  The gravitino in models with a small violation of R-parity is a
well-motivated decaying dark matter candidate that leads to a cosmological
scenario that is consistent with big bang nucleosynthesis and thermal
leptogenesis. The gravitino lifetime is cosmologically long-lived since its
decays are suppressed by the Planck-scale as well as the small R-parity
violating parameter. We discuss the signals in different cosmic-ray species
coming from the decay of gravitino dark matter, namely gamma rays, positrons,
antiprotons, antideuterons and neutrinos. Comparison to cosmic-ray data can be
used to constrain the parameters of the model.

High Energy Physics - Phenomenology;High Energy Astrophysical Phenomena