubble open inflation for string landscape

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 MG12@Paris

2. 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 ??? MG12@Paris

3. 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. Eternal inflating “megaverse” MG12@Paris

4. Eternal Inflation and metastablevacua + • Superstring theory: most promising candidate for theory of everything The enormous number of metastablevacua appears in LEET of string theory! We can choose different metastable vacuum We should mention that eternal inflation divide whole universe into exponentially large domains corresponding to different metastable vacuum . One can see that the eternal inflation leads to the exponentially production of string vacuum. String Landscape Eternal inflating “megaverse” MG12@Paris We are focusing !

5. 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 tunneling tunneling • Can we observe these effects ??? • What’s the observational properties ??? • … Global minimum MetastableVacua Susskind (‘03), Freivogel and Susskind (‘04),Freivogel et al. (‘06),… Garriga, Tanaka and Vilenkin (‘99)Bousso and Polchinski (‘00),Douglas and Kachru (‘07),… MetastableVacua MG12@Paris

6. Outline Introduction (finish) One bubble open Inflation and dynamics inside bubble Conclusion and future direction MG12@Paris

7. Open Inflation 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 adS. 2. Bubble nucleation occurs through quantum tunneling. = Coleman-De Luccia (CDL) instanton Analytic continuation to Lorentzian regime leads to O(3,1) open expanding bubble 3. Vfalse potential Vtrue O(4) sym → O(3,1) sym 4. slow-roll inflation and reheating occurs. It solves entropy problem in this regime. local minimum global minimum scalar field Gott III (‘82), Got III and Statler (‘84),Sasaki, Tanaka, Yamamoto and Yokoyama (‘93), … MG12@Paris

8. Open Inflation Open FRW universe time const surface • action • We assume O(4)-symmetric bounce solution : Analytic continuation to Lorentz regime leads to openexpanding universe. Euclidean region Cauchy surface MG12@Paris

9. Dynamics inside our bubble We found that in string landscape, “dynamics inside bubble” is most important ! The condition for Coleman-De Lucciainstanton [ 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 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 second-stage of the inflation becomes much lower than the Planck density: Hfalse >> Htrue steep slope low energy There might exist the rolling down phase with sufficient long period !!! field MG12@Paris

10. Tensor-type perturbation One can expand metric perturbation by using mode function: Square amplitude is given by [Garriga, Montes, Sasaki and Tanaka (’98,’99)] Tunneling effects : Transfer inside bubble Spatial harmonic function on open universe H-1 Log[physical scale] Transfer includes the information of the dynamics inside our bubble ! Large angle Sasaki, Tanaka and Yakushige (‘97) showed that thelarge angle modes gives significant contribution to spectrum in thin-wall case. where Small angle High energy Log[a] present time MG12@Paris

11. Amplitude for tensor-type perturbation Fluctuations evolves Fluctuations floze-in We found that the amplitude can be estimated by using following two time-scale ! tfroze: froze-intime1/a2=ρφpot+ρφkin teq:potential-kineticequality time ρφpot=ρφkin where Energy density 1/a2 : energy density for openness attractor Log ρφpot : potential energy density H2 =1/a2+ρφpot+ρφkin ????? ρφkin : kinetic energy density ρφpot What’s happened??? ????? ρφkin 1/a2 teq tfroze Log[scale factor] MG12@Paris Nucleation point

12. Evolution inside bubble Open FRW universe Just after the tunneling, the dominant component of the universe is spatial curvature : 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 teq:potential-kineticequality time ρφpot=ρφkin Euclidean region tfroze: froze-intime1/a2=ρφpot+ρφkin MG12@Paris

13. Very Steep Slope potential Large Evolutionary effects : Hfalse>> Htrue • tfroze>> teq We found that ρφpotand ρφkin dramatically falls downaftert=teq!!! • Same as usual thin-wall case !!! Very steep slope ρφpot 1/a2 low energy Hfalse2 field Froze-in Amplitude is determined by the Hubble inside the bubble even in steep slope ! Htrue2 ρφkin usual scale-invariant spectrum MG12@Paris

14. Marginal Steep Slope potential Marginal Evolutionary effects : Hfalse> Htrue • tfroze~ teq We found that ρφpotand ρφkin dramatically falls down after t=teq~tfroze!!! • Large enhancement can occur !!! Merginal steep slope 1/a2 low energy ρφpot Hfalse2 Amplitude for large angle mode is determined by the Hubble outside the bubble. field ρφkin Htrue2 Amplitude for small angle mode is determined by the Hubble inside the bubble. MG12@Paris

15. Marginal Steep Slope • For small mode index = large anglemode • spectrum become enhanced ! • For large mode index = small angle mode • spectrum is scale-invariant ! Potentialinside bubble Inflation field Large evolutionary effects Log[power spectrum] Log[mode index] Thin-wall MG12@Paris

16. 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, Future direction • Mild slope • Very steep slope • Marginal steep slope Same as usual thin-wall case • Scalar-type perturbations leads to supercurvature mode. • Multi-field extension leads to classical anisotropy. • Non-Gaussianity due to the vacuum choice Large enhancement can occur if one chooses specific parameters. MG12@Paris