Comment on “ Big Bang Nucleosynthesis and Active-Sterile Neutrino Mixing : Evidence for Maximal ν μ ↔ ν τ Mixing in Super Kamiokande ? ”

The paper " Big Bang Nucleosynthesis and Active-Sterile Neutrino Mixing: Evidence for Maximal ν µ ↔ ν τ Mixing in Super Kamiokande? " by X. Shi and G. M. Fuller (astro-ph/9810075) discusses the cosmological implications of the ν µ → ν s solution to the atmospheric neutrino anomaly. It incorrectly concludes that a lower bound on the ν τ mass of 15 eV is needed in order for the ν µ → ν s oscillations to be consistent with a Big Bang Nucleosynthesis upper bound on the effective number of neutrino flavours of 3.3. Since such a large ν τ mass is disfavoured from large scale structure formation considerations, the strong, but incorrect, conclusion is made that cosmology favours the ν µ → ν τ solution to the atmospheric neutrino problem. We explain the nature of the error. We conclude that cosmology is, at present, consistent with both the ν µ → ν s and ν µ → ν τ possibilities.