Matter-Dark Energy Transition: A Dynamical Systems Approach

TL;DR

This paper uses a dynamical systems approach to analyze the transition from matter domination to dark energy domination in the universe by focusing on the ratio of their energy densities, offering a new perspective on cosmic evolution.

Contribution

It introduces a novel method that emphasizes the ratio of matter to dark energy densities, providing deeper insights into the transition dynamics using dynamical systems techniques.

Findings

Identifies critical points in the matter-dark energy ratio evolution.

Provides a detailed phase space analysis of the transition.

Offers potential explanations for the timing of cosmic acceleration.

Abstract

In this study, we deviate from the traditional examination of the evolving universe through the scale factor and instead consider a parameter \(\chi_{ME}\), defined by the ratio of two competing energy densities: matter (DM) and dynamic dark energy (DDE). While the scale factor's role is not neglected, it is inherently embedded within the evolution equations of these competing energy densities. By employing dynamical systems techniques, we investigate the behaviour of this ratio \(\chi_{ME}\) to understand the dynamics surrounding the cosmological transition from matter domination to dark energy domination. This methodological shift allows for a more nuanced analysis of the matter-to-dark energy transition.