On Lie Point Symmetries of Einstein's equations for the Friedmann-Roberstson-Walker Cosmology

TL;DR

This paper analyzes the Lie point symmetries of Einstein's equations in Friedmann-Robertson-Walker cosmology, classifying their structure and reducing the equations using symmetry invariants to facilitate solutions.

Contribution

It identifies the symmetry groups of Einstein's equations in this cosmological model and employs these symmetries to simplify the differential equations involved.

Findings

Symmetry groups are either two- or three-dimensional solvable groups.

Invariants allow reduction of second-order equations to first-order systems.

Proper time formulation reveals additional variational symmetries.

Abstract

We study the Lie point symmetries of Einstein's equations for the Friedmann-Roberstson-Walker Cosmology. They form either a two - dimensional or a three - dimensional solvable group depending on the form of the self interacting potential. Using the invariants of the group we reduce the second order system of differential equations into a first order system. Writing the action in terms of the proper time we study the point symmetries and the variational symmetries of the resulting equations.