A re-analysis of gravitino dark matter in the constrained MSSM

We re-consider the gravitino as dark matter in the framework of the Constrained MSSM. We include several recently suggested improvements on: (i) the thermal production of gravitinos, (ii) the calculation of the hadronic spectrum from NLSP decay and (iii) the BBN calculation including stau bound-state effects. In most cases we find an upper bound on the reheating temperature T_R ≲ a few × 10⁷GeV from over-production of ⁶Li from bound state effects. We also find an upper limit on the stau lifetime of 3 × 10⁴sec, which is nearly an order of magnitude larger than the simple limit 5 × 10³sec often used to avoid the effect of bound-state catalysis. The bound on T_R is relaxed to ≲ a few × 10⁸GeV when we use a more conservative bound on ⁶Li/⁷Li, in which case a new region at small stau mass at ∼ 100GeV and much longer lifetimes opens up. Such a low stau mass region can be easily tested at the LHC.