  Gravity takes care of both inflation and subsequent reheating in
Starobinsky's R^2-model. The latter is due to inflaton gravitation decays
dominated by scalar particle production. It is tempting to suggest that dark
matter particles are also produced in this process. Since free scalars being
too hot cannot serve as viable dark matter (Phys.Lett.B700:157-162,2011), we
further study the issue considering two options: scalars with non-minimal
coupling to gravity and superheavy scalars generated at inflationary stage. We
found that the first option allows for viable warm or cold dark matter if
scalar mass exceeds 0.8 MeV. The second option implies supercold dark matter
with particle mass 10^16 GeV, which production is saturated at the end of
inflation when inflaton-dependent scalar mass rapidly changes and violates
adiabaticity. Similar result holds for superheavy fermion dark matter.
