# Understanding gravitational particle production in quintessential inflation

## TL;DR

This paper analyzes gravitational particle production during the transition from inflation to kination in quintessential inflation models, showing how decay timing affects reheating temperature and compatibility with Big Bang Nucleosynthesis.

## Contribution

It applies the diagonalization method to compute superheavy particle energy density and explores decay timing constraints to avoid overproduction of gravitational waves.

## Key findings

- Decay must occur after kination ends to prevent GW overproduction.
- Maximum reheating temperature is in the TeV range.
- Ensures compatibility with Big Bang Nucleosynthesis.

## Abstract

The diagonalization method, introduced by a group of Russian scientists at the beginning of seventies, is used to compute the energy density of superheavy massive particles produced due to a sudden phase transition from inflation to kination in quintessential inflation models, the models unifying inflation with quintessence originally proposed by Peebles-Vilenkin. These superheavy particles must decay in lighter ones to form a relativistic plasma, whose energy density will eventually dominate the one of the inflaton field, in order to have a hot universe after inflation. In the present article we show that, in order that the overproduction of Gravitational Waves (GWs) during this phase transition does not disturb the Big Bang Nucleosynthesis (BBN) success, the decay has to be produced after the end of the kination regime, obtaining a maximum reheating temperature in the TeV regime.