Gravitino Dark Matter in Tree Level Gauge Mediation with and without
  R-parity
  We investigate the cosmological aspects of Tree Level Gauge Mediation, a
recently proposed mechanism in which the breaking of supersymmetry is
communicated to the soft scalar masses by extra gauge interactions at the tree
level. Embedding the mechanism in a Grand Unified Theory and requiring the
observability of sfermion masses at the Large Hadron Collider, it follows that
the Lightest Supersymmetric Particle is a gravitino with a mass of the order of
10 GeV. The analysis in the presence of R-parity shows that a typical Tree
Level Gauge Mediation spectrum leads to an overabundance of the Dark Matter
relic density and a tension with the constraints from Big Bang Nucleosynthesis.
This suggests to relax the exact conservation of the R-parity. The underlying
SO(10) Grand Unified Theory together with the bounds from proton decay provide
a rationale for considering only bilinear R-parity violating operators. We
finally analyze the cosmological implications of this setup by identifying the
phenomenologically viable regions of the parameter space.
