Exact Solutions for Cosmological Models with a Scalar Field

TL;DR

This paper derives exact cosmological solutions in scalar-tensor gravity by identifying Noether symmetries, determining specific forms of coupling and potential functions, advancing understanding of scalar field cosmologies.

Contribution

It introduces a method to find exact solutions in scalar-tensor cosmology through symmetry analysis, specifying forms of coupling and potential functions.

Findings

Exact solutions for scalar-tensor cosmology derived

Specific forms of coupling function and potential identified

Enhanced understanding of scalar field dynamics in cosmology

Abstract

We consider the existence of a Noether symmetry in the scalar-tensor theory of gravity in flat Friedman Robertson Walker (FRW) cosmology. The forms of coupling function $\omega(\phi)$ and generic potential $V(\phi)$ are obtained by requiring the existence of a Noether symmetry for such theory. We derive exact cosmological solutions of the field equations from a point-like Lagrangian.