Collider signals of gravitino dark matter in bilinearly broken R-parity

In models with gauge mediated supersymmetry breaking the gravitino is the lightest supersymmetric particle. If R-parity is violated the gravitino decays, but with a half-live far exceeding the age of the universe and thus is, in principle, a candidate for the dark matter. We consider the decays of the next-to-lightest supersymmetric particle, assumed to be the neutralino. We show that in models where the breaking of R-parity is bilinear, the condition that R-parity violation explains correctly the measured neutrino masses fixes the branching ratio of the decay ${\tilde \chi}^0_1 \to {\tilde G}\gamma$ in the range $10^{-3}-10^{-2}$, if the gravitino mass is in the range required to solve the dark matter problem, i.e. of the order (few) 100 eV. This scenario is therefore directly testable at the next generation of colliders.