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Galaxy Clusters and Gamma-Ray Lines: Probing Gravitino Dark Matter with the Fermi LAT

If dark matter particles are not perfectly stable, their decay products might be seen in the cosmic-ray fluxes. A natural candidate for decaying dark matter is the gravitino in R-parity violating scenarios. In the relevant GeV-TeV energy range, the Fermi Large Area Telescope (LAT) is now measuring cosmic gamma-ray fluxes with an unprecedented precision. We use the Fermi LAT gamma-ray data to search for signatures from gravitino dark matter particles, concentrating on gamma-ray lines and galaxy cluster observations. Implications of our results for the decay length of the next-to-lightest superparticle, which could be seen at the LHC in the near future, are discussed.