Comment on "Big Bang Nucleosynthesis and Active-Sterile Neutrino Mixing: Evidence for Maximal ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ Mixing in Super Kamiokande?"

Abstract

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.

Comments: 8 pages, 1 Figure, LaTeX, epsfig