Updated Nucleosynthesis Constraints on Unstable Relic Particles

We revisit 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, he3, he4, li6 and li7. We derive analytic approximations that complement and check the full numerical calculations. Considerations of the abundances of he4 and li6 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 ~100 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 GeV, which could be a potential difficulty for some models of inflation. We discuss possible ways of evading this problem.