Gravitino dark matter and the cosmic lithium abundances

Supersymmetric extensions of the standard model of particle physics assuming the gravitino to be the lightest supersymmetric particle (LSP), and with the next-to-LSP (NLSP) decaying to the gravitino during big bang nucleosynthesis (BBN), are analyzed. Particular emphasis is laid on their potential to solve the Li-7 problem, observations leading to an apparent 2 to 4 overproduction of Li-7 with respect to standard big bang nucleosynthesis predictions, their production of cosmologically important amounts of Li-6, as well as the resulting gravitino dark matter densities in these models. The study includes several improvements compared to prior studies concerning NLSP hadronic branching ratios, the evaluation of hadronic NLSP decays on BBN, BBN catalytic effects, updated nuclear reaction rates, and relies on a complete calculation of the NLSP thermal abundance, interfacing state-of-the-art computer packages. Heavy gravitinos in the constrained minimal supersymmetric standard model are reanalyzed, whereas light gravitinos in gauge-mediated supersymmetry breaking scenarios are studied for the first time in the context of the lithium problems. It is confirmed that decays of NLSP staus to heavy gravitinos, while producing all the dark matter, may at the same time resolve the Li-7 problem. For NLSP decay times approximate to 10(3) sec, such scenarios also lead to cosmologically important Li-6 (and possibly Be-9) abundances. However, as such scenarios require heavy greater than or similar to 1 TeV staus they are likely not testable at the LHC. It is found that decays of NLSP staus to light gravitinos may lead to significant Li-6 (and Be-9) abundances, whereas NLSP neutralinos decaying into light gravitinos may solve the Li-7 problem. Though both scenarios are testable at the LHC they may not lead to the production of the bulk of the dark matter. A section of the paper outlines particle properties required to significantly reduce the Li-7 abundance, and/or enhance the Li-6 (and possibly Be-9) abundances, by the decay of an arbitrary relic particle.