Dynamics and chaos in the unified scalar field cosmology II. System in a finite box

TL;DR

This paper analyzes the global dynamics of unified dark matter cosmological models using a bounded variable approach, providing new insights into critical points, trajectories, and chaos in the system.

Contribution

It introduces a new bounded variable framework for better analysis of the system's critical points and explores the chaotic nature of the cosmological model.

Findings

Bounded variable space improves control over critical points.

Analysis of physically motivated trajectories and their relation to the scale factor.

Discussion on the presence or absence of chaos in the system.

Abstract

We revisit the global dynamics of unified dark matter cosmological models and analyze it in a new dynamical system setting. In particular, by defining a suitable set of variables we obtain a bounded variable space, a feature that allows a better control of the critical elements of the system. First, we give a comprehensive cosmological interpretation of the critical points. Then, we turn our focus on particular representative trajectories with physically motivated initial conditions studied in the first paper of the series, and we discuss how the scale factor relates to the equation of state parameter. We review and complement these results in the light of the new variable approach by discussing the issue whether the system is chaotic or not.