Gravitational reheating and superheavy Dark Matter creation after
  inflation with non-minimal coupling
  We discuss the gravitational creation of superheavy particles $\chi$ in an
inflationary scenario with a quartic potential and a non-minimal coupling
between the inflaton $\varphi$ and the Ricci curvature: $\xi \varphi^2 R/2$. We
show that for large constants $\xi >> 1$, there can be abundant production of
particles $\chi$ with masses largely exceeding the inflationary Hubble rate
$H_{infl}$, up to $(a~few) \times \xi H_{infl}$, even if they are conformally
coupled to gravity. We discuss two scenarios involving these gravitationally
produced particles $\chi$. In the first scenario, the inflaton has only
gravitational interactions with the matter sector and the particles $\chi$
reheat the Universe. In this picture, the inflaton decays only due to the
cosmic expansion, and effectively contributes to dark radiation, which can be
of the observable size. The existing limits on dark radiation lead to an upper
bound on the reheating temperature. In the second scenario, the particles
$\chi$ constitute Dark Matter, if substantially stable. In this case, their
typical masses should be in the ballpark of the Grand Unification scale.
