  In the Starobinsky model of inflation, the observed dark matter abundance can
be produced from the direct decay of the inflaton field only in a very narrow
spectrum of close-to-conformal scalar fields and spinors of mass $\sim 10^7$
GeV. This spectrum can be, however, significantly broadened in the presence of
effective non-renormalizable interactions between the dark and the visible
sectors. In particular, we show that UV freeze-in can efficiently generate the
right dark matter abundance for a large range of masses spanning from the keV
to the PeV scale and arbitrary spin, without significantly altering the heating
dynamics. We also consider the contribution of effective interactions to the
inflaton decay into dark matter.
