1. Nobuchika Okada (KEK) Brane World Cosmologies IX Workshop on High Energy Physics Phenomenology 03 January – 14 January, 2006 Institute of Physics, Sachivalaya Marg, Bhubaneswar

2. 1. Introduction Robertson-Walker metric: Einstein equation: with The Standard Big Bang Cosmology Friedmann eq. For radiation:

3. Time Temp. high low Inflation? Reheating  most of the particles are in thermal equilibrium Big Bang Nucleosynthesis Equal epoch Matter dominated era Radiation dominated era Thermal history of the universe decoupling from thermal plasma production from thermal plasma

4. Interesting topics in particle cosmology  Cosmology needs New Physics Example: Inflation: inflation models (inlfaton, inflaton potential,..) Baryogenesis: models producing baryon asymmetry in the universe Dark Matter: no candidate in the Standard Model These topics have been studied for many years based on the 4D Standard Cosmology (standard expansion law)

5. Note that final results depend on the cosmological model If the expansion low of the early universe is non-standard, the results can be altered from those in the standard cosmology Brane world cosmology is a well-known example such a non-standard cosmological model

6. ``3-brane’’ 2. Brane world cosmology Randall-Sundrum model (static solution) Randall & Sundrum, PRL 83 (1999) 3370; PRL 83 (1999) 4699 5 th dim. is compactified on

7. Solving Einstein’s equations with cosmological constants in bulk on branes Metric ansatz 4 dimensional Poincare invariance Others = 0

8.   IFsatisfied  Solution consistent with the orbifold Z2 symmetry:

9. 4-dim. effective Planck scale Solution: Free parameters: : 5D Planck scale : AdS curvature : Warp factor with a constraint

10. Graviton KK mode KK mode decomposition Mode equation (volcano potential)

11. KK mode configuration localize around y=0 brane localize around y=pi brane Graviton KK mode mass KK mode configuration We live here

12. Which brane are we living on? Two cases: 1) IR brane at y=pi (RS 1) 2) UV brane at y=0 (RS 2) (1) ``RS 1’’ model Warp down of the scale  solution to hierarchy problem with Strong interactions among KK gravitons and SM particles SM

13. (2) ``RS 2’’ model Weak interactions among KK gravitons and SM particles SM Alternative to compactification Even in the limit, we can reproduce 4D gravity correctly Newton potential for continuum KK mode 4D gravity

14. Brane world cosmology Original RS model  static solution We want a realistic cosmological solution Shiromizu et al., PRD 62, 024012 (2000) Binetury et al., PLB 477, 285 (2000) Langlois, PTP Suppl. 148, 181 (2003), references therein Metric ansatz: Einstein equation: with the junction conditions Assume stabilization of the 5 th dimension

15. Effective Freedmann equation on a brane By tuning the Standard Cosmology New term dominating when New term so-called ``dark radiation’’ with C being a constant free parameter Note: to reproduce the 4D Standard Cosmology at low scale RS type model RS 2 type model

16. where Cosmological constraint: BBN constraint Not to spoil the success of BBN  at * We take C=0 for simplicity Modified Freedmann equation in Brane World Cosmology

17.  Brane World Cosmology era  Standard Cosmology era Radiation dominated era: If the ``transition temperature’’ is low enough, the non-standard expansion law affects some physics processes and the final result can be altered from those examined in the SC. Standard cosmology is recovered at low temperature! ``transition temperature’’

18. Time Temp. high low Inflation? Reheating  most of the particles are in thermal equilibrium Big Bang Nucleosynthesis Equal epoch Matter dominated era Radiation dominated era Thermal history of the brane universe decoupling from thermal plasma production from thermal plasma Non-standard Standard Model independent BBN cosmological constraint 

19. 3-1: Chaotic inflation on the brane 3. Brane world cosmological effects Maartens et al.,, PRD 62, 041301 (2000) E.O.M of inflaton: Slow-roll parameters: Number of e-folds: If, inflation takes place in brane cosmology era  Enhances slow-roll and the e-folding number in any model

20. Example) the simplest chaotic inflation: with is found to be consistent with observed anisotropies in the CMB Low scale inflation  we can take any  in 4D standard cosmology  fixed, high scale inflation

21. 3-2: thermal relic density of dark matter NO & Seto, PRD 70, 083531, 2004 After WMAP results Dark energy: 73% Dark matter: 23% Baryon: 4% The flat universe dominated by unknown energy densities Candidate for the Dark Mater No candidate in the Standard Model! Neutral, stable, suitable mass & interaction etc.  Weak Interacting Massive Particle (WIMP) in physics beyond SM Example: neutral LSP in SUSY model with R-parity  neutralino

22. Boltzmann equation:  : average of annihilation cross section Relic abundance of the dark matter

23. Example: In the limit The standard case: Brane world case: Enhancement of the relic density in the brane world cosmology

24. Application: neutralino dark matter in minimal SUGRA model WMAP data Lahanas & Nanopoulos, PLB 568 (2003) 55 Very narrow allowed region!

25. How is the allowed region changed in the brane world cosmology? Nihei, NO & Seto, PRD 71, 063535 (2005) Numerical analysis Modification of the code DarkSUSY (Gondolo et al., JCAP 0407, 008 (2004))

26. Allowed region shrinks and eventually disappears as M5 decreases Nihei, NO & Seto, PRD 71, 063535 (2005) Standard Cosmology

27. Region shrinks WMAP 2 sigma Allowed region appears by the enhancement

28. Application 2: wino-like dark matter in anomaly mediation model In AMSB, neutralino is wino-like  annihilation process is very effective  large neutralino mass is favored If we consider the wino-like dark matter in the brane world cosmology  Enhancement of relic density  neutralino mass becomes small

29. Model: AMSB + universal soft scalar mass @ GUT scale Standard Cosmology Nihei, N.O. & Seto, hep-ph/0509231 Rough estimation gives

30. 3-3. cosmological gravitino problem Gravitino couples to ordinary matters through only gravitational couplings  long life time If gravitino has mass smaller than 10 TeV, it decays after BBN  decay products would destroy successfully synthesized light nuclei by photo-dissociation and hadro-dissociation To avoid this problem, number density of the gravitino produced from the thermal plasma is severely constrained  upper bound on the reheating temperature after infaltion

31. The Boltzmann equation relevant to the gravitino production process  For Kawasaki & Moroi, PTP 93, 879 (1995) Kawasaki, Kohri & Moroi, Astro-ph/0402249 is problematic in inflation scenario thermal leptogenesis scenario Gravitino problem

32. Kawasaki, Kohri & Moroi, astro-ph/0402249

33. Brane world cosmological solution to the gravitino problem NO & Seto, PRD 71, 023517, 2004 The Boltzman equations for gravitino production is modified in the brane world cosmology Const.

34. Therefore, we can avoid overproduction of gravitinos by independently of the reheating temperature In brane world cosmology The gravitino problem can be solved with the transition temperature low enough

35. 3.4 Thermal leptogenesis in the brane world cosmology N.O & Seto, hep-ph/0507279 In thermal leptogenesis scenario, the condition for out-of-equilibrium decay of the lightest right-handed neutrinos leads to the upper bound on the lightest light neutrino mass Leptogenesis is one of the most interesting scenario for Brayogenesis very simple & related neutrino oscillation physics Considering neutrino oscillation data  hierarchical light neutrino mass spectrum is favored

36. How is the result altered in brane world cosmology ? Out-of-equilibrium decay in brane world cosmology era If the out-of-equilibrium decay occurs in brane world cosmology eara, the upper bound on the lightest neutrino mass becomes mild! Thermal leptogenesis can be realized even in the case of degenerate light neutrino mass spectrum For detailed numerical studies, see Bento et al., hep-ph/0508213

37. 4. Summary There exists a ``realistic’’ example of the non-standard cosmology, the ``RS 2’’ brane world cosmology, in which the expansion law is modified at high temperature but it smoothly connects to the standard cosmology at low temperature << transition temperature. If the transition temperature or is low enough, the results obtained in the standard cosmology can be altered Inflation scenario gravitiono problem, thermal leptogenesis (WIMP) dark matter relic density