# Energy Density, Temperature and Entropy Dynamics in Perturbative Reheating

## TL;DR

This paper analyzes the dynamics of energy density, temperature, and entropy during perturbative reheating after inflation, introducing key time scales and deriving related physical quantities for non-instantaneous reheating scenarios.

## Contribution

It provides new computations and refined concepts for the evolution of energy densities and temperatures during perturbative reheating with a non-zero equation-of-state parameter.

## Key findings

- Identifies two fundamental time scales: $t_{max}$ and $t_{reh}$.
- Derives energy densities and temperatures at these key times.
- Calculates the horizon entropy $S_{hor}$ for $w
eq 0$.

## Abstract

We discuss the perturbative decay of the energy density of a non standard inflaton field $\rho_{\phi}$ and the corresponding creation of the energy density of the relativistic fields $\rho_r$ 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 time scales. The first one, $t_\text{max}$, occurs when the energy density $\rho_r$ reaches its largest value, slightly after the beginning of the reheating phase. The second one, $t_\text{reh}$, is the time in which the reheating is completely realized and the thermalization is attained. By assuming a non-instantaneous reheating phase, we are able to derive the energy densities and the temperatures of the produced relativistic bath at $t_\text{max}$ and $t_\text{reh}$, as well as the value of the corresponding horizon entropy $S_\text{hor}$, for an Equation-of-State (EoS) parameter $w\ne 0$.