Exact Scalar-Tensor Cosmological Models

TL;DR

This paper derives exact solutions for scalar-tensor cosmological models using symmetry techniques, explaining different phases of the Universe's expansion including acceleration and deceleration.

Contribution

It introduces a method to find exact solutions in scalar-tensor theories with arbitrary coupling functions, expanding understanding of cosmological evolution.

Findings

Exact solutions describing accelerating and decelerating universe phases

Application of Lie group and Noether symmetry methods to scalar-tensor models

Potential to model both early inflation and late-time acceleration

Abstract

Scalar-tensor gravitational theories are important extensions of standard general relativity, which can explain both the initial inflationary evolution, as well as the late accelerating expansion of the Universe. In the present paper we investigate the cosmological solution of a scalar-tensor gravitational theory, in which the scalar field $\phi $ couples to the geometry via an arbitrary function $F(\phi $). The kinetic energy of the scalar field as well as its self-interaction potential $V(\phi )$ are also included in the gravitational action. By using a standard mathematical procedure, the Lie group approach, and Noether symmetry techniques, we obtain several exact solutions of the gravitational field equations describing the time evolutions of a flat Friedman-Robertson-Walker Universe in the framework of the scalar-tensor gravity. The obtained solutions can describe both accelerating and decelerating phases during the cosmological expansion of the Universe.