Gravitino dark matter and the lithium primordial abundance within a pre-BBN modified expansion

We present supersymmetric scenarios with gravitino LSP and stau NLSP in the case of a non-standard model of cosmology with the addition of a dark component in the pre-BBN era. In the context of the standard model of cosmology, gravitino LSP has drawn quite some attention as it is a good candidate for dark matter. It is produced in scattering processes during reheating after inflation and from the decay of the stau. With a long lifetime, the stau decays during Big Bang Nucleosynthesis. It is strongly constrained by the abundance of light elements but can however address the known "BBN lithium problem". It requires fairly massive staus $\mstau \gtrsim 1 \unit{TeV}$ and puts an upper bound on the reheating temperature $T_R \simeq 10^7\unit{GeV}$ which does not satisfy the requirements for thermal leptogenesis. For the non-standard cosmological scenario, the reheating temperature bound can be strongly relaxed $T_R\gg 10^9 \unit{GeV}$ and the lithium-7 problem solved with a stau typical mass of $\mstau \sim 600-700 \unit{GeV}$ and down to $\sim 400 \unit{GeV}$ with a very important dark component that could enable possible production and detection at the LHC.