Cosmological nucleosynthesis and active-sterile neutrino oscillations with small mass differences: The nonresonant case

We study the nonresonant oscillations between left-handed electron neutrinos nu(e) and nonthermalized sterile neutrinos nu(s) in the early Universe plasma. The case when nu(s) do not thermalize until 2 MeV and the oscillations become effective after nu(e) decoupling is discussed. As far as for this model the rates of the expansion of the Universe, neutrino oscillations, and neutrino interactions with the medium may be comparable, we have analyzed the kinetic equations for the neutrino density matrix, accounting simultaneously for these processes. The evolution of neutrino ensembles was described numerically by integrating the kinetic equations for the neutrino density matrix in momentum space for small mass differences delta m(2)less than or equal to 10(-7) eV(2). This approach allowed us to study precisely the evolution of the neutrino number densities, energy spectrum distortion, and the asymmetry between neutrinos and antineutrinos due to oscillations for each momentum mode. We have performed a complete numerical analysis for the full range of the oscillations parameters of the model of the influence of the nonequilibrium nu(e) <-> nu(s) oscillations on the primordial production of He-4. The exact kinetic approach enabled us to calculate the effects of neutrino population depletion, the distortion of the neutrino spectrum, and the generation of neutrino-antineutrino asymmetry on the kinetics of neutron-to-proton transitions during the primordial nucleosynthesis epoch and correspondingly on cosmological He-4 production. It was shown that the neutrino population depletion and spectrum distortion play an important role. The asymmetry effect, in case the lepton asymmetry is accepted initially equal to the baryon one, is proved to be negligible for the discussed range of delta m(2). Constant helium contours in the delta m(2)-theta plane were calculated. Thanks to the exact kinetic approach more precise cosmological constraints on the mixing parameters were obtained. [S0556-2821(98)04115-0]