Motivated by the absence of SUSY signal at LHC, we consider a scenario where supersymmetry is broken at a scale above the reheating temperature and/or the inflaton mass. The low energy particle content consists then only in Standard Model states and a gravitino. We investigate the possibility that the latter provides the main component of dark matter through the annihilation of thermalized Standard Model particles. We identify the parameter space allowed by the cosmological constraints, allowing the possibility of large reheating temperature compatible with
leptogenesis scenarios, alleviating the so called "gravitino problem"