Cosmological nucleosynthesis and active-sterile neutrino oscillations with small mass differences: the resonant case

Abstract

We have provided a numerical study of the influence of the resonant active-sterile neutrino oscillations between electron and sterile neutrinos, on the primordial production of helium-4. The evolution of the neutrino ensembles was followed selfconsistently with the evolution of the nucleons, using exact kinetic equations for the neutrino density matrix and the nucleon number densities in momentum space, from the time of neutrino decoupling till the freeze-out of nucleons at 0.3 MeV. The exact kinetic approach enabled us to study precisely the neutrino depletion, spectrum distortion and neutrino mixing generated asymmetry due to oscillations at each momentum mode, and to prove that their effect on nucleosynthesis is considerable. We have calculated the dependence of the primordially produced helium-4 Y_p on the oscillation parameters for the full range of mixing parameters of the model of oscillations with small mass differences less than 10^{-7} eV^2. We have obtained iso-helium contours on the oscillation parameters plane. Cosmological constraints on oscillation parameters, more precise than the existing ones, were extracted, due to the exact kinetic approach and the proper account for the neutrino spectrum distortion and the oscillations generated asymmetry.