Multi-fluid cosmology in Einstein gravity: analytical solutions

TL;DR

This paper reviews exact analytical solutions of Einstein's equations for multi-fluid cosmological models, including modern and classical solutions, with a focus on their explicit forms and applications.

Contribution

It provides a unified notation, explicit solutions, and a comprehensive review of both old and new solutions involving multiple fluids and scalar fields in cosmology.

Findings

Explicit solutions for multi-fluid universes are presented.

Relations between different solution forms are clarified.

Modern solutions involving interacting fluids and scalar fields are discussed.

Abstract

We review analytical solutions of the Einstein equations which are expressed in terms of elementary functions and describe Friedmann-Lema\^itre-Robertson-Walker universes sourced by multiple (real or effective) perfect fluids with constant equations of state. Effective fluids include spatial curvature, the cosmological constant, and scalar fields. We provide a description with unified notation, explicit and parametric forms of the solutions, and relations between different expressions present in the literature. Interesting solutions from a modern point of view include interacting fluids and scalar fields. Old solutions, integrability conditions, and solution methods keep being rediscovered, which motivates a review with modern eyes.