1. Precise calculation of the relic neutrino density Sergio Pastor (IFIC) ν JIGSAW 2007 TIFR Mumbai, February 2007 In collaboration with T. Pinto, G, Mangano, G. Miele, O. Pisanti and P.D. Serpico NPB 729 (2005) 221, NPB 756 (2006) 100

2. Outline Precise calculation of the relic neutrino density New results in the SM and in presence of electron-neutrino NSI Introduction: the Cosmic Neutrino Background Relic neutrino decoupling

3. The CNB

4. T~MeV t~sec Neutrinos coupled by weak interactions (in equilibrium) Primordial Nucleosynthesis

5. T~MeV t~sec Free-streaming neutrinos (decoupled) Cosmic Neutrino Background Neutrinos coupled by weak interactions (in equilibrium) Neutrinos keep the energy spectrum of a relativistic fermion with eq form Primordial Nucleosynthesis

6. Number density Energy density Massless Massive m ν >>T Neutrinos decoupled at T~MeV, keeping a spectrum as that of a relativistic species The Cosmic Neutrino Background

7. Relic neutrino decoupling

8. T ν = T e = T γ 1 MeV  T  m μ Neutrinos in Equilibrium

9. Neutrino decoupling As the Universe expands, particle densities are diluted and temperatures fall. Weak interactions become ineffective to keep neutrinos in good thermal contact with the e.m. plasma Rate of weak processes ~ Hubble expansion rate Rough, but quite accurate estimate of the decoupling temperature Since ν e have both CC and NC interactions with e ± T dec ( ν e ) ~ 2 MeV T dec ( ν μ,τ ) ~ 3 MeV

10. T~MeV t~sec Free-streaming neutrinos (decoupled) Cosmic Neutrino Background Neutrinos coupled by weak interactions (in equilibrium) Neutrinos keep the energy spectrum of a relativistic fermion with eq form

11. At T~m e, electron- positron pairs annihilate heating photons but not the decoupled neutrinos Neutrino and Photon (CMB) temperatures

12. Precise calculation of neutrino decoupling: SM + flavour oscillations

13. But, since T dec ( ν ) is close to m e, neutrinos share a small part of the entropy release At T~m e, e + e - pairs annihilate heating photons Non-instantaneous neutrino decoupling f =f FD (p,T )[1+δf(p)]

14. At T~m e, electron- positron pairs annihilate heating photons but not the decoupled neutrinos Neutrino and Photon (CMB) temperatures

15. Momentum-dependent Boltzmann equation 9-dim Phase SpaceProcess  P i conservation Statistical Factor + evolution of total energy density:

16. For T>2 MeV neutrinos are coupled Between 2>T/MeV>0.1 distortions grow At lower temperatures distortions freeze out Evolution of f ν for a particular momentum p=10T

17. Final spectral distortion

18. e ,  δf x10

19. At T<m e, the radiation content of the Universe is Relativistic particles in the Universe

20. At T<m e, the radiation content of the Universe is Effective number of relativistic neutrino species Traditional parametrization of the energy density stored in relativistic particles Relativistic particles in the Universe # of flavour neutrinos: Bounds from BBN and from CMB+LSS

21. At T<m e, the radiation content of the Universe is Effective number of relativistic neutrino species Traditional parametrization of the energy density stored in relativistic particles N eff is not exactly 3 for standard neutrinos Relativistic particles in the Universe # of flavour neutrinos:

22.  e (%)   (%)   (%) N eff Instantaneous decoupling 1.401020003 SM 1.39780.940.43 3.046 Dolgov, Hansen & Semikoz, NPB 503 (1997) 426 Mangano et al, PLB 534 (2002) 8 Results

23. Neutrino oscillations in the Early Universe Neutrino oscillations are effective when medium effects get small enough Compare oscillation term with effective potentials Strumia & Vissani, hep-ph/0606054 Oscillation term prop. to Δm 2 /2E First order matter effects prop. to G F [n(e - )-n(e + )] Second order matter effects prop. to G F E/M Z 2 [ρ(e - )+ρ(e + )] Coupled neutrinos Previous work by Hannestad, PRD 65 (2002) 083006

24. Around T~1 MeV the oscillations start to modify the distortion The variation is larger for e Effects of flavour neutrino oscillations on the spectral distortions

25. Around T~1 MeV the oscillations start to modify the distortion The variation is larger for e The difference between different flavors is reduced Effects of flavour neutrino oscillations on the spectral distortions Oscillations smooth the flavour dependence of the distortion

26.  e (%)   (%)   (%) N eff Instantaneous decoupling 1.401020003 SM 1.39780.940.43 3.046 +3ν mixing (θ 13 =0) 1.39780.730.52 3.046 +3ν mixing (sin 2 θ 13 =0.047) 1.39780.700.560.523.046 Mangano et al, NPB 729 (2005) 221 Results

27. Changes in CNB quantities Contribution of neutrinos to total energy density today (3 degenerate masses) Present neutrino number density

28. Precise calculation of neutrino decoupling: Non-standard neutrino- electron interactions

29. Electron-Neutrino NSI New effective interactions between electron and neutrinos

30. Electron-Neutrino NSI Breaking of Lepton universality (  =  ) Flavour-changing (  ≠  ) Limits on from scattering experiments, LEP data, solar vs Kamland data… Berezhiani & Rossi, PLB 535 (2002) 207 Davidson et al, JHEP 03 (2003) 011 Barranco et al, PRD 73 (2006) 113001

31. Analytical calculation of T dec in presence of NSI Contours of equal T dec in MeV with diagonal NSI parameters SM

32. Neff varying the neutrino decoupling temperature

33. Effects of NSI on the neutrino spectral distortions Here larger variation for ,  Neutrinos keep thermal contact with e-  until smaller temperatures

34.  e (%)   (%)   (%) N eff Instantaneous decoupling 1.401020003 +3ν mixing (θ 13 =0) 1.39780.730.52 3.046  L ee = 4.0  R ee = 4.0 1.38129.473.83 3.357 Mangano et al, NPB 756 (2006) 100 Results Very large NSI parameters, FAR from allowed regions

35.  e (%)   (%)   (%) N eff Instantaneous decoupling 1.401020003 +3ν mixing (θ 13 =0) 1.39780.730.52 3.046  L ee = 0.12  R ee = -1.58  L  = -0.5  R  = 0.5  L e  = -0.85  R e  = 0.38 1.39372.211.660.523.120 Mangano et al, NPB 756 (2006) 100 Results Large NSI parameters, still allowed by present lab data

36. Departure from N eff =3 not observable from present cosmological data Mangano et al, hep-ph/0612150

37. …but maybe in the near future ? Forecast analysis: CMB data Bowen et al MNRAS 2002 ΔN eff ~ 3 (WMAP) ΔN eff ~ 0.2 (Planck) Bashinsky & Seljak PRD 69 (2004) 083002 Example of future CMB satellite

38. The small spectral distortions from relic neutrino—electron processes can be precisely calculated, leading to N eff =3.046 (or up to 3 times more including NSI) Conclusions ν Cosmological observables can be used to bound (or measure) neutrino properties, once the relic neutrino spectrum is known