Energy density, temperature, and entropy dynamics in perturbative reheating

We discuss the perturbative decay of the energy density of a nonstandard inflaton field ρϕ and the corresponding creation of the energy density of the relativistic fields ρr at the end of inflation, in the perfect fluid description, refining some concepts and providing some new computations. In particular, the process is characterized by two fundamental timescales. The first one, tmax, occurs when the energy density ρr reaches its largest value, slightly after the beginning of the reheating phase. The second one, treh, is the time in which the reheating is completely realized and the thermalization is attained. By assuming a noninstantaneous reheating phase, we are able to derive the energy densities and the temperatures of the produced relativistic bath at tmax and treh, as well as the value of the corresponding horizon entropy Shor, for an equation-of-state parameter w≠0.