Dynamics of the $\Lambda$CDM model of the universe from the aspect of the dynamical systems theory

TL;DR

This paper applies dynamical systems theory to analyze the $$CDM cosmological model, revealing new relationships between the universe's expansion and density parameters, assuming non-interacting perfect fluids.

Contribution

It introduces a dynamical systems approach to the $$CDM model and derives new dependencies between key cosmological variables.

Findings

New dynamical relationships between scale factor and density parameters

Physical interpretation of the dynamical system in cosmology

Framework for analyzing universe evolution using dynamical systems

Abstract

In this paper we exploit the theory of the dynamical systems to study the dynamics of the standard cosmological model of the universe, which is known as the $\Lambda$CDM model. We assume that the matter content in our universe consists of barotropic perfect fluids without mutual interaction. Furthermore, we present the appropriate physical interpretation, as well as new dependencies between the scale expansion factor of the universe and cosmological density parameters.