  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.
