The $\nu_\mu \leftrightarrow \nu_s$ interpretation of the atmospheric neutrino data and cosmological constraints
The data on atmospheric neutrinos can be explained assuming the existence of oscillations between muon neutrinos and light sterile neutrinos with mixing close to maximal, and Delta_m^2 approximately equal to 3 E-3 (eV^2). This interpretation of the data is in potential conflict with the successes of big bang nucleosynthesis (BBN), since oscillations can result in a too large contribution of the sterile state to the energy density of the universe at the epoch of nucleosynthesis. The possibility to evade these cosmological constraints has been recently the object of some controversy. In this work we rediscuss this problem and find that the inclusion of a small mixing of the sterile state with tau neutrino can result in the generation of a large lepton asymmetry that strongly suppress the muon-sterile neutrino oscillations eliminating the possible conflict with BBN bounds. In this scheme the mass of the tau neutrino must be larger than few eV's and is compatible with cosmological bounds. Our calculation is performed using a Pauli-Boltzmann method. In this approach it is also possible to develop analytic calculations that allow physical insight in the processes considered and give support to the numerical results.