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Quintom Bounce with a Galileon Model

Learn about the Quintom bounce theory in Galileon models and its implications for early universe cosmology, including alternatives to inflation and the role of Galileon theories in avoiding singularity problems. Speaker: Taotao Qiu

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Quintom Bounce with a Galileon Model

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  1. Quintom Bounce with a Galileon Model Chung-Yuan Christian University, Taiwan & Institute of High Energy Physics, Beijing Based on 1108.0593 Collaborated with J. Evslin, Y. F. Cai, M. Z. Li, X. M. Zhang Speaker: Taotao Qiu

  2. Outline • Why Quintom bounce? • Quintom bounce of galileon model • Background • Perturbation • Conclusion • outlook

  3. WHY QUINTOM BOUNCE?

  4. Standard Models of the Early Universe Big Bang Cosmology vs. Inflation Cosmology Big Bang Inflation Problems/constraints from theoretical/observational aspects: (such as BBN,CMB(COBE), etc) The age of galaxies The redshift of the galactic spectrum The He abundance The prediction of CMB temperature Flatness problem Horizon problem Monopole problem Singularity problem Structure formation problem

  5. Standard Models of the Early Universe Big Bang Cosmology vs. Inflation Cosmology Big Bang Inflation Problems/constraints from theoretical/observational aspects: (such as BBN,CMB(COBE), etc) The age of galaxies The redshift of the galactic spectrum The He abundance The prediction of CMB temperature Flatness problem Horizon problem Monopole problem Singularity problem Structure formation problem

  6. The Alternatives of Inflation • Pre-big bang Scenario • Ekpyrotic Scenario • String gas/Hagedorn Scenario • Non-local SFT Scenario • Bouncing Scenario

  7. Ekpyrotic Model The collision of two M branes in 5D gives rise to a nonsingular cyclic universe, and the description of effective field theory in 4D is 1 DE domination 2 decelerated expansion 3 turnaround 4 ekpyrotic contracting phase 5 before big crunch 6 a singular bounce in 4D 7 after big bang 8 radiation domination 9 matter domination J. Khoury, B. Ovrut, P. Steinhardt and N. Turok, Phys. Rev. D 64, 123522 (2001)

  8. Ekpyrotic Model The collision of two M branes in 5D gives rise to a nonsingular cyclic universe, and the description of effective field theory in 4D is 1 DE domination 2 decelerated expansion 3 turnaround 4 ekpyrotic contracting phase 5 before big crunch 6 a singular bounce in 4D 7 after big bang 8 radiation domination 9 matter domination Failure of effective field theory description, uncertainty involved in perturbations.

  9. (Non-singular) Bounce Cosmology IR size with Low energy scale contraction expansion Singularity problem avoided! Formalism: Contraction: Expansion: Bouncing Point: Nearby: ( ) In order to connect this process to the observable universe (radiation dominant, matter dominant, etc), w goes to above -1 So w crosses -1, namely Quintom bounce! Y. Cai, T. Qiu, Y. Piao, M. Li and X. Zhang, JHEP 0710:071, 2007 If w>-1 at the beginning, w will cross twice.

  10. Realization of a Quintom Bounce Quintom realization: No-Go theorem As for any kind of matter, which is (1) in 4D classical Einstein Gravity, (2)described by single simple component (either perfect fluid or single scalar field with lagrangian as ), and (3) coupled minimally to Gravity or other matter, its Equation of State can never cross the cosmological constant boundary (w=-1). Bo Feng et al., Phys. Lett. B 607, 35 (2005); A. Vikman, Phys. Rev. D 71, 023515 (2005); Gong-Bo Zhao et al., Phys. Rev. D 72, 123515 (2005); J. Xia, Y. Cai, T. Qiu, G. Zhao and X. Zhang, Int.J.Mod.Phys.D17:1229-1243,2008. To realize Quintom, one of the conditions should be violated i) Double field Quintom bounce: Y. Cai, T. Qiu, R. Brandenberger, Y. Piao, X. Zhang, JCAP 0803:013,2008; Y. Cai, T. Qiu, J. Xia, X. Zhang, Phys.Rev.D79:021303,2009. ii) Single field Quintom bounce with higher derivative term: (also known as Lee-Wick Bounce) Y. Cai, T. Qiu, R. Brandenberger, X. Zhang, Phys.Rev.D80:023511,2009; J. Karouby, T. Qiu, R. Brandenberger, Phys.Rev.D84:043505,2011.

  11. Galileon Theories Problem with Quintom bounce: Usually, both of the two cases have more than two DYNAMICAL degrees of freedom, which will contain ghost modes. Recently: a kind of Galileon theory has been proposed! Galileon Models: Lagrangian with higher derivative operator, but the equation of motion remains second order, so the model can have w cross -1 without ghost mode. • Nicolis et al., Phys.Rev.D79:064036,2009; • C. Deffayet et al., Phys.Rev.D79:084003,2009. Basically 5 kinds of Galileon model: But can be generalized… C. Deffayet et al., arXiv:1103.3260 [hep-th]

  12. Cosmological Applications of Galileon Theories • Galileon as dark energy models: • R. Gannouji,M. Sami, Phys.Rev.D82:024011,2010. • A. De Felice, S. Tsujikawa, Phys.Rev.Lett.105:111301,2010. • C. Deffayet,O. Pujolas,I. Sawicki, A. Vikman, JCAP 1010:026,2010. • Galileon as inflation and slow expanstion models: • P. Creminelli, A. Nicolis, E. Trincherini, JCAP 1011:021,2010. • T. Kobayashi,M. Yamaguchi,J. Yokoyama, Phys.Rev.Lett.105:231302,2010. • C. Burrage,C. de Rham,D. Seery,A. Tolley, JCAP 1101:014,2011. • K. Kamada, T. Kobayashi, M. Yamaguchi, J. Yokoyama, Phys.Rev.D83:083515,2011. • Z. Liu, J. Zhang, Y. Piao, arXiv:1105.5713 [astro-ph.CO] • Observational constraints on Galileon models: • S. Nesseris,A. De Felice, S. Tsujikawa, Phys.Rev.D82:124054,2010 • A. Ali,R. Gannouji, M. Sami, Phys.Rev.D82:103015,2010. • Galileon as spherically symmetric models: • D. Mota, M. Sandstad,T. Zlosnik, JHEP 1012:051,2010. • … … … … … … Can Galileon be used as bounce models???

  13. Quintom bounce with a galileon model BackgroundPerturbation

  14. Our New Bounce Model with Galileon The action: which was also used in arXiv: 1007.0027 for “Galileon Genesis”. Stress energy tensor: From which we get energy density and pressure: where

  15. Solution for Bounce to Happen From the Friedmann Equation we get the Hubble parameter: where Reality of square root: So we get one property of the field: evolve as a monotonic function! Considering , and thus is monotonic increasing, so the first term in H, is always larger than 0. In order to have bounce, H must reach 0, so negative branch is chosen.

  16. Asymptotic solution of Our Model Equation of motion: with Hubble parameter: In contracting phase: Analysis of the asymptotic behavior when inconsistent ! I. Terms in EoM has different orders of t EoM becomes: II. inconsistent ! i) inconsistent ! ii) consistent ! iii) The only consistent solution has a radiation dominant behavior!

  17. Numerical Plots of Our Model (1) Plots of Hubble parameter and scale factor in our model: Parameter choice: Reheating? Bounce can happen naturally in our model around t=30.

  18. Numerical Plots of Our Model (2) Plots of field and EoS w in our model: behaves as a monotonic function, and the equation of state is approximately 1/3 (radiation-dominant like) in contracting phase, and cross -1 before bounce in our model.

  19. QUINTOM BOUNCE WITH A GALILEON MODELBACKGROUNDPERTURBATION

  20. Perturbation Theory • Theoretical aspects: stability must be guaranteed! • Observational aspects: should obtain a (nearly) scale-invariant power spectrum and small tensor-to-scalar ratio Why perturbations? Primordial perturbations provide seeds for structure formation and explains why our current universe is not complete isotropic. Two constraints for linear perturbations:

  21. Perturbations of Our Bounce Model Perturbed metric in ADM form: lapse function inverse shift vector Perturbed action: Constraint equations: Gauge: uniform Solution:

  22. Stability of Perturbation of Our Model Up to second order There are two kinds of instabilities at linear level: • Ghost instability: • Gradient instability: In our model, is positive definite: no ghost instability! is model dependent: have to be checked numerically.

  23. Stability of Perturbation of Our Model Numeric plots for and Both and are positive all over the bouncing process, and we have which also behaves like radiation!

  24. Spectrum of Perturbation of Our Model Equation of motion: set In radiation dominant phase: Effective mass like a massless scalar field! Blue spectrum inconsistent with observational data! Solution:

  25. Mechanism of Getting Scale Invariant Power Spectrum An alternative: Curvaton Mechanism Curvaton: a light scalar field other than inflaton to produce curvature perturbation. The simplest curvaton model: with The equation of motion: where Power spectrum: Solution: Curvature perturbation: For Gaussian part: D. Lyth and D. Wands, Phys.Lett.B524:5-14,2002.

  26. Curvaton Mechanism in Our Model Our model: due to the background, in order to have scale invariant power spectrum, curvaton have to couple kinetically to the Galileon field Our curvaton action: The equation of motion: In radiation dominant phase: The general solution:

  27. Scale Invariant Power Spectrum from Curvaton Subhorizon solution: Superhorizon solution: From matching condition: and are independent of k! There are two cases of getting scale invariant power spectrum: • q=2: • q=-4: constant growing decaying constant

  28. Back reaction of the Curvaton Field Question: will the growth of energy density of destroy the process of bounce? The energy density of : From the equation of motion: In contracting phase where the universe is radiation-like: In order for not to destroy the background evolution: one needs In our case which can produce scale invariant power spectrum: • q=2: Safe from back reaction of • q=-4: Needs severe fine-tuning.

  29. Tensor Perturbation of Our Model Perturbed metric: Perturbed action (up to second order): Expand the tensor perturbation: Equation of motion:

  30. Tensor Perturbation of Our Model In radiation dominant phase: like a massless scalar field! Solution: Tensor spectrum: Spectrun index: Blue spectrum! In observable region we have , namely the spectrum is severely suppressed, so the tensor-to-scalar ratio WMAP data predicts quite small r, so is consistent with our model! D. Larson et al. [WMAP collaboration], arXiv:1001.4635 [astro-ph.CO].

  31. Conclusion • Bounce needs equation of state w cross -1, namely Quintom • Bounce can be in form of galileon, where there are only two dynamical degrees of freedom and ghost can be eliminated. • Quintom bounce in Galileon form: • Background behavior: Radiation-dominant like. • Perturbation1:free from instability but cannot provide scale invariant power spectrum • Perturbation2: The way of providing scale-invariant power spectrum is curvaton. In our model there are two cases. • Perturbation3:The back reaction is small in one case, but the other case needs fine tuning. • Perturbation4: The tensor spectrum is blue and the tensor-to-scalar ratio is small.

  32. Outlook • Final state of reheating • Nongaussianities

  33. Reheating Reheating is important in inflationary scenario! Through reheating, inflaton decay to matter and radiation after inflation Reheating mechanisms: • Normal:L. Kofman, A. Linde, A. Starobinsky, Phys.Rev.Lett.73:3195-3198,1994. • Geometric: B. Bassett, S. Liberati, Phys.Rev.D58:021302,1998. • Curvaton: Bo Feng, Ming-zhe Li, Phys.Lett.B564:169-174,2003. • …… The motivation of reheating in our bounce model: • In galileon cosmology, reheating can help avoid divergence • L. Levasseur, R. Brandenberger, A. Davis, arXiv:1105.5649 • In bouncing cosmology, reheating is also important and maybe different from normal inflation • T. Qiu, K. Yang, JCAP 1011:012,2010. Y. Cai, R. Brandenberger, X. Zhang, arXiv:1105.4286  “Galileon genesis”, P. Creminelli et al., 1007.0027 Our bounce model What is the reheating process like of our Galileon bounce model???

  34. Non-gaussianities Non-Gaussianities is important for 1) meeting the more and more accurate observational data and 2) distinguishing the over models for early universe • WMAP-7 data: • Planck data: Definition: Observational constraints: E. Komatsu et al., arXiv:1001.4538. Planck collaboration, astro-ph/0604069. Theoretical results: • For canonical single scalar field inflation: • X. Chen, M. Huang, S. Kachru, G. Shiu, JCAP 0701:002,2007. • For bounce cosmology: new shape with sizable amplitude and • Y. Cai, W. Xue, R. Brandenberger, X. Zhang, JCAP 0905:011,2009. What will the non-Gaussianities behave like for our Galileon bounce model???

  35. 谢谢！ THANKS FOR ATTENTION!

  36. Galileon genesis Our bounce model “Galileon genesis”, 1007.0027

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