Dynamical Systems in Cosmology

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.

38 pages. To appear in Proceedings of ERE-99

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• Exact anisotropic brane cosmologies
• Scalar Cosmology with Multi-exponential Potentials
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• The Similarity Hypothesis in General Relativity
• Interacting viscous dark fluids
• Qualitative analysis of Kantowski-Sachs metric in a generic class of $f(R)$ models
• Qualitative analysis of a scalar-tensor theory with exponential potential
• Algebraic integrability of FRW-scalar cosmologies