Gravitino dark matter with a high reheating temperature, e.g. for thermal leptogenesis, implies an upper bound on the masses of superparticles. In the case of broken R-parity the constraints from primordial nucleosynthesis are naturally satisfied and decaying gravitinos lead to characteristic signatures in high energy cosmic rays. Together with low-energy observables one obtains a window of superparticle masses, which is expected to be probed at the LHC.