Abstract: First, I discuss the out-of-equilibrium production of scalar dark matter (DM) from the inflaton condensate during inflation and reheating. Here I assume that this scalar dark matter is only minimally coupled to gravity and consider the regime of purely gravitational dark matter. For the purely gravitational regime, scalar dark matter quanta are copiously excited during inflation resulting in an infrared (IR) dominated distribution function and a relic abundance that overcloses the universe for a reheating temperature T_{reh} > 34 GeV. I discuss the reheating mechanism and compare perturbative and non-perturbative calculations of the energy density in radiation, and compare the resulting energy density based on these different approaches. I also briefly discuss the isocurvature constraints. This talk is based on arXiv:2206.08940 and arXiv:2109.13280.