Updated nucleosynthesis constraints on unstable relic particles

We reexamine the upper limits on the abundance of unstable massive relic particles provided by the success of big-bang nucleosynthesis calculations. We use the cosmic microwave background data to constrain the baryon-to-photon ratio, and incorporate an extensively updated compilation of cross sections into a new calculation of the network of reactions induced by electromagnetic showers that create and destroy the light elements deuterium, ${}^3$He, ${}^4$He, ${}^6$Li and ${}^7$Li. We derive analytic approximations that complement and check the full numerical calculations. Considerations of the abundances of ${}^4$He and ${}^6$Li exclude exceptional regions of parameter space that would otherwise have been permitted by deuterium alone. We illustrate our results by applying them to massive gravitinos. If they weigh $\sim 100\mathrm{GeV},$ their primordial abundance should have been below about ${10}^{-13}$ of the total entropy. This would imply an upper limit on the reheating temperature of a few times ${10}^7\mathrm{GeV},$ which could be a potential difficulty for some models of inflation. We discuss possible ways of evading this problem.