Constraints on massive tau neutrinos and their cosmological implications.

We point out the following astrophysical consequences of a tau neutrino with mass in the MeV range: (i) if it has a small electric charge which will allow it to become a cold dark matter of the universe, then present limits on the 511 KeV gamma ray line rule out the possibility that it contributes an $\Omega_{\nu_{\tau}}$ between .1 to 1 making it unsuitable as a cold dark matter candidate; (ii) if an electrically neutral MeV range $\nu_{\tau}$ decays to $\nu_e + \chi$ ( where $\chi$ is a massless boson) , then its lifetime is bounded by SN1987A observations to be within a window $.05~~sec.\leq \tau(\nu_{\tau})~\leq 300~sec./(m_{\nu_{\tau}}~in~ MeV)$ a range which may be of interest from the point of view of structure formation. Encouraged by the overlap between the range allowed in (ii) above and that required for a proposed structure formation mechanism by Dodelson et al., we search for simple extensions of the standard model, where such masses and lifetimes may arise for natural values of parameters and show that the already existing singlet majoron and low scale left-right models have this property. We also comment on possible familon models for this decay.