Comment on "Big Bang Nucleosynthesis and Active-Sterile Neutrino Mixing: Evidence for Maximal νμ↔ ντ Mixing in Super Kamiokande?"

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