  We study production of gravitino and Polonyi particles in the minimal
Starobinsky-Polonyi $\mathcal{N}=1$ supergravity with inflaton belonging to a
massive vector supermultiplet. Our model has only one free parameter given by
the scale of spontaneous SUSY breaking triggered by Polonyi chiral superfield.
The vector supermultiplet generically enters the action non-minimally, via an
arbitrary real function. This functon is chosen to generate the inflaton scalar
potential of the Starobinsky model. Our supergravity model can be reformulated
as an abelian supersymmetric gauge theory with the vector gauge superfield
coupled to two (Higgs and Polonyi) chiral superfields interacting with
supergravity, where the $U(1)$ gauge symmetry is spontaneously broken. We find
that Polonyi and gravitino particles are efficiently produced during inflation.
After inflation, perturbative decay of inflaton also produces Polonyi particles
that rapidly decay into gravitinos. As a result, a coherent picture of
inflation and dark matter emerges, where the abundance of produced gravitinos
after inflation fits the CMB constraints as a Super Heavy Dark Matter (SHDM)
candidate. Our scenario avoids the notorous gravitino and Polonyi problems with
the Big Bang Nucleosynthesis (BBN) and DM overproduction.
