Comment on "Big Bang Nucleosynthesis and Active-Sterile Neutrino Mixing: Evidence for Maximal $ν_μ\leftrightarrow ν_τ$ Mixing in Super Kamiokande?"
The paper "Big Bang Nucleosynthesis and Active-Sterile Neutrino Mixing: Evidence for Maximal $ν_μ\leftrightarrow ν_τ$ Mixing in Super Kamiokande?" by X. Shi and G. M. Fuller (astro-ph/9810075) discusses the cosmological implications of the $ν_μ\to ν_s$ 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 $ν_μ\to ν_s$ oscillations to be consistent with a Big Bang Nucleosynthesis upper bound on the effective number of 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 $ν_μ\to ν_τ$ solution to the atmospheric neutrino problem. We explain the nature of the error. We conclude that cosmology is, at present, consistent with both the $ν_μ\to ν_s$ and $ν_μ\to ν_τ$ possibilities.