3.5 keV x-ray line from decaying gravitino dark matter

Extremely weakly interacting particles like the gravitino may be stable enough on cosmological time scales to constitute a good dark matter candidate even in the presence of $R$-parity violation. We consider the possibility that the recently identified 3.5 keV x-ray line can be generated in light gravitino decays to neutrinos and photons. We find that this is indeed possible in loop processes induced by trilinear lepton-number-violating couplings. We show that in order to avoid overproduction of gravitinos, the reheating temperature has to be at most around 100 GeV to 1 TeV. Finally we briefly discuss associated LHC phenomenology due to a relatively light gluino and multijet/multilepton events from $R$-parity-violating decays of neutralinos.