Class of exact solutions for a cosmological model of unified gravitational and quintessence fields

TL;DR

This paper introduces a novel exact solution for Einstein's equations in a universe with quintessence, unifying geometry and dark matter, and explores its implications for cosmic acceleration and evolution.

Contribution

It presents a new method to derive exact solutions for a cosmological model with quintessence, uniquely determining the potential and extending to include matter and radiation.

Findings

Produces perpetual accelerated expansion for positive curvature universe

Hubble parameter exhibits a maximum and then decreases

Solution differs from previous inflation models

Abstract

A new approach to tackle Einstein equations for an isotropic and homogeneous Friedmann--Robertson--Walker Universe in the presence of a quintessence scalar field is devised. It provides a way to get a simple exact solution to these equations. This solution determines the quintessence potential uniquely and it differs from solutions which have been used to study inflation previously. It relays on a unification of geometry and dark matter implemented through the definition of a functional relation between the scale factor of the Universe and the quintessence field. For a positive curvature Universe, this solution produces perpetual accelerated expansion rate of the Universe, while the Hubble parameter increases abruptly, attains a maximum value and decreases thereafter. The behavior of this cosmological solution is discussed and its main features are displayed. The formalism is extended to include matter and radiation.