On exact solutions to the scalar field equations in standard cosmology

TL;DR

This paper introduces a straightforward algebraic technique for deriving exact solutions to scalar field equations in flat FRW cosmology, simplifying the analysis of inflationary models and extending to perfect fluid scenarios.

Contribution

It presents a novel algebraic method to find exact solutions for scalar fields in cosmology, applicable to various potentials and perfect fluids.

Findings

Method successfully derives solutions for typical inflationary potentials.

Applicable to perfect fluids with curvature k>=0 and fixed gamma.

Simplifies analysis of scalar field dynamics in cosmology.

Abstract

A simple algebraic method to obtain exact solutions to the scalar field equations in spatially flat FRW cosmology is derived. The field potential fuction is reduced to two terms which can be used to determine some characteristic inflationary variables. To demonstrate the method, exact solutions resembling typical potentials of general interest are worked out. Finally, it is shown that this method of solution is also applicable to a perfect fluid in the same metric, for a curvature k>=0 and fixed gamma.