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					       Baryogenesis
            &
RSII Braneworld Cosmology
              Nuno M. C. Santos
            Institut für Theoretische Physik
                 Universität Heildelberg


                    Kosmologietag
              Bielefeld, May 11 – 12, 2006
 Energy densities in the Universe

                                       This is also a large mystery!




   ?
Dark Energy




   ?
Dark Matter
              Bielefeld, 11 May 2006                                   2
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
                                                              Sakharov conditions
       departure from thermal equilibrium
                                                                                      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, Gravitational baryogenesis, ...
                             Bielefeld, 11 May 2006                                                              3
                                  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                                       4
                                                       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                                                         5
     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 heavy Majorana 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 heavy Majorana neutrinos decay into leptons and
                                         Higgs scalars they violate lepton number, and the
                                         interference between the tree-level and the one-loop
  Leptogenesis                           amplitudes yields a non-zero CP-asymmetry. This leads to a
                                         lepton asymmetry which is then partially converted into
  Fukugita & Yanagida, PLB 1986          baryon asymmetry by sphaleron processes.


                                          Bielefeld, 11 May 2006                                                                   6
                                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                                                                   (SM)
                                                                                      (MSSM)
 Efficient above the EW scale                                                 Kuzmin et al 1985
                                                                           Khlebnikov et al 1985

                                  Bielefeld, 11 May 2006                                           7
                       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              8
              Randall-Sundrum II braneworld
Randall-Sundrum II         [Randall & Sundrum, PRL 1999]                   Modification of the 4D Einstein
                                                                           equations induced on the brane
 AdS bulk (negative cosmological constant           )
 with a Z2 reflection symmetry
 One brane with tension
 Five-dimensional Planck mass
                                                                                             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
More stringent bound by                                                    the Friedmann equation be sufficiently small
requiring the theory to reduce                                             at scales ~O(MeV)
to Newtonian gravity on scales
larger than 1 mm

                                                  Bielefeld, 11 May 2006                                                        9
                              Inflation
Driven by a 4D scalar field            The high energy corrections
   trapped on the brane             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




                                                       One gets for the inflationary observables:




                              Bielefeld, 11 May 2006                                                               10
  What are the implications
   of the brane regime for
baryogenesis / leptogenesis?




           Bielefeld, 11 May 2006   11
                      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




  In an expanding Universe,                              If B-violating processes exist in thermal equilibrium, then a
  it dynamically breaks CPT                              net baryon asymmetry can survive after their decoupling




        effective chemical
       potential for baryons

                                            Bielefeld, 11 May 2006                                                        12
                     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




  In an expanding Universe,                              If B-violating processes exist in thermal equilibrium, then a
  it dynamically breaks CPT                              net baryon asymmetry can survive after their decoupling




                  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                                                          13
                              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                                                        14
         Solution of the Boltzmann equations
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




                                                                                 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                                                      15
                               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                                                         16
        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   17
    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                                                 18
     The efficiency factor



SC
BC




                BC                  SC


           Bielefeld, 11 May 2006        19
                  Lower bounds on M1 , M5 and Tt
A lower bound on M1 can be obtained from the condition




  For fully hierarchical neutrinos                            SC

                                                              BC



This bound implies, in turn, a lower bound on the gravity scale




                                                                      In the favoured neutrino mass range




                                             Bielefeld, 11 May 2006                                         20
                          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
                                          BC                       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

                                          Bielefeld, 11 May 2006                                                           21
Bielefeld, 11 May 2006   22
                                             for


                  Leptogenesis scenario in braneworld cosmology is
                   consistent with quasi-degenerate light neutrinos.


Bielefeld, 11 May 2006                                                 23
Modification on the early Universe phenomena
         Inflation and Baryogenesis

                                       Randall-Sundrum II
                                       (Inflation)
                                       Gravitational baryogenesis
                                       Thermal leptogenesis




           Bielefeld, 11 May 2006                                    24
          Conclusions: thermal leptogenesis
         Standard Cosmology                                       Brane Cosmology



         Strong washout regime                                   Weak washout regime




 SC                                                         BC




Quasi-degenerate light neutrino mass                              Compatible with quasi-degenerate
        spectrum disfavored                                         light neutrino mass spectrum

                                       Bielefeld, 11 May 2006                                        25
Modification on the early Universe phenomena
         Inflation and Baryogenesis

                                       Randall-Sundrum II
                                       (Inflation)
                                       Gravitational baryogenesis
                                       Thermal leptogenesis
                                       Gravitino production




             Late time effects
   Accelerated expansion of the Universe

                                     DGP model




           Bielefeld, 11 May 2006                                    26

				
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