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An unstable gravitino with lifetime longer than $10^{26}$ sec or so has beenproposed as a possible dark matter candidate in supergravity models withR-parity breaking. We find a natural realization of this idea in the minimalsupersymmetric left-right models where left-right symmetry breaking scale inthe few TeV range. It is known that in these models, R-parity must break inorder to have parity breaking as required by low energy weak interactions. Thesub-eV neutrino masses imply that R-parity breaking effects in this model mustbe highly suppressed. This in turn makes the gravitino LSP long lived enough,so that it becomes the dark matter of the Universe. It also allows detectabledisplaced vertices at the LHC from NLSP decays. We present a detailed analysisof the model and some aspects of its rich phenomenology.

A Model With Dynamical R-parity Breaking and Unstable Gravitino Dark Matter