Dynamical Systems in Cosmology

TL;DR

This paper reviews how dynamical systems theory helps analyze the long-term behavior of various cosmological models, including perfect fluids, scalar fields, and string-inspired models, highlighting their asymptotic states.

Contribution

It provides a comprehensive overview of dynamical systems applications in cosmology, emphasizing self-similar solutions and asymptotic analysis of different models.

Findings

Characterization of asymptotic states in perfect fluid models

Analysis of scalar field models with exponential potentials

Discussion of string effective action cosmologies

Abstract

Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary differential equations. We begin with a brief review of dynamical systems theory. We then discuss cosmological models as dynamical systems and point out the important role of self-similar models. We review the asymptotic properties of spatially homogeneous perfect fluid models in general relativity. We then discuss some results concerning scalar field models with an exponential potential (both with and without barotropic matter). Finally, we discuss some isotropic cosmological models derived from the string effective action.