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