Gravitational Production of Dark Matter during Reheating

Abstract: We consider the direct $s$-channel gravitational production of dark matter during the reheating process. Independent of the identity of the dark matter candidate or its non-gravitational interactions, the gravitational process is always present and provides a minimal production mechanism. During reheating, a thermal bath is quickly generated with a maximum temperature $T_{\rm max}$, and the temperature decreases as the inflaton continues to decay until the energy densities of radiation and inflaton oscillations are equal, at $T_{\rm RH}$. During these oscillations, $s$-channel gravitational production of dark matter occurs. We show that the abundance of dark matter (fermionic or scalar) depends primarily on the combination $T_{\rm max}^4/T_{\rm RH} M_P^3$. We find that a sufficient density of dark matter can be produced over a wide range of dark matter masses: from a GeV to a ZeV.