  We confront the signals expected from unstable gravitino dark matter with
observations of indirect dark matter detection experiments in all possible
cosmic-ray channels. For this purpose we calculate in detail the gravitino
decay widths in theories with bilinear violation of R parity, particularly
focusing on decay channels with three particles in the final state. Based on
these calculations we predict the fluxes of gamma rays, charged cosmic rays and
neutrinos expected from decays of gravitino dark matter. Although the predicted
spectra could in principal explain the anomalies observed in the cosmic-ray
positron and electron fluxes as measured by PAMELA and Fermi LAT, we find that
this possibility is ruled out by strong constraints from gamma-ray and
antiproton observations.
  Therefore, we employ current data of indirect detection experiments to place
strong constraints on the gravitino lifetime and the strength of R-parity
violation. In addition, we discuss the prospects of forthcoming searches for a
gravitino signal in the spectrum of cosmic-ray antideuterons, finding that they
are in particular sensitive to rather low gravitino masses. Finally, we discuss
in detail the prospects for detecting a neutrino signal from gravitino dark
matter decays, finding that the sensitivity of neutrino telescopes like IceCube
is competitive to observations in other cosmic ray channels, especially for
rather heavy gravitinos.
  Moreover, we discuss the prospects for a direct detection of gravitino dark
matter via R-parity violating inelastic scatterings off nucleons. We find that,
although the scattering cross section is considerably enhanced compared to the
case of elastic gravitino scattering, the expected signal is many orders of
magnitude too small in order to hope for a detection in underground detectors.
