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

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 appearance of peaks in the evolution of the density contrast.