Primordial nucleosynthesis with a decaying τ neutrino

Mass-lifetime limits are derived for the four generic decay modes assuming that the abundance of the massive τ neutrino is determined by its electroweak annihilations. In general, nucleosynthesis excludes a τ neutrino of mass 0.4 MeV--30 MeV for lifetimes greater than about 300 sec. These nucleosynthesis bounds are timely since the current laboratory upper bounds to the τ-neutrino mass are around 30 MeV, and together the two bounds very nearly exclude a long-lived τ neutrino more massive than about 0.4 MeV. Further, our nucleosynthesis bounds together with other astrophysical and laboratory bounds exclude a τ neutrino of mass 0.4 MeV--30 MeV of any lifetime that decays with EM daughter product(s). We use our results to constrain the mass times relic abundance of a hypothetical, unstable species with similar decay modes. Finally, we note that a τ neutrino of mass 1 MeV to 10 MeV and lifetime 0.1 sec--10 sec whose decay products include an electron neutrino can reduce the 4He yield to less than that for two massless neutrino species. This fact could be relevant if the primordial mass fraction of 4He is found to be less than about 0.23 and can also lead to a modification of the nucleosynthesis bound to the number of light (much-lt 1 MeV) neutrino (and other) particle species