Dynamics of Modified Chaplygin Gas in Brane World Scenario: Phase Plane Analysis

TL;DR

This paper explores the dynamics of modified Chaplygin gas as dark energy in brane world models, analyzing phase space and stability to address cosmic coincidence and late-time acceleration.

Contribution

It introduces a coupled dark energy-dark matter model with modified Chaplygin gas in brane cosmology, providing numerical solutions and phase space analysis.

Findings

Stable scaling solutions found in both brane models

Background dynamics support accelerated expansion

Power law expansion near critical points

Abstract

In this work we investigate the background dynamics when dark energy is coupled to dark matter with a suitable interaction in the universe described by brane cosmology. Here DGP and the RSII brane models have been considered separately. Dark energy in the form of modified Chaplygin gas is considered. A suitable interaction between dark energy and dark matter is considered in order to at least alleviate (if not solve) the cosmic coincidence problem. The dynamical system of equations is solved numerically and a stable scaling solution is obtained. A significant attempt towards the solution of the cosmic coincidence problem is taken. The statefinder parameters are also calculated to classify the dark energy models. Graphs and phase diagrams are drawn to study the variations of these parameters. It is also seen that the background dynamics of modified Chaplygin gas is completely consistent with the notion of an accelerated expansion in the late universe. Finally, it has been shown that the universe in both the models follows the power law form of expansion around the critical point, which is consistent with the known results.