Global cosmological dynamics for the scalar field representation of the modified Chaplygin gas

TL;DR

This paper analyzes the global dynamics of a scalar field model for the modified Chaplygin gas in flat FLRW cosmology, introducing new bounded variables to study the system's behavior and solution stability.

Contribution

It introduces a novel set of bounded variables that enable a regular dynamical system analysis of the scalar field representation of the modified Chaplygin gas.

Findings

Exact modified Chaplygin gas solution appears as a straight line in phase space.

No solutions remain close to the perfect fluid solution throughout evolution.

Solutions can stay close during intermediate times if the potential has a global minimum.

Abstract

In this paper we investigate the global dynamics for the minimally coupled scalar field representation of the modified Chaplygin gas in the context of flat FLRW cosmology. The tool for doing this is a new set of bounded variables that lead to a regular dynamical system. It is shown that the exact modified Chaplygin gas perfect fluid solution appears as a straight line in the associated phase plane. It is also shown that no other solutions stay close to this solution during their entire temporal evolution, but that there exists an open subset of solutions that stay arbitrarily close during an intermediate time interval, and into the future in the case the scalar field potential exhibits a global minimum.