1. Does WMAP data constrain the lepton asymmetry of the Universe to be zero? M. Lattanzi*, R. Ruffini, G.V. Vereshchagin Dip. di Fisica - Università di Roma “ La Sapienza ” ICRA – International Center for Relativistic Astrophysics Albert Einstein Century International Conference Paris, 18 – 22 July 2005 * ML participation to this meeting has been supported by the Royal Astronomical Society

2. The advent of the so-called “Precision Cosmology” has allowed to measure the values of the cosmological parameters with ever-increasing accuracy. (Spergel et al., 2003)

3. The cosmological observables are sensitive to neutrino properties and can then be used to determine them. For example, the relation: together with  . 1, yields (using h = 0.7): (Gerstein & Zel’dovich, 1966)

4. Thermal equilibrium between  e §,  Perfect lepton symmetry No mechanisms for entropy generation other than e + e - annihilation Stable neutrinos No interactions that diminishes the number of neutrinos Absence of right-handed neutrinos 3 neutrino species, (nearly) degenerate in mass Only one unknown quantity:  m In the standard cosmological scenario, the following assumptions about neutrinos are made: The Standard Scenario

5. The cosmological observables are sensitive to neutrino properties and can then be used to determine them. WMAP + 2dFGRS + Ly-a Forest  m i < 0.7 eV (Spergel et al., 2003) From tritium  -decay: m e < 2.8 eV (Bonn et al., 2002) From 0  : |m ee | < 0.5 eV (Klapdor-Kleingrothaus, 2001)

6. Spergel et al., 2003 WMAPex+2dF+Ly   m  0.7 eV 95% CL Hannestad, 2003WMAP+2dF  m  1 eV 95% CL Allen, Schmidt & Bridle, 2003 WMAPex+2dF+XLF  m  0.56 § 0.26 eV 68% CL Barger, Marfatia & Tregre, 2004 WMAPex+2dF+SDSS +HST  m  0.74 eV 95% CL Tegmark et al., 2004WMAP+SDSS  m  1.7 eV 95% CL Hannestad & Raffelt, 2004 WMAP+2dF+SDSS+ HST+SN I a m  0.34 eV (std) m  1.0 eV (3+1) 95% CL Crotty & Lesgourgues, 2004 WMAP+ACBAR+2dF +SDSS+HST+SN I a  m  0.6 ¥ 1.5 eV 95% CL Summary of cosmological bounds on m However, the total mass is just part of the story.

7. Each one of the above assumptions could be not valid in presence of physics beyond the Standard Model of particle physics, including (but not limited to) : Existence of Majorons Annihilation of supersymmetric particles Existence of sterile neutrinos Non-standard leptogenesis (es. Affleck-Dine scenarios) Existence of right handed neutrinos To what extent cosmological observables can constraint these non-standard scenarios? Non-Standard Scenarios

8. Thermal Evolution Supposing a thermal spectrum, the neutrinos follow a Fermi- Dirac distribution: =  d  T d From this we can compute the energy density and the number density: In the standard scenario: for each species. It is then customary to define:

9. Parameterization of Non-Standard Scenarios In principle, the following parameters are needed in order to fully describe the neutrino sector in a non-standard scenario: The number N of neutrino species; N values of mass m i ; N values of degeneracy parameter  i ; N values of temperature T i ; The total effective number of relativistic species N eff However, in practice every cosm. obs. is sensitive only to some of (or to some combination of) the above parameters

10. Lepton Asymmetry At the present, there are no observational evidence that the L.A. of the Universe is small (i.e., comparable to the baryon asymmetry). Several well-motivated particle physics scenario producing a large lepton asymmetry exists. Testing the prediction of such scenarios would be very important, since it could shed light on leptogenesis and baryogenesis, and give information on the elements of the neutrino mixing matrix. The presence of a lepton asymmetry involves a non zero neutrino degeneracy parameter  (i.e., dimensionless chemical potential). However this is not enough, since standard BBN and neutrino oscillation strongly disfavour a non-zero degeneracy parameter. Some other species is required in order to avoid equalization. Minimum number of extra parameters is two:  and N eff

11. Effect on the CMB spectrum The neutrino energy density determines the redshift of matter - radiation equality. Modes that enter the horizon during the radiation dominated era are boosted. Shifting z eq forward, the height of the first peak increases. (Lesgourgues & Pastor, 1999)

12. Effect on the matter spectrum The density perturbations in the neutrino gas are erased by the large velocity (Landau damping or free streaming) until the neutrinos are in ultrarelativistic regime This produces, in the power spectrum of matter perturbations, a small-scale damping (affected scales are the ones smaller than the horizon size at the time of UR-NR transition) :

13. Effect on the power spectrum The amount of damping is proportional to the fraction of matter in neutrinos

14. Effect on the primordial nucleosynthesis A larger (smaller) radiation density implies a higher freeze-out temperature and then a smaller (larger) neutron-to-proton ratio. An excess (lack) of neutrinos with respcet to antineutrinos in the electronic sector results in a smaller (larger) neutron-to-proton ratio.

15. The presence of  changes shape of the distribution function of neutrinos. Three main effects: Larger number density at the presen time: Larger energy density: Different velocity distribution (larger mean speed and more populated tail of particles with “large” momentum). Important for Landau damping Effects of Lepton Asymmetry

16. Distribution of momenta for  =0, 1, 3 Different velocity distribution (larger mean speed and more populated tail of particles with “large” momentum).

17. Time evolution of the mean squared speed for  =0 and m =0.1, 1 eV.

18. Different velocity distribution (larger mean speed and more populated tail of particles with “large” momentum). Time evolution of the “sound speed” normalize to the case  =0, per  =1, 2, 3

19. We consider a flat  CDM model described by the usual parameters (  b,  m, h, n, , A). We parameterize the neutrino sector with 3 parameters: The density parameter of neutrinos  ´  h 2 ; A common degeneracy parameter  The extra energy density in UR species other than neutrinos: where Likelihood analysis (ML, Ruffini & Vereshchagin, submitted to PRD)

20. We consider the following region in parameter space 0.020 ·  b · 0.028 0.10 ·  m · 0.18 0.90 · n · 1.10 0 ·  · 0.30 0.70 · A · 1.10 0 ·  · 0.03 0 ·  · 2.0 0 ·  N eff oth · 2.0 We sample the likelihood function with respect to the TT and TE WMAP spectra on a grid of 5 equispaced points in every direction We use a modified version of the code CMBFast to compute the theoretical spectra Assunzioni:  = 1 h = 0.72 N = 3 Parameter Space

22. Neutrino mass: 0 is preferred value @95% confidence level, m < 1.2 eV This is quite in agreement with previous analyses (somewhat looser, probably due to too large spacing in thegrid)

23. Number of extra relativistic species : 0.70 is preferred value @95% confidence level, -0.5 <  N eff < 2 This is also quite in agreement with previous analyses (see eg Crotty, Lesgourgues and Pastor 2003 and 2004)

24. Degeneracy Parameter and Lepton Asymmetry: |  | = 0.70 (|L|=0.46) is the preferred value @95% confidence level, 0 < |  | < 1.1 0 < |L| < 0.8

25. We have also computed the 95% confidence region for , for different values the number of extra relativistic species The smaller is  N eff oth, the largest is the best-fit value of the degeneracy parameter. For low values, zero deg. par. is outside the 95% CL. Correlation between  and  N eff oth  N eff oth  0 0.65 § 0.58 0.50.42 +0.58 -0.42 1.00.18 +0.58 -0.18 1.5< 0.53 2.0< 0.29

26. Summary In the standard cosmological scenario, the only unknown parameter related to relic neutrinos is the sum of masses (considered nearly degenerate). However, non-standard models are motivated by extensions of the standard model of particle physics. One possible modification is the introduction of a cosmological lepton asymmetry. Although WMAP data are well-fitted by asymmetric models, nevertheless they seem not to rule out a lepton-symmetric Universe. This is probably due to the fact that CMB measurements cannot disentangle lepton asym. from other sources of extra energy density. The linear part of the matter power spectrum could help for this. Anyway, preference for non-zero  N is an hint for the presence of physics beyon SM.