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 “${}^7\mathrm{Li}$ problem,” observations leading to an apparent 2 to 4 overproduction of ${}^7\mathrm{Li}$ with respect to standard big bang nucleosynthesis predictions, their production of cosmologically important amounts of ${}^6\mathrm{Li}$, 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 ${}^7\mathrm{Li}$ problem. For NLSP decay times $\approx {10}^3\sec$, such scenarios also lead to cosmologically important ${}^6\mathrm{Li}$ (and possibly ${}^9\mathrm{Be}$) abundances. However, as such scenarios require heavy $\gtrsim 1\mathrm{TeV}$ staus they are likely not testable at the LHC. It is found that decays of NLSP staus to light gravitinos may lead to significant ${}^6\mathrm{Li}$ (and ${}^9\mathrm{Be}$) abundances, whereas NLSP neutralinos decaying into light gravitinos may solve the ${}^7\mathrm{Li}$ 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 ${}^7\mathrm{Li}$ abundance, and/or enhance the ${}^6\mathrm{Li}$ (and possibly ${}^9\mathrm{Be}$) abundances, by the decay of an arbitrary relic particle.

• Received 20 March 2009

DOI:https://doi.org/10.1103/PhysRevD.80.063509