Form invariance symmetry generates a large set of FRW cosmologies

TL;DR

This paper demonstrates that form invariance symmetry in Einstein's equations for flat FRW cosmologies generates a broad class of equivalent models through transformations of key cosmological variables.

Contribution

It introduces a new symmetry framework using form invariance transformations to generate diverse cosmological solutions from a seed model.

Findings

Transformations form a Lie group acting on cosmological variables.

Linear FITs produce dualities and generate multiple cosmologies.

Applicable to perfect fluids and scalar field models.

Abstract

We show that Einstein's field equations for spatially flat Friedmann-Robertson-Walker (FRW) space times have a form invariance symmetry (FIS) realized by the form invariance transformations (FIT) which are indeed generated by an invertible function of the source energy density. These transformations act on the Hubble expansion rate, the energy density, and pressure of the cosmic fluid; likewise such transformations are endowed with a Lie group structure. Each representation of this group is associated with a particular fluid and consequently a determined cosmology, so that, the FIS defines a set of equivalent cosmological models. We focus our seek in the FIT generated by a linear function because it provides a natural framework to express the duality and also produces a large sets of cosmologies, starting from a seed one, in several contexts as for instance in the cases of a perfect fluid source and a scalar field driven by a potential depending linearly on the scalar field kinetic energy density.