Gravitino Dark Matter and Light Element Adundances

We discuss the scenario where the gravitino is the lightest supersymmetric particle and the long-lived next-to-lightest sparticle (NSP) is the neutralino or the stau, the charged partner of the tau lepton. In this case staus form bound states with several nuclei, affecting the cosmological abundances of Li6 and Li7 by enhancing nuclear rates that would otherwise be strongly suppressed. We consider the effects of these enhanced rates on the final abundances produced in Big-Bang nucleosynthesis (BBN), including injections of both electromagnetic and hadronic energy during and after BBN. We show that if the stau lifetime is longer than 10^3-10^4 s, the abundances of Li6 and Li7 are far in excess of those allowed by observations. For shorter lifetimes of order 1000 s, it appears that stau bound state effect could reduce the Li7 abundance from standard BBN values while at the same time enhancing the Li6 abundance, creating a region where both lithium abundances match their plateau values.