Reconciling sterile neutrinos with big bang nucleosynthesis

We re-examine the big bang nucleosynthesis (BBN) bounds on the mixing of neutrinos with sterile species. These bounds depend on the assumption that the relic neutrino asymmetry $L_{\nu}$ is very small. We show that for $L_{\nu}$ large enough (greater than about $10^{-5}$) the standard BBN bounds do not apply. We apply this result to the sterile neutrino solution to the atmospheric neutrino anomaly and show that for $L_{\nu} > 7 \times 10^{-5}$ it is consistent with BBN. The BBN bounds on sterile neutrinos mixing with electron neutrinos can also be weakened considerably.