Nobuchika Okada (KEK)

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

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

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

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. 2. Brane world cosmology Randall & Sundrum, PRL 83 (1999) 3370; PRL 83 (1999) 4699 Randall-Sundrum model (static solution) ``3-brane’’ 5th 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.   IF satisfied  Solution consistent with the orbifold Z2 symmetry:

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

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 SM Warp down of the scale  solution to hierarchy problem with Strong interactions among KK gravitons and SM particles

13. (2) ``RS 2’’ model SM Weak interactions among KK gravitons and SM particles 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 Shiromizu et al., PRD 62, 024012 (2000) Binetury et al., PLB 477, 285 (2000) Langlois, PTP Suppl. 148, 181 (2003), references therein Original RS model  static solution We want a realistic cosmological solution Metric ansatz: Einstein equation: Assume stabilization of the 5th dimension with the junction conditions

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

17. Radiation dominated era: ``transition temperature’’ • Brane World Cosmology era  Standard Cosmology era Standard cosmology is recovered at low temperature! 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.

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

19. 3. Brane world cosmological effects 3-1:Chaotic inflation on the brane 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 The flat universe dominated by unknown energy densities Dark energy: 73% Dark matter: 23% Baryon: 4% 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. Relic abundance of the dark matter Boltzmann equation: : average of annihilation cross section 

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

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

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

27. WMAP 2 sigma Region shrinks 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 Nihei, N.O. & Seto, hep-ph/0509231 Standard Cosmology 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  Kawasaki & Moroi, PTP 93, 879 (1995) Kawasaki, Kohri & Moroi, Astro-ph/0402249 For Gravitino problem is problematic in inflation scenario thermal leptogenesis scenario

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. In brane world cosmology Therefore, we can avoid overproduction of gravitinos by independently of the reheating temperature 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 Leptogenesis is one of the most interesting scenario for Brayogenesis very simple & related neutrino oscillation physics 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 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