In the standard picture of big-bang nucleosynthesis the yields of D, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ only agree with their inferred primordial abundances provided the fraction of critical density contributed by baryons is between 1% and 15%. If the τ neutrino has a mass between 20 MeV and 30 MeV and a lifetime between 200 sec and 3000 sec and its decay products include electron neutrinos this crucial bound is relaxed by a factor of 10. Experiments at ${\mathit{e}}^{\pm }$ colliders should soon test this possibility.

• Received 28 April 1994

DOI:https://doi.org/10.1103/PhysRevD.50.6130