Nonradiative decay of the neutrino and primordial nucleosynthesis

We derive constraints on the mass and the lifetime of nonradiatively decaying neutrinos from the primordial nucleosynthesis. The existence of massive unstable neutrinos affects the expansion of the universe even if the decay is nonradiative. Thus, the abundances of light elements turn out to be different from those in the universe without massive unstable neutrinos. The abundances of the elements are also changed if massive neutrinos decay into electron-neutrinos, and they change the neutron/proton ratio. We calculated the primordial nucleosynthesis in the early universe with massive unstable tau-neutrinos taking these effects into account, and found that the existence of tau-neutrinos with mass and lifetime in the ranges (1) τν > or approx. 20 s, 1 MeV < or approx. mν < or approx. 100 MeV, and (2) 1 s<τν < or approx. 10 s, mν ≅ 1 MeV, must be ruled out. (orig.)