Reconciling Sterile Neutrinos with Big Bang Nucleosynthesis

We reexamine 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 ${10}^{-5\mathrm{}}$) 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 $L_{\nu }>7\mathrm{}\times {10}^{-5\mathrm{}}$ it is consistent with BBN. The BBN bounds on sterile neutrinos mixing with electron neutrinos can also be weakened considerably.