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ASPECTS OF HORAVA-LIFSHITZ COSMOLOGY

Investigating cosmological scenarios in a universe governed by Horava-Lifshitz gravity, including phase-space analysis, bouncing solutions, observational constraints, thermodynamic aspects, and perturbative instabilities.

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ASPECTS OF HORAVA-LIFSHITZ COSMOLOGY

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  1. ASPECTS OF HORAVA-LIFSHITZ COSMOLOGY Emmanuel N. Saridakis Physics Department, University of Athens Greece E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  2. Goal • We investigate cosmological scenarios in a universe governed by Horava-Lifshitz gravity • Note: A consistent or interesting cosmology is not a proof for the consistency of the underlying gravitational theory E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  3. Talk Plan • 1) Introduction: Horava-Lifshitz gravity and cosmology • 2) Phase-space analysis and late-time cosmological behavior • 3) Bouncing solutions and cyclic behavior • 4) Observational Constraints • 5) Thermodynamic aspects • 6) Perturbative instabilities • 7) Conclusions-Prospects E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  4. Introduction • Horava-Lifshitz gravity: power-countingrenormalizable, UVcomplete • IR fixed point: General Relativity • Good UV behavior: Anisotropic, Lifshitz scalingbetween time and space • Theoretical and conceptual problems (instabilities etc)?Open subject. [Horava, PRD 79] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  5. Introduction: Horava-Lifshitz gravity (detailed-balanced) (extrinsic curvature) (Cotton tensor) [Kiritsis, Kofinas, NPB 821] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  6. Introduction: Horava-Lifshitz cosmology • Cosmological framework: (projectability) • Matter content: [Kiritsis, Kofinas, NPB 821] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  7. Introduction: Horava-Lifshitz cosmology • Friedmann Equations (under detailed balance): and [Kiritsis, Kofinas, NPB 821] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  8. Introduction: Horava-Lifshitz cosmology • FriedmannEquations (under detailed balance): and • Effectivedark energy: [Kiritsis, Kofinas, NPB 821] [Leon, Saridakis, JCAP 0911] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  9. Introduction: Horava-Lifshitz cosmology • FriedmannEquations (beyond detailed balance): • Effectivedark energy: [Elizalde et al, CQG 27] [Leon, Saridakis, JCAP 0911] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  10. Phase-space analysis • Transform cosmological system to its autonomous form: • Linear Perturbations: • Eigenvalues of determine type and stability of C.P [Leon, Saridakis, JCAP 0911] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  11. Phase-space analysis Detailed balance • P3: Stable with P11: Saddle with [Leon, Saridakis, JCAP 0911] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  12. Phase-space analysis • Beyond Detailed Balance (4D problem) • Stable solution with and (eternally expanding) • Small probability (non-hyperbolid C.P) for an Oscillating solution (The terms responsible for the bounce, and the c.c responsible for the turnaround) [Leon, Saridakis, JCAP 0911] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  13. Bounce and Cyclic behavior • Contracting ( ), bounce ( ), expanding ( ) near and at the bounce • Expanding ( ), turnaround ( ), contracting ( ) near and at the turnaround E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  14. Bounce and Cyclic behavior • Contracting ( ), bounce ( ), expanding ( ) near and at the bounce • Expanding ( ), turnaround ( ), contracting ( ) near and at the turnaround • Bounce and cyclicity can be easily obtained [Brandenberger, PRD 80] [Cai, Saridakis, JCAP 0910] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  15. Bounce and Cyclic behavior • Input: oscillatory • Output: • Reconstructed [Cai, Saridakis, JCAP 0910] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  16. Bounce and Cyclic behavior • Input: • Output: [Cai, Saridakis, JCAP 0910] [Cai, Saridakis, JCAP 0910] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010 E.N.Saridakis - Ischia, Sept 2009

  17. Bounce and Cyclic behavior • Input: • Output: • Important: Processing of perturbations [Cai, Saridakis, JCAP 0910] [Brandenberger, PRD 80,b] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  18. A more realistic dark energy • In all the above discussion • Observational indications that today • Possible solution: Insert a new scalar (canonical) field (see also f(R) Horava-Lifshitz cosmology ) • Quintessence, Phantom and Quintom Cosmology easily acquired [Saridakis, EJPC 65] [Nojiri, Odintsov, CQG27] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  19. Observational constraints(detailed-balance) • Use observational data (SNIa, BAO, CMB, BBN) to constrain the parameters of the theory • Include matter and standard radiation hydrodynamically: • Fix . Units E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  20. Observational constraints(detailed-balance) • Use observational data (SNIa, BAO, CMB, BBN) to constrain the parameters of the theory • Include matter and standard radiation hydrodynamically: • Fix . Units • 4 dimensionless parameters to be fitted: (we fix at its WAMP5 best fit value) [Dutta, Saridakis, JCAP 1001] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  21. Observational constraints (detailed-balance) • At present: • Total radiation (standard plus “dark”) at Nucleosynthesis: : effective neutrino species. • Thus, 4 dimensionless parameters to be fitted (we fix in terms of ) [Olive,et al, Phys. Rept. 333] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  22. Observational constraints (detailed-balance) • At present: • Total radiation (standard plus “dark”) at Nucleosynthesis: : effective neutrino species. • Thus, 4 dimensionless parameters to be fitted (we fix in terms of ) • 2 free parameters: [Olive,et al, Phys. Rept. 333] [Dutta, Saridakis, JCAP 1001] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  23. Observational constraints (detailed-balance) • So: • And thus in 1σ: [Dutta, Saridakis, JCAP 1001] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  24. Observational constraints (beyond detailed-balance) • We fix at their WAMP5 best fit values and is given in terms of them • So 4dimensionless parameters to be fitted: (at present) (Nucleosynthesis) • 2 free parameters: for given values of [Dutta, Saridakis, JCAP 1001] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  25. Observational constraints (beyond detailed-balance) • So: • And thus in 1σ: [Dutta, Saridakis, JCAP 1001] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  26. Observational constraints on λ • Concerning cosmological observations is expected to be veryclose to its IR value 1. • We perform an overall observational fitting, allowing to vary along with the other parameters of the theory. • Detailed balance: • Beyond detailed balance: • Repeat the aforementioned procedure. [Dutta, Saridakis, JCAP 1005] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  27. Observational constraints on λ • Detailed balance: • Beyond detailed balance [Dutta, Saridakis, JCAP 1005] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  28. Thermodynamic Aspects • Known connection between gravity and thermodynamics. • Field EquationsFirst Law of Thermodynamics. • For a universe bounded by the apparent horizon one calculates the entropy of the universecontent, plus that of the horizon itself. Furthermore, all the “fluids” inside the universe have the sametemperature with horizon. E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  29. Thermodynamic Aspects • Known connection between gravity and thermodynamics. • Field EquationsFirst Law of Thermodynamics. • For a universe bounded by the apparent horizon one calculates the entropy of the universecontent, plus that of the horizon itself. Furthermore, all the “fluids” inside the universe have the sametemperature with horizon. • In an FRW universe in GR: [R.G.Cai, Kim, JHEP0502] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  30. Thermodynamic Aspects • Known connection between gravity and thermodynamics. • Field EquationsFirst Law of Thermodynamics. • For a universe bounded by the apparent horizon one calculates the entropy of the universecontent, plus that of the horizon itself. Furthermore, all the “fluids” inside the universe have the sametemperature with horizon. • In an FRW universe in GR: • In the same lines for the Generalized Second Law (GSL) of Thermodynamics (entropy time-variation of the universe content plus that of the horizon to be non-negative) [R.G.Cai, Kim, JHEP0502] [Bamba, Geng, Tsujikawa, PLB 6880502] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  31. GSL in Horava-Lifshitz cosmology (detailed balance) • The universe contains only matter. For its entropytime-variation: with . with and • So: E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  32. GSL in Horava-Lifshitz cosmology (detailed balance) • The universe contains only matter. For its entropytime-variation: with . with and • So: • The temperature of the universe content is equal to that of the horizon: (depends only on the universe geometry) • The entropy of the horizon equals that of a black hole, with as a horizon: [R.G.Cai, Ohta PLB 679, PRD 81] [Jamil, Saridakis, Setare 1003.0876 [hep-th] ] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  33. GSL in Horava-Lifshitz cosmology • In total: • Clearly GSL is conditionallyviolated. Things are worsebeyond detail balance, where the correction has not a standard sign. [Jamil, Saridakis, Setare 1003.0876 [hep-th] (to appear in JCAP)] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  34. GSL in Horava-Lifshitz cosmology • In total: • Clearly GSL is conditionallyviolated. Things are worsebeyond detail balance, where the correction has not a standard sign. • Should we take other horizon? Can we definetemperature, entropy or the horizon itself in HL cosmology? • Or another “sign” against HL gravity? • Interesting and Open Issues. [Jamil, Saridakis, Setare 1003.0876 [hep-th] (to appear in JCAP)] [Kiritsis, Kofinas, JHEP 1001 ] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  35. Perturbative instabilities? • So far we discussed about HL cosmology. A consistent cosmology is not a proof for the consistency of the underlying gravitational theory. (It is necessary but not sufficient) • Is HL gravity robust? E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  36. Perturbative instabilities? • So far we discussed about HL cosmology. A consistent cosmology is not a proof for the consistency of the underlying gravitational theory. (It is necessary but not sufficient) • Is HL gravity robust? • Perturbations before analytic continuation: vector modes transverse ( ) tensor mode transverse and traceless ( ) • In “synchronous” gauge: • Degrees of freedom: (scalar), (vector), (tensor) [Bogdanos, Saridakis, CQG 27] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  37. Perturbative instabilities? • Fourier transforming, the dispersion relation for at low k: at high k: For tensor mode we get: • Beyond detail balance (assume ) we get: for scalar modes in the UV: tensor modes: E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  38. Perturbative instabilities? • Fourier transforming, the dispersion relation for at low k: at high k: For tensor mode we get: • Beyond detail balance (assume ) we get: for scalar modes in the UV: tensor modes: • Cannot fix everything with analytic continuation: (apart from the fact that this could radically change the renormalizability properties of the theory) • One could take Λ=0 but what about the light speed? [Bogdanos, Saridakis, CQG 27] [Charmousis, et al, JHEP 0908] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  39. Healthy extension of Horava-Lifshitz gravity? • So, one should search for extendedversions of Horava-Lifshitz gravity: with [Kiritsis, PRD 81] [R.G.Cai, Zhang 1008.5048] [Blas, et al, PRL 104] E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  40. Conclusions • i) Horava-Lifshitz gravity applied as a cosmological framework Horava-Lifshitz cosmology. Very interesting. • ii) Interesting late-time solution sub-classes, revealed by phase-space analysis. Amongst them an eternally expanding DE dominated universe. • iii) We can obtain bouncing and cyclic behavior • iv) We can use observations to constrain the model parameters. λ is constrained in • v) The generalized second law of thermodynamics is not valid • vi) However, there may be problems at Horava-Lifshitz gravity itself. Perturbative instabilities, that cannotbe easily cured. • vii) Search for healthy extensions E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  41. Outlook • Many cosmological subjects are open. Amongst them: • i) Calculate the Parametrized-Post-Newtonian (PPN) parameters for HL cosmology. • ii) Constrain observationally the minimal extended version • iii) Examine the generalized second law in the extended version • iv) And of course provide clues, arguments, indications and proofs that Horava-Lifshitz gravity is indeed the underlyingtheory of gravity. E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

  42. THANK YOU! E.N.Saridakis – Hsinchu-Taiwan, Nov 2010

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