High energy cosmic rays from the decay of gravitino dark matter

We study high energy cosmic rays from the decay of the gravitino dark matter in the framework of supersymmetric model with $R$-parity violation. Even though $R$ parity is violated, the lifetime of the gravitino, which is assumed to be the lightest superparticle, can be longer than the present age of the Universe if $R$-parity violating interactions are weak enough. We have performed a detailed calculation of the fluxes of gamma ray and positron from the decay of the gravitino dark matter. We also discuss the implication of such a scenario to present and future observations of high energy cosmic rays. In particular, we show that the excess of the gamma-ray flux observed by Energetic Gamma Ray Experiment Telescope and the large positron fraction observed by High Energy Antimatter Telescope can be simultaneously explained by the cosmic rays from the decay of the gravitino dark matter.