Mathematical properties of cosmological models with accelerated expansion

TL;DR

This paper reviews mathematical solutions to Einstein's equations that describe accelerated expansion in cosmology, exploring their properties, theorems, and connections to physical models including exotic matter types.

Contribution

It provides a comprehensive review of mathematical properties and theorems related to cosmological models with accelerated expansion, including both classical and exotic matter scenarios.

Findings

Reviewed solutions with positive cosmological constant and scalar fields

Explored mathematical theorems related to accelerated expansion models

Discussed exotic models like Chaplygin gas, tachyons, and k-essence

Abstract

An introduction to solutions of the Einstein equations defining cosmological models with accelerated expansion is given. Connections between mathematical and physical issues are explored. Theorems which have been proved for solutions with positive cosmological constant or nonlinear scalar fields are reviewed. Some remarks are made on more exotic models such as the Chaplygin gas, tachyons and $k$-essence.