Dynamics of dark energy models and centre manifolds

TL;DR

This paper explores the dynamics of dark energy models involving three-forms and phantom fields, using centre manifold theory to analyze stability when linear methods are insufficient.

Contribution

It provides a concise introduction to centre manifold theory and demonstrates its application in analyzing complex dark energy models with zero eigenvalues.

Findings

Centre manifold theory effectively analyzes stability in dark energy models.

Explicit examples illustrate the application of the theory.

Enhances understanding of dynamical behavior in cosmological models.

Abstract

We analyse dark energy models where self-interacting three-forms or phantom fields drive the accelerated expansion of the Universe. The dynamics of such models is often studied by rewriting the cosmological field equations in the form of a system of autonomous differential equations, or simply a dynamical system. Properties of these systems are usually studied via linear stability theory. In situations where this method fails, for instance due to the presence of zero eigenvalues in the Jacobian, centre manifold theory can be applied. We present a concise introduction and show explicitly how to use this theory in two concrete examples.