Abstract
Supersymmetric extensions of the standard model of particle physics assumingthe gravitino to be the lightest supersymmetric particle (LSP), and with thenext-to-LSP decaying to the gravitino during Big Bang nucleosynthesis, areanalyzed. Particular emphasis is laid on their potential to solve the "Li7problem", an apparent factor 2-4 overproduction of Li7 in standard Big Bangnucleosynthesis (BBN), their production of cosmologically important amounts ofLi6, as well as the resulting minimum gravitino dark matter densities in thesemodels. The study includes several improvements compared to prior studies.Heavy gravitinos in the constrained minimal supersymmetric standard model(CMMSM) are reanalyzed, whereas light gravitinos in gauge-mediatedsupersymmetry breaking scenarios (GMSB) are studied for the first time. It isconfirmed that decays of NLSP staus to heavy gravitinos, while producing allthe dark matter, may at the same time resolve the Li7 problem. For NLSP decaytimes ~ 1000 sec, such scenarios also lead to cosmologically important Li6 (andpossibly Be9) abundances. However, as such scenarios require heavy > 1 TeVstaus they are likely not testable at the LHC. It is found that decays of NLSPstaus to light gravitinos may lead to significant Li6 (and Be9) abundances,whereas NLSP neutralinos decaying into light gravitinos may solve the Li7problem. Though both scenarios are testable at the LHC they may not lead to theproduction of the bulk of the dark matter. A section of the paper outlinesparticle properties required to significantly reduce the Li7 abundance, and/orenhance the Li6 (and possibly Be9) abundances, by the decay of an arbitraryrelic particle.