Massive Decaying Tau Neutrino and Big Bang Nucleosynthesis

It has been pointed out by Hata et al. that the standard big bang nucleosynthes gives a poor fit to the primordial abundances of light elements inferred from observational data and the BBN predictions are consistent with observations if the effective number of neutrino species N_{\nu} is about 2.1. We study the effect on BBN of an unstable massive $\tau$ neutrino with mass 1-40 MeV and lifetime 10^{-4}-10^{3} sec and find that if 0.01 \lesssim \tau_{\nutau} \lesssim 1 sec and 10 \lesssim m_{\nutau} \lesssim 24 MeV, the theoretical predictions agree with the observational data.