  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 m_{3/2} \gsim 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
m_{3/2} \sim 10 GeV. In this case, a clear signal can be expected from GLAST in
the near future.
