# The Peebles -- Vilenkin quintessential inflation model revisited

## TL;DR

This paper revisits and refines the Peebles-Vilenkin quintessential inflation model, aligning it more closely with recent cosmological observations by reducing it to two key parameters and calculating them based on observational data.

## Contribution

It introduces an improved PV model with only two parameters, deriving their values from observational data and dynamical system analysis.

## Key findings

- The inflaton mass is determined from the scalar perturbation spectrum.
- The parameter M is calculated considering the reheating temperature and observational data.
- The model's parameters are consistent with current cosmological observations.

## Abstract

We review the well-known Peebles-Vilenkin (PV) quintessential inflation model and discuss its possible improvements in agreement with the recent observations. The improved PV model depends only on two parameters: the inflaton mass $m$, and another smaller mass $M$; where the latter has to be chosen in order to undertake that, at present time, the dark energy density of the universe is approximately about 70\% of the total energy budget of the universe. The value of the inflaton mass $m$ is calculated using the observational value of the power spectrum of the scalar perturbations, and the value of mass $M$, which depends on the reheating temperature, is calculated by solving the corresponding dynamical system whose initial conditions are taken at the matter-radiation equality and are obtained from three observational data: the red shift at the matter-radiation equality, the ratio of the matter energy density to the critical one at the present time and the current value of the Hubble parameter.