Constraints on the Reheating Temperature in Gravitino Dark Matter Scenarios

Considering gravitino dark matter scenarios, we study constraints on the reheating temperature of inflation. We present the gauge-invariant result for the thermally produced gravitino yield to leading order in the Standard Model gauge couplings. Within the framework of the constrained minimal supersymmetric Standard Model (CMSSM), we find a maximum reheating temperature of about 10^7 GeV taking into account bound-state effects on the primordial $^6$Li abundance. We show that late-time entropy production can relax this constraint significantly. Only with a substantial entropy release after the decoupling of the lightest Standard Model superpartner, thermal leptogenesis remains a viable explanation of the cosmic baryon asymmetry within the CMSSM.