1. G. Mangano NOVE2006@Venezia 1 Relic Neutrino Distribution Gianpiero Mangano INFN, Sezione di Napoli Italy

2. 2G. ManganoNOVE2006@Venezia

3. 3G. ManganoNOVE2006@Venezia Pseudo-thermal distribution: T = 1.95 K Number density ( v + v ): 112 cm -3 /flavor Mean kinetic energy: 10 -7 (eV/m) eV Direct searches:   G F 2 m e E v  10 -50 (E v /eV) cm 2 hopeless ? Standard picture Indirect searches: cosmological observables neutrino influence weak + gravity (T> 1 MeV) gravity (T< 1 MeV)

4. 4G. ManganoNOVE2006@Venezia How strong are present (and future) bounds on exotic features in v distribution? General parametrization P n orthogonal polynomials with respect to Fermi-Dirac distribution a n in one to one correspondence with moments of distribution Q n

5. 5G. ManganoNOVE2006@Venezia unstable v’s:  tot, LSS, CMB, e + flux v chemical potential: BBN, LSS v mass:  tot, LSS,UHECR v oscillations and magnetic moments: BBN non-thermal effects: CMB, LSS,…

6. 6G. ManganoNOVE2006@Venezia Neutrinos and BBN New species couples to gravity and speed up expansion 3 H 2 = 8  G  N eff : increasing the relativistic energy density speeds up the expansion and increases the 4 He mass fraction Y p is the only free parameter (standard scenario) Baryons are now well constrained by CMB  b h 2 = 0.023(2) CMB + Deuterium BBN Cuoco et al 2004

7. 7G. ManganoNOVE2006@Venezia 1) chemical potentials  contribute to N eff 2) a positive electron neutrino chemical potential (more neutrinos than antineutrinos) favour n  p processes with respect to p  n processes. Dolgov et al 2002 Cuoco et al 2004

8. 8G. ManganoNOVE2006@Venezia Neutrinos and CMB N eff affects the radiation-matter equality point ISW: Integrated Sachs-Wolfe Effect on acoustic peaks The large number of cosmological parameters does not allow for a stringent limit

9. 9G. ManganoNOVE2006@Venezia Neutrinos and Large Scale Structures neutrinos suppress inhomogeneities which grow for gravitational instability until they become nonrelativistic m v =1.2 eV m v =2.3 eV m v =4.6 eV m v =6.9 eV Key parameters:

10. 10G. ManganoNOVE2006@Venezia

11. 11G. ManganoNOVE2006@Venezia Decoupling and distortion Residual v interactions at e + -e - annihilation stage produce non- thermal features Kinetic eq. x=m a P i orthogonal polynomial for measure 1/exp(x)+1  f/f therm ka

12. 12G. ManganoNOVE2006@Venezia No mixing: z=T a  e  x N eff 1.4 0.94% 0.43% 3.04 Effects of v oscillations Description in terms of density matrix  Mangano et al 2002 Dolgov et al 2002 Mangano et al 2005 E electron/positron energy density Three regimes: At high temperatures (x<0.3) oscillations suppressed by medium effects When electron density (adiabatically) decreases: MSW regime Vacuum oscillations driven by M 2 /p

13. 13G. ManganoNOVE2006@Venezia

14. 14G. ManganoNOVE2006@Venezia No mixing: z=T a  e  x N eff 1.4 0.73% 0.52% 3.05 Result for s 12 2 =0.3, s 23 2 =0.5, s 13 =0,  m 2 solar =8 10 -5 eV 2,  m 2 atm =2.2 10 -3 eV 2, Very tiny effect Small effect on 4 He mass fraction:  Y=2 10 -4

15. 15G. ManganoNOVE2006@Venezia A model Cuoco, Lesgourgues, Mangano and Pastor 2005 Extra neutrinos from out of equilibrium decay of scalars after neutrino decoupling In the instantaneous decay limit at T D Non thermal features in neutrino distributions Effects seen in CMB and LSS

16. 16G. ManganoNOVE2006@Venezia Bounds from BBN  particles (decoupled) should not contribute too much to the expansion rate H A < 0.1 at 95% C.L.

17. 17G. ManganoNOVE2006@Venezia Present constraints from CMB (WMAP+ACBAR+VSA+CBI) and LSS (2dFGRS+SDSS) + SNIa data (Riess et al.) Model: standard  CDM + nonthermal v’s C l and P(k) computed using CAMB code (Lewis and Challinor 2002) Likelihoods (using COSMOMC Lewis and Bridle 2002))

18. 18G. ManganoNOVE2006@Venezia Degeneracies:  DM, N eff and m 0 N eff >4 not forbidden by BBN ! Future perspectives: can we remove the degeneracy?

19. 19G. ManganoNOVE2006@Venezia Forecast: “conservative”: Planck+ SDSS “ambitious”: CMBPOL+ 40 h -3 Gpc survey with k max =0.1 h Mpc -1 m 0 and  v h 2 (q) large degeneracy

20. 20G. ManganoNOVE2006@Venezia If we add extra relativistic particles the situation gets even more involved For each non thermal model there is a “twin” model with extra thermal relativistic particles, sharing the same value of N eff,  v h 2 but a different value of the neutrino mass scale. Way to solve the degeneracy: independent information on the absolute neutrino mass scale (beta decay experiments)

21. 21G. ManganoNOVE2006@Venezia Summary Too many neutrinos around: Likely: purely thermal distribution which can be very hardly (or not at all) measured in the future Unlikely but possible: exotic features in v distributions opening new perspectives for new physics After all: Neutrinos enjoy to falsify theoretical physicist expectations