Cosmic infinity: a dynamical system approach

Abstract

Dynamical system techniques are extremely useful to study cosmology. It turns out that in most of the cases, we deal with finite isolated fixed points corresponding to a given cosmological epoch. However, it is equally important to analyse the asymptotic behaviour of the universe. On this paper, we show how this can be carried out for 3-form models. In fact, we show that there are fixed points at infinity mainly by introducing appropriate compactifications and defining a new time variable that washes away any potential divergence of the system. The richness of 3-form models allows us as well to identify normally hyperbolic non-isolated fixed points. We apply this analysis to three physically interesting situations: (i) a pre-inflationary era; (ii) an inflationary era; (iii) the late-time dark matter/dark energy epoch.