Dynamical system analysis of logotropic dark fluid with a power law in the rest-mass energy density

TL;DR

This paper uses dynamical system analysis to study a flat universe filled with a logotropic dark fluid coupled with dark matter, revealing a late-time accelerated expansion and phantom crossing behavior.

Contribution

It introduces an approximation for the logotropic dark fluid's pressure as an infinite series, enabling a dynamical system approach to analyze universe evolution.

Findings

Universe evolves to a late-time accelerated phase dominated by logotropic dark energy.

Intermediate phase where logotropic fluid behaves as dark matter.

Model predicts crossing of the phantom divide line.

Abstract

We consider a spatially flat FLRW universe. We assume that it is filled with dark energy in the form of logotropic dark fluid coupled with dark matter in the form of a perfect fluid having a barotropic equation of state. We employ dynamical system tools to obtain a complete qualitative idea of the evolution of such a universe. It is interesting to note that we ought to consider an approximation for the pressure of the logotropic dark fluid in the form of an infinite series so as to be able to construct the autonomous system required for a dynamical system study. This series form provides us with a power law in the rest-mass energy density of the logotropic dark fluid. We compute the critical points of the autonomous system and analyze these critical points by applying linear stability theory. Our analysis reveal a scenario of late-time accelerated universe dominated by the logotropic fluid which behaves as cosmological constant, preceded by an intermediate phase of the Universe dominated by logotropic fluid which behaves as dark matter in the form of perfect fluid. Moreover, it also crosses the phantom divide line.