Gravitational scalar production with a generic reheating scenario

Gravitational production of decoupled scalars during inflationary and post-inflationary phases is efficient and can lead to over-production. We study this production with various reheating scenarios such as a generic power-law inflaton potential $V_{\rm inf}\propto \phi^k$ as well as a multi-stage reheating scenario. We derive constraints on the scalar self-interaction coupling $\lambda_s$, the mass $m_s$, and coefficients of quantum gravity-induced operators. We find that the constraints depend sensitively on the reheating dynamics. Our analysis demonstrates that universal gravity effects do not necessarily spoil the predictivity of non-thermal dark matter scenarios with $k < 4$ and low reheating temperatures, as an extended reheating phase dilutes gravitationally-produced relics. For $k > 4$, on the other hand, the relic abundance is enhanced during the reheating phase, leading to stringent constraints on the scalar. In multi-stage reheating, we show that the enhancement/dilution effect of subsequent reheating phases factorises.