  Gravitino dark matter, together with 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. Electron and positron fluxes from gravitino decays cannot explain both,
the PAMELA positron fraction and the electron + positron flux recently measured
by Fermi LAT. The observed fluxes require astrophysical sources. The measured
antiproton flux allows for a sizable contribution of decaying gravitinos to the
gamma-ray spectrum, in particular a line at an energy below 300 GeV.
