Gravitational particle creation for dark matter and reheating

The purely gravitational dark matter (PGDM) which interacts with the standard model particles only by gravitational interaction has recently been discussed. Due to its feeble interaction, PGDM may be produced mainly by the gravitational particle creation, which plays an important role in the reheating after kinetically driven inflation and some potential-driven inflation without subsequent inflaton oscillating phase. Therefore, we consider the possibility of the gravitational reheating model which can also explain the present PGDM density at the same time. We consider a model where two massive scalar fields are incorporated into the standard model besides the inflation sector. We show that the gravitational particle creation prevails over the thermal creation --- the freeze-in process --- and it can actually explain the reheating and the present abundance of dark matter if one of the scalar particles is as heavy as the Hubble parameter during inflation $\sim10^{13}$ GeV and finally decays into radiation via sufficiently weak coupling, and the other is a stable PGDM with its mass of the order of $10^3$ GeV.