Antimatter signatures of gravitino dark matter decay

The scenario of gravitino dark matter with broken R-parity naturally reconciles three paradigms that, albeit very well motivated separately, seem to be in mutual conflict: supersymmetric dark matter, thermal leptogenesis and standard big bang nucleosynthesis. Interestingly, the products of the gravitino decay could be observed, opening the possibility of indirect detection of gravitino dark matter. In this paper, we compute the positron and the antiproton fluxes from gravitino decay. We find that a gravitino with a mass of m(3/2) similar to 150 GeV and a lifetime of tau(3/2) similar to 10(26) s could simultaneously explain the EGRET anomaly in the extragalactic diffuse gamma ray background and the HEAT excess in the positron fraction. However, the predicted antiproton flux tends to be too large, although the prediction suffers from large uncertainties and might be compatible with present observations for certain choices of propagation parameters.