A mathematical analysis of the evolution of perturbations in a modified Chaplygin gas model

TL;DR

This paper analytically and numerically investigates the evolution of density perturbations in a flat cosmological model with a modified Chaplygin gas, aiming to distinguish it from other models with similar scale factor evolution.

Contribution

It provides a unique analytical characterization of perturbation evolution in the modified Chaplygin gas model, including spheroidal wave functions and numerical peak analysis.

Findings

Density contrast evolution can be described by spheroidal wave functions.

Numerical results show peaks in the density contrast evolution.

The model's properties can distinguish it from other cosmological models.

Abstract

One approach in modern cosmology consists in supposing that dark matter and dark energy are different manifestations of a single `quartessential' fluid. Following such idea, this work presents a study of the evolution of perturbations of density in a flat cosmological model with a modified Chaplygin gas acting as a single component. Our goal is to obtain properties of the model which can be used to distinguish it from another cosmological models which have the same solutions for the general evolution of the scale factor of the universe, without the construction of the power spectrum. Our analytical results, which alone can be used to uniquely characterize the specific model studied in our work, show that the evolution of the density contrast can be seen, at least in one particular case, as composed by a spheroidal wave function. We also present a numerical analysis which clearly indicates as one interesting feature of the model the appearence of peaks in the evolution of the density constrast.