Indirect searches for gravitino dark matter

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.