Gravitational reheating formulas and bounds in oscillating backgrounds

TL;DR

This paper derives formulas and bounds for the reheating temperature in cosmological models where heavy scalar particles are gravitationally produced during inflaton oscillations, considering different decay scenarios.

Contribution

It provides new analytic formulas and bounds for reheating temperatures in scenarios involving gravitational particle production during inflaton oscillations.

Findings

Derived formulas for reheating temperature based on particle energy density and decay rate.

Established bounds for maximum reheating temperature at the transition to radiation dominance.

Used the Born approximation to obtain analytic expressions for reheating temperature.

Abstract

In this article we calculate the reheating temperature in the cosmological scenarios where heavy scalar particles are gravitationally produced, due to a conformally coupled interaction between a massive scalar quantum field and the Ricci scalar, during the oscillations of the inflaton field. We explore two distinct cases, namely the one in which these particles decay during the domination of the inflaton's energy density and the other one where the decay occurs after this phase. For each scenario, we have derived formulas to calculate the reheating temperatures based on the energy density of the produced particles and their decay rate. We establish bounds for the maximum reheating temperature, defined as the temperature reached by the universe when the decay of gravitationally produced particles concludes at the onset of the radiation-dominated epoch. Finally, we use the Born approximation to find analytic formulas for the reheating temperature.