Dynamical System Analysis of Interacting Variable Modified Chaplygin Gas Model in FRW Universe

TL;DR

This paper analyzes the dynamical behavior of a variable modified Chaplygin gas model interacting with dark matter in a flat FRW universe, identifying stable solutions and their cosmological implications.

Contribution

It introduces a dynamical system approach to the interacting variable modified Chaplygin gas model and finds stable attractor solutions relevant for late-time cosmic evolution.

Findings

Existence of a stable scaling (attractor) solution at late times.

The universe can evolve up to a quintessence stage within the model.

Calculated cosmological parameters and distances around the critical point.

Abstract

In this work, we have considered interacting dynamical model taking variable modified Chaplygin gas which plays as dark energy coupled to cold dark matter in the flat FRW universe. Since the nature of dark energy and dark matter is still unknown, it is possible to have interaction between them and we choose the interaction term in phenomenologically. We have converted all the equations in the dynamical system of equations by considering the dimensionless parameters and seen the evolution of the corresponding autonomous system. The feasible critical point has been found and for the stability of the dynamical system about the critical point, we linearize the governing equation around the critical point. We found that there exists a stable scaling (attractor) solution at late times of the Universe and found some physical range of $n$ and the interaction parameter $c$. We have shown that for our calculated physical range of the parameters, the Universe explores upto quintessence stage. The deceleration parameter, statefinder parameters, Hubble parameter and the scale factor have been calculated around the critical point. Finally some consequences around the critical point i.e., the distance measurement of the Universe like lookback time, luminosity distance, proper distance, angular diameter distance, comoving volume, distance modulus and probability of intersecting objects have been analyzed before and after the present age of the Universe.