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The $\mu\nu$SSM provides a solution to the $\mu$-problem of the MSSM andexplains the origin of neutrino masses by simply using right-handed neutrinosuperfields. Given that R-parity is broken in this model, the gravitino is anatural candidate for dark matter since its lifetime becomes much longer thanthe age of the Universe. We consider the implications of gravitino dark matterin the $\mu\nu$SSM, analyzing in particular the prospects for detecting gammarays from decaying gravitinos. If the gravitino explains the whole dark mattercomponent, a gravitino mass larger than 20 GeV is disfavored by the isotropicdiffuse photon background measurements. On the other hand, a gravitino with amass range between 0.1-20 GeV gives rise to a signal that might be observed bythe FERMI satellite. In this way important regions of the parameter space ofthe $\mu\nu$SSM can be checked.

Gamma-ray detection from gravitino dark matter decay in the $\mu\nu$SSM