BIG-BANG NUCLEOSYNTHESIS CONSTRAINTS ON MASSIVE, UNSTABLE NEUTRINOS

The tau-neutrino, if sufficiently massive, must be unstable. Big Bang Nucleosynthesis (BBN) can provide constraints on the upsilon(tau) mass and lifetime. The modification to the energy density of the early Uni verse in the case of a massive tau -neutrino which decays via upsilon( tau) --> upsilon(mu) + phi (where phi is a weakly coupled massless sca lar) is described and the results of BBN production of the light eleme nts is presented. Consistency with the primordial abundances of D,(3) He(,)7 Li and, especially, He-4 leads to constraints on the mass (m(up silon tau)) and Lifetime (tau(upsilon tau)) of the tau-neutrino. Very massive upsilon(tau)(m(upsilon tau) greater than or equal to 5 - 10MeV ), up to the ARGUS bound of 31MeV, are only allowed for short lifetime s (less than or equal to 40sec). Much lighter (m(upsilon tau) less tha n or equal to 0.01MeV)upsilon(tau) are permitted for lifetimes longer than similar to 0.01 sec but, m(upsilon tau)(MeV) less than or equal t o 10 tau(upsilon)(sec) for shorter lifetimes.