Introduction to the application of the dynamical systems theory in the study of the dynamics of cosmological models of dark energy

TL;DR

This paper introduces the application of dynamical systems theory to cosmological models of dark energy, demonstrating how these tools reveal the asymptotic behavior of models like DM and scalar fields, in a pedagogical manner.

Contribution

It provides a basic, accessible introduction to dynamical systems methods in cosmology, highlighting their effectiveness in analyzing dark energy models.

Findings

Dynamical systems tools effectively analyze asymptotic cosmological behaviors.

Application to DM and scalar field models illustrates their utility.

The approach is pedagogical, suitable for educational purposes.

Abstract

The theory of the dynamical systems is a very complex subject which has brought several surprises in the recent past in connection with the theory of chaos and fractals. The application of the tools of the dynamical systems in cosmological settings is less known in spite of the amount of published scientific papers on this subject. In this paper a -- mostly pedagogical -- introduction to the application in cosmology of the basic tools of the dynamical systems theory is presented. It is shown that, in spite of their amazing simplicity, these allow to extract essential information on the asymptotic dynamics of a wide variety of cosmological models. The power of these tools is illustrated within the context of the so called $\Lambda$CDM and scalar field models of dark energy. This paper is suitable for teachers, undergraduate and postgraduate students from physics and mathematics disciplines.