Infinite dimensional symmetry groups of the Friedmann equations

TL;DR

This paper identifies infinite-dimensional symmetry groups of Friedmann equations with a perfect fluid and cosmological constant, enabling transformations between solutions with different equations of state.

Contribution

It derives the symmetry generators for the Friedmann equations, revealing an infinite-dimensional symmetry group that generalizes and extends previous results.

Findings

Symmetry group is infinite-dimensional with arbitrary functions.

Solutions with different equations of state can be mapped to each other.

Provides a method to generate complex solutions from simple known cases.

Abstract

We find the symmetry generators for the Friedman equations emanating from a perfect fluid source, in the presence of a cosmological constant term. The relevant dynamics is seen to be governed by two coupled, first order ordinary differential equations, the continuity and the quadratic constraint equation. Arbitrary functions appear in the components of the symmetry vector, indicating the infinity of the group. When the equation of state is considered as arbitrary but ab initio given, previously known results are recovered and/or generalized. When the pressure is considered among the dynamical variables, solutions for models with different equations of state are mapped to each other; thus enabling the presentation of solutions to models with complicated equations of state starting from simple known cases.