How neutrino oscillations can induce an effective neutrino number of less than 3 during Big Bang Nucleosynthesis

Ordinary-sterile neutrino oscillations can generate significant neutrino asymmetry in the early Universe. In this paper we extend this work by computing the evolution of neutrino asymmetries and light element abundances during the Big Bang Nucleosynthesis (BBN) epoch. We show that a significant electron-neutrino asymmetry can be generated in a way that is approximately independent of the oscillation parameters $\delta m^2$ and $\sin^2 2\theta$ for a range of parameters in an interesting class of models. The numerical value of the asymmetry leads to the prediction that the effective number of neutrino flavours during BBN is either about 2.5 or 3.4 depending on the sign of the asymmetry. Interestingly, one class of primordial deuterium abundance data favours an effective number of neutrino flavours during the epoch of BBN of less than 3.