Relic neutrino asymmetries and big bang nucleosynthesis in a four neutrino model

Oscillations between ordinary and sterile neutrinos can generate large neutrino asymmetries in the early universe. These asymmetries can significantly affect big bang nucleosynthesis (BBN) through modification of nuclear reaction rates. We study this phenomenon within a model consisting of the three ordinary neutrinos plus one sterile neutrino that can be motivated by the neutrino anomalies and the dark matter problem. We calculate how the lepton asymmetries produced evolve at temperatures where they impact on BBN. The effect of the asymmetries on primordial helium production is determined, leading to an effective number of neutrino flavours during BBN of either about 2.7 or 3.1 depending on the sign of the lepton asymmetry.