Cosmic infinity: A dynamical system approach

TL;DR

This paper applies dynamical system techniques to cosmology, specifically analyzing the asymptotic behavior of 3-form models by identifying fixed points at infinity through compactification and new time variables.

Contribution

It introduces a method to analyze the asymptotic behavior of 3-form cosmological models by identifying fixed points at infinity using compactification and redefined time variables.

Findings

Fixed points at infinity identified in 3-form models

Introduction of compactification techniques for dynamical systems

Discovery of hyperbolic non-isolated fixed points

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-forms model. 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.