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.