Abstract: We study the decoupling process of neutrinos in the early universe in the presence of three-flavour oscillations. The evolution of the neutrino spectra is found by solving the corresponding momentum-dependent kinetic equations for the neutrino density matrix, including for the first time the proper collision integrals for both diagonal and off-diagonal elements. This improved calculation modifies the evolution of the off-diagonal elements of the neutrino density matrix and changes the deviation from equilibrium of the frozen neutrino spectra. However, it does not vary the contribution of neutrinos to the cosmological energy density in the form of radiation, usually expressed in terms of the effective number of neutrinos, N-eff. We find a value of N-eff = 3.045, in agreement with previous theoretical calculations and consistent with the latest analysis of Planck data. This result does not depend on the ordering of neutrino masses. We also consider the effect of non-standard neutrino-electron interactions (NSI), predicted in many theoretical models where neutrinos acquire mass. For two sets of NSI parameters allowed by present data, we find that Neff can be reduced down to 3.040 or enhanced up to 3.059.

Abstract: In the framework of a 3+1 scheme with an additional inert state, we consider the thermalisation of sterile neutrinos in the early Universe taking into account the full 4 x 4 mixing matrix. The evolution of the neutrino energy distributions is found solving the momentum-dependent kinetic equations with full diagonal collision terms, as in previous analyses of flavour neutrino decoupling in the standard case. The degree of thermalisation of the sterile state is shown in terms of the effective number of neutrinos, N-eff, and its dependence on the three additional mixing angles (theta(14), theta(24), theta(34)) and on the squared mass difference Delta m(41)(2) is discussed. Our results are relevant for fixing the contribution of a fourth light neutrino species to the cosmological energy density, whose value is very well constrained by the final Planck analysis. For the preferred region of active-sterile mixing parameters from short-baseline neutrino experiments, we find that the fourth state is fully thermalised (N-eff similar or equal to 4).

Abstract: Recent Cosmic Microwave Background (CMB) results from the Planck satellite, combined with previous CMB data and Hubble constant measurements from the Hubble Space Telescope, provide a constraint on the effective number of relativistic degrees of freedom 3.62(-0.48)(+0.50) at 95% CL. New Planck data provide a unique opportunity to place limits on models containing relativistic species at the decoupling epoch. We present here the bounds on sterile neutrino models combining Planck data with galaxy clustering information. Assuming N-eff active plus sterile massive neutrino species, in the case of a Planck+WP+HighL+HST analysis we find m(nu,sterile)(eff) < 0.36 eV and 3.14 < N-eff < 4.15 at 95% CL, while using Planck+WP+HighL data in combination with the full shape of the galaxy power spectrum from the Baryon Oscillation Spectroscopic Survey BOSS Data Relase 9 measurements, we find that 3.30 < N-eff < 4.43 and m(nu,sterile)(eff) < 0.33 eV both at 95% CL with the three active neutrinos having the minimum mass allowed in the normal hierarchy scheme, i.e. Sigma m(nu) similar to 0.06 eV. These values compromise the viability of the (3 + 2) massive sterile neutrino models for the parameter region indicated by global fits of neutrino oscillation data. Within the (3 + 1) massive sterile neutrino scenario, we find m(nu,sterile)(eff) < 0.34 eV at 95% CL. While the existence of one extra sterile massive neutrino state is compatible with current oscillation data, the values for the sterile neutrino mass preferred by oscillation analyses are significantly higher than the current cosmological bound. We review as well the bounds on extended dark sectors with additional light species based on the latest Planck CMB observations.