Baryogenesis & RSII Braneworld Cosmology

1. Baryogenesis & RSII Braneworld Cosmology Nuno M. C. Santos Institut für Theoretische Physik Universität Heildelberg Kosmologietag Bielefeld, May 11 – 12, 2006

2. Baryons = 5% Energy densities in the Universe This is also a large mystery! ? Dark Energy Dark Matter 95 % ? Bielefeld, 11 May 2006

3. The baryon asymmetry of the Universe Bennet et al, AJ 2003; Spergel et al, AJ 2003 • The observed baryon asymmetry should be generated dynamically after inflation Baryogenesis • Matter-antimatter asymmetry can be dynamically generated in an expanding Universe if: • B is not conserved • C and CP are violated • departure from thermal equilibrium Sakharov conditions Sakharov, JETPL 1967 If CPT is violated, a baryon number can arise even in thermal equilibrium • Several mechanism have been proposed to generate the baryon asymmetry of the Universe: • Electroweak baryogenesis, GUT baryogenesis, Affleck-Dine mechanism, Leptogenesis,Spontaneous baryogenesis, Gravitationalbaryogenesis,... Bielefeld, 11 May 2006

4. Outline • Introduction: baryogenesis via leptogenesis and neutrinos • Braneworld cosmology: Randall-Sundrum II model • Gravitational baryogenesis • Thermal leptogenesis in the brane • The efficiency factor • Bounds on the neutrino parameters and on M5 and Tt • Conclusions In colaboration with: M.C. Bento and R. González Felipe (IST, Lisbon) Phys. Rev. D 71 (2005) 123517 [ArXiv: hep-ph/0504113] Phys. Rev. D 73 (2006) 023506 [ArXiv:hep- ph/0508213] Bielefeld, 11 May 2006

5. Neutrinos WMAP I + 2dFGRS gives • Large scale structure data can put an upper limit on the ratio due to the neutrino free streaming effect Bennet et al, AJ 2003 These upper limit is complemented by the results from neutrino oscillation experiments Strumia & Vissani 2005, Fogli et al 2005 • With these data alone, one cannot order the neutrino states by their mass in only one way. • The three independent mass square differences satisfy • The neutrino mass spectrum can be further classified into 1 1 2 2 For the case of 3 degenerate neutrino species, the WMAP limit on the sum of the neutrino masses gives Bielefeld, 11 May 2006

6. One of the most attractive ideas for explaining small neutrino masses is the one based on the Seesaw Mechanism Minkowski, PLB 1977 Gell-Mann, Ramond & Slansky, 1979 Yanagida, 1979 Glashow, 1980 Mohapatra & Senjanovic, PRL 1980 The tiny masses of light neutrinos are naturally understood if we introduce heavyMajorana neutrinos to the SM. By integrating out the heavy right-handed neutrinos, one obtains the small Majorana masses for light neutrinos Thanks to MIKE LESTER (and FRJ) When the heavyMajorana neutrinos decay into leptons and Higgs scalars they violate lepton number, and the interference between the tree-level and the one-loop amplitudes yields a non-zero CP-asymmetry. This leads to a lepton asymmetry which is then partially converted into baryon asymmetry by sphaleron processes. Leptogenesis Fukugita & Yanagida, PLB 1986 Bielefeld, 11 May 2006

7. Leptogenesis Fukugita & Yanagida, PLB 1986 Leptogenesis via heavy Majorana neutrino decay Asymmetry in the lepton number Seesaw Mechanism Neutrino masses Can be converted into baryon number through Sphalerons Non-perturbative effects Violate B+L Conserve B-L Efficient above the EW scale (SM) (MSSM) Kuzmin et al 1985 Khlebnikov et al 1985 Bielefeld, 11 May 2006

8. Introducing the branes Theories formulated in extra dimensions have been around since the early XXth century Kaluza-Klein theory for the unification of gravity and electromagnetism Superstring theory is naturally and consistently formulated only in a space-time with 10 dimensions. Our observable Universe could be a surface, the brane, embedded in a higher dimensional space-time - the bulk. Modification on the early Universe phenomena: Inflation, Baryogenesis,… Late time effects: accelerated expansion of the Universe (DGP model) Bielefeld, 11 May 2006

9. Randall-Sundrum II • AdS bulk (negative cosmological constant ) with a Z2 reflection symmetry • One brane with tension • Five-dimensional Planck mass [Randall & Sundrum, PRL 1999] Randall-Sundrum II braneworld Modification of the 4D Einstein equations induced on the brane Shiromizu, Maeda & Sasaki, PRD 2000 … FRW metric on the brane Binetruy et al, PLB 2000 … Projection of the 5D Weyl tensor Successful BBN requires that the change in the expansion rate due to the new terms in the Friedmann equation be sufficiently small at scales ~O(MeV) More stringent bound by requiring the theory to reduce to Newtonian gravity on scales larger than 1 mm Bielefeld, 11 May 2006

10. One gets for the inflationary observables: Inflation Driven by a 4D scalar field trapped on the brane The high energy corrections provide increased Hubble damping This makes slow-roll inflation possible even for potentials that would be too steep in SC Maartens, Wands, Bassest & Heard, PRD 2000 ………. COBE normalization Brane Standard Bielefeld, 11 May 2006

11. What are the implications of the brane regime for baryogenesis / leptogenesis? Bielefeld, 11 May 2006

12. effective chemical potential for baryons Gravitational Baryogenesis The crucial ingredient is an interaction between the derivative of the Ricci scalar curvature and the baryon-number (B) current Davoudiasl, Kitano, Kribs, Murayama & Steinhardt, PRL 2004 If B-violating processes exist in thermal equilibrium, then a net baryon asymmetry can survive after their decoupling In an expanding Universe, it dynamically breaks CPT Bielefeld, 11 May 2006

13. Gravitational Baryogenesis The crucial ingredient is an interaction between the derivative of the Ricci scalar curvature and the baryon-number (B) current Davoudiasl, Kitano, Kribs, Murayama & Steinhardt, PRL 2004 If B-violating processes exist in thermal equilibrium, then a net baryon asymmetry can survive after their decoupling In an expanding Universe, it dynamically breaks CPT One needs • During radiation dominated epoch in standard cosmology • In the braneworld scenario can be easily realised Shiromizu & Koyama, JCAP 2004 • This mechanism has also been implemented in a braneworld with Gauss-Bonnet term Bento, Felipe & Santos, PRD 2005 Bielefeld, 11 May 2006

14. Thermal Leptogenesis The relevant processes are: Boltzmann equations Buchmüller, Di Bari & Plümacher, Ann. Phys. 2005 Decays (D) and inverse decays (ID) L = 1 scatterings ID + L = 1 & L = 2 scatterings Relevant only for large z Bielefeld, 11 May 2006

15. Assuming that right-handed neutrinos are hierarchical, , and that the decays of the heavier neutrinos do not influence the final value of the B-L asymmetry, the baryon asymmetry generated by N1 can be conveniently parameterized as Solution of the Boltzmann equations efficiency factor Buchmüller, Di Bari & Plümacher, Ann. Phys. 2005 Giudice et al, NPB 2004 Buchmüller, Di Bari & Plümacher, Ann. Phys. 2005 Bielefeld, 11 May 2006

16. The CP asymmetry It is convenient to write the CP-asymmetry as the product For a normal hierarchy In the case of hierarchical and quasi-degenerate light neutrinos Buchmüller, Di Bari & Plümacher, NPB 2002, NPB 2003 The CP-asymmetry reaches its maximum for fully hierarchical neutrinos Bielefeld, 11 May 2006

17. Thermal leptogenesis in the RSII brane During radiation domination the expansion rate is given by: Departure from thermal equilibrium is controlled by the decay parameter BC  Bielefeld, 11 May 2006

18. Effective neutrino mass and decay parameter The effective mass neutrino parameter is a crucial quantity for thermal leptogenesis • A lower bound is always verified Fujji, Hamaguchi & Yanagida, PRD 2002 • There is no model independent upper bound but if there are no strong cancelations due to phase relations between different matrix elements Buchmüller, Di Bari & Plümacher, NPB 2002, NPB 2003 Standard Cosmology Brane Cosmology mildly strong washout regime leptogenesis lies in the weak washout regime Bielefeld, 11 May 2006

19. SC BC The efficiency factor SC BC Bielefeld, 11 May 2006

20. Lower bounds on M1 , M5 and Tt A lower bound on M1 can be obtained from the condition SC For fully hierarchical neutrinos BC This bound implies, in turn, a lower bound on the gravity scale In the favoured neutrino mass range Bielefeld, 11 May 2006

21. Light neutrino masses As we have seen, the L = 2 processes with heavy neutrino exchange generate a contribution to the washout rate which depends on the absolute mass scale At low temperatures the contribution  W dominates over W0 Buchmüller, Di Bari & Plümacher, Ann. Phys. 2005 The presence of W modifies the total efficiency factor zB value at which the lepton asymmetry is no longer produced SC The dependence of the washout term on M1 is cancelled out in the BC regime. The W contribution to the total washout depends only on the fundamental scale M5 and the absolute neutrino mass scale  the exponential suppression in the efficiency factor becomes relevant only for large values of M5 or absolute neutrino mass scale BC Bielefeld, 11 May 2006

22. Bielefeld, 11 May 2006

23. for Leptogenesis scenario in braneworld cosmology is consistent with quasi-degenerate light neutrinos. Bielefeld, 11 May 2006

24. Modification on the early Universe phenomena Inflation and Baryogenesis • Randall-Sundrum II • (Inflation) • Gravitational baryogenesis • Thermal leptogenesis Braneworld Cosmology Bielefeld, 11 May 2006

25. SC BC Conclusions: thermal leptogenesis Standard Cosmology Brane Cosmology Weak washout regime Strong washout regime Quasi-degenerate light neutrino mass spectrum disfavored Compatible with quasi-degenerate light neutrino mass spectrum Bielefeld, 11 May 2006

26. Modification on the early Universe phenomena Inflation and Baryogenesis • Randall-Sundrum II • (Inflation) • Gravitational baryogenesis • Thermal leptogenesis • Gravitino production Braneworld Cosmology Late time effects Accelerated expansion of the Universe • DGP model Bielefeld, 11 May 2006