  Polonyi-Starobinsky (PS) supergravity is the N=1 supergravity model of
Starobinsky inflation with spontaneous supersymmetry breaking (after inflation)
due to Polonyi superfield, and inflaton belonging to a massive vector
supermultiplet. The PS model is used for an explicit realization of the
(super-heavy) gravitino dark matter scenario in cosmology. We find a potential
instability in this model, and offer a mechanism for its removal by adding a
Fayet-Iliopoulos (FI) term.
