The choice of variables in cosmological dynamical systems

Abstract

Dynamical systems techniques are a powerful tool to analyse systems of ordinary differential equations, written in an appropriate form. For a given theory of gravity, the cosmological field equations typically lead to a system of ordinary differential equations. Casting these cosmological equations into the form of a dynamical system requires a careful choice of the dynamical variables. Despite this being a critical step, relatively little is said about this process in the literature. We discuss how different variable choices affect the information that can be extracted from the Friedmann equations. We begin by reviewing the standard cosmological model with dark matter, radiation, and dark energy, and include quintessence models. We revisit well-known models with an exponential potential using new variables. This discussion is then extended to models with scalar fields and more intricate coupling terms.