Studies of neutrino asymmetries generated by ordinary-sterile neutrino oscillations in the early Universe and implications for big bang nucleosynthesis bounds

Ordinary-sterile neutrino oscillations can generate a significant lepton number asymmetry in the early Universe. We study this phenomenon in detail. We show that the dynamics of ordinary-sterile neutrino oscillations in the early Universe can be approximately described by a single integrodifferential equation which we derive from both the density matrix and Hamiltonian formalisms. This equation reduces to a relatively simple ordinary first-order differential equation if the system is sufficiently smooth (static limit). We study the conditions for which the static limit is an acceptable approximation. We also study the effect of the thermal distribution of neutrino momenta on the generation of lepton number. We apply these results to show that it is possible to evade (by many orders of magnitude) the big bang nucleosynthesis (BBN) bounds on the mixing parameters $\delta m^2$ and ${\sin }^{2}2{\theta }_0$ describing ordinary-sterile neutrino oscillations. We show that the large angle or maximal vacuum oscillation solution to the solar neutrino problem does not significantly modify BBN for most of the parameter space of interest, provided that the $\tau$ and/or $\mu$ neutrinos have masses greater than about 1 eV. We also show that the large angle or maximal ordinary-sterile neutrino oscillation solution to the atmospheric neutrino anomaly does not significantly modify BBN for a range of parameters.