Cosmological and Astrophysical Bounds on Neutrino Masses and Lifetimes
  The best upper bounds on the masses of stable and unstable light neutrinos derive from the upper bound on the total mass density, as inferred from the lower limit $t_0> 13$ Gyr on the dynamical age of the Universe: If the Universe is matter-dominated, $m_\nu<35(23)\times$ max$ [1, (t_0/\tau_\nu)^{1/2}]$ eV, according as a cosmological constant is (is not) allowed. The best constraints on the radiative decay of light neutrinos derive from the failure to observe prompt gamma rays accompanying the neutrinos from Supernova 1987A: For any $m_{\nu} > 630$ eV, this provides a stronger bound on the neutrino transition moment than that obtained from red giants or white dwarfs. For $m_\nu > 250$ eV or $\tau_\nu < t_{rec}\sim 7\times 10^{12}$ sec, the upper limit on the radiative branching ratio is even smaller than that obtained from the limits on $\mu$-distortion of the cosmic background radiation. Our results improve on earlier cosmological and radiative decay constraints by an overall factor twenty, and allow neutrinos more massive than 35 eV, only if they decay overwhelmingly into singlet majorons or other new particles. 
Sidney A. Bludman