Active-sterile neutrino oscillations in the early Universe with the complete mixing matrix

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 × 4 mixing matrix. The evolution of the neutrino energy distributions is found solving the momentum-dependent kinetic equations with full diagonal collision terms. 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 (θ 14, θ 24, θ 34) and on the squared mass difference ∆m 2 41 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 ≃ 4).