Self-similar spherically symmetric cosmological models with a perfect fluid and a scalar field

TL;DR

This paper analyzes self-similar, spherically symmetric cosmological models with a perfect fluid and scalar field, revealing their global dynamical behavior and possible evolutionary outcomes such as recollapse or eternal expansion.

Contribution

It introduces new variables for a compact state space and applies dynamical systems methods to derive comprehensive global results for these cosmological models.

Findings

Models evolve from a massless scalar field initial singularity.

Depending on parameters, models either recollapse or expand forever.

Special cases include no fluid or massless scalar field, illustrating asymptotic behaviors.

Abstract

Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are utilised to analyse the models. Due to the existence of monotone functions global dynamical results can be deduced. In particular, all of the future and past attractors for these models are obtained and the global results are discussed. The essential physical results are that initially expanding models always evolve away from a massless scalar field model with an initial singularity and, depending on the parameters of the models, either recollapse to a second singularity or expand forever towards a flat power-law inflationary model. The special cases in which there is no barotropic fluid and in which the scalar field is massless are considered in more detail in order to illustrate the asymptotic results. Some phase portraits are presented and the intermediate dynamics and hence the physical properties of the models are discussed.