We explore the consequences of a time-dependent inflaton Equation-of-State (EoS) parameter in the context of the post-inflationary perturbative Boltzmann reheating. In particular, we numerically solve the perturbative coupled system of Boltzmann equations involving the inflaton energy density, the radiation energy density and the related entropy density and temperature of the produced particle thermal bath. We exploit reasonable Ansatze for the EoS and discuss the robustness of the Boltzmann system. We also comment on the possible microscopic origin related to a time dependent inflaton potential, discussing the consequences on a preheating stage and the related (primordial) gravitational waves.
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