Relationship between (2+1) and 3+1)--Friedmann--Robertson--Walker cosmologies

TL;DR

This paper establishes a correspondence between (2+1) and (3+1) Friedmann--Robertson--Walker cosmologies with specific state equations, providing a method to derive solutions in one from the other for perfect fluids and scalar fields.

Contribution

It introduces a theorem linking (2+1) and (3+1) cosmological solutions under general state equations, expanding the understanding of their interrelation.

Findings

A theorem connecting (2+1) and (3+1) solutions is demonstrated.

The work provides a method to derive one cosmology from the other.

Applications of the theorem are discussed.

Abstract

In this work we establish the correspondence between solutions to the Friedmann--Robertson--Walker cosmologies for perfect fluid and scalar field sources, where both ones fulfill state equations of the form $p+\rho=\gamma f(\rho)$, not necessarily linear ones. Such state equations are of common use in the case of matter--fluids, nevertheless, for a scalar field, they introduce relationships on the potential and kinetic scalar field energies which restrict the set of solutions. A theorem on this respect is demonstrated: From any given (3+1)--cosmological solution, obeying the quoted state equations, one can derive its (2+1)--cosmological counterpart or vice-versa. Some applications are given.