Gravitino dark matter in R-parity breaking vacua

We show that in the case of small R-parity and lepton number breaking couplings, primordial nucleosynthesis, thermal leptogenesis and gravitino dark matter are naturally consistent for gravitino masses m3/2 >or similar 5 GeV. We present a model where R-parity breaking is tied to B-L breaking, which predicts the needed small couplings. The metastable next-to-lightest superparticle has a decay length that is typically larger than a few centimeters, with characteristic signatures at the LHC. The photon flux produced by relic gravitino decays may be part of the apparent excess in the extragalactic diffuse gamma-ray flux obtained from the EGRET data for a gravitino mass m3/2∝10 GeV. In this case, a clear signal can be expected from GLAST in the near future. (orig.)