Abstract
Supersymmetric models provide very interesting scenarios to account for the dark matter of the Universe. In this talk we discuss scenarios with gravitino dark matter in R-parity breaking vacua, which not only reproduce very naturally the observed dark matter relic density, but also lead to a thermal history of the Universe consistent with the observed abundances of primordial elements and the observed matter-antimatter asymmetry. In this class of scenarios the dark matter gravitinos are no longer stable, but decay with very long lifetimes into Standard Model particles, thus opening the possibility of their indirect detection. We have computed the expected contribution from gravitino decay to the primary cosmic rays and we have found that a gravitino with a mass of 150 GeV and a lifetime of 10^26 s could simultaneously explain the EGRET anomaly in the extragalactic gamma-ray background and the HEAT excess in the positron fraction.
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