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) SQG1

Spatially quite flat universe  Ω 0,obs ～１ : spatially quite flat WMAP observational data indicates that Completely consistent Why should we study “ openness ” now ??? Why should we study “ openness ” now ??? [Dunkley et al. (‘08)]  almost flat : Ω 0,standard ～ 1 Standard inflationary scenario leads to [e.g. Linde (‘08)]

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 !

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”

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 The inflationary model with tunneling transition = Open Inflation Landscape Global minimum Metastable Vacua tunneling  Can we observe these effects ???  What’s the observational properties ???  …

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 V false V true 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. 4.4.

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  action

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),…] H false >> H true 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

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

t froze : froze-in time 1/a 2 = ρ φpot + ρ φkin t eq : potential-kinetic equality time ρ φpot = ρ φkin 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 attractor 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 perturbation

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 φkin

 Very Steep Slope Large Evolutionary effects : H false >> H true potential Very steep slope field low energy Froze-in 1/a 2 ρ φkin ρ φpot H false 2 H true 2 Same 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 and ρ φkin dramatically falls down after t=t eq !!!

 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 inside the bubble. ρ φpot and ρ φkin dramatically falls down after t=t eq ~t froze !!! potential Merginal steep slope field low energy

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

 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