Gravitino Dark Matter without R-parity
  Cosmological issues are examined when gravitino is the lightest superparticle (LSP) and R-parity is broken. Decays of the next lightest superparticles occur rapidly via R-parity violating interaction, and thus they do not upset the big-bang nucleosynthesis, unlike the R-parity conserving case. The gravitino LSP becomes unstable, but its lifetime is typically much longer than the age of the Universe. It turns out that observations of diffuse photon background coming from radiative decays of the gravitino do not severely constrain the gravitino abundance, and thus the gravitino weighing less than around 1 GeV can be dark matter of the Universe when bilinear R-parity violation generates a neutrino mass which accounts for the atmospheric neutrino anomaly. 
Fumihiro Takayama and Masahiro Yamaguchi