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 $\text{treh}\text{lsim}\mathrm{a}\mathrm{f}\mathrm{e}\mathrm{w}\times {10}^7\text{gev}$ from over-production of ${}^6\mathrm{L}\mathrm{i}$ from bound state effects. We also find an upper limit on the stau lifetime of $3\times {10}^4\sec$, which is nearly an order of magnitude larger than the simple limit $5\times {10}^3\sec$ often used to avoid the effect of bound-state catalysis. The bound on $\text{treh}$ is relaxed to $\lsim {\rm a few}\times 10^8\gev$whenweuseamoreconservativeboundon${^6}{\rm Li}/{^7}{\rm Li}$,inwhichcaseanewregionatsmallstaumassat$\sim 100\gev$ and much longer lifetimes opens up. Such a low stau mass region can be easily tested at the LHC.