Dynamical Equilibrium States of a Class of Irrotational Non-Orthogonally Transitive $G_{2}$ Cosmologies II: Models With One Hypersurface-Orthogonal Killing Vector Field

TL;DR

This paper analyzes a class of inhomogeneous cosmological models with specific symmetry properties, revealing two well-behaved classes: one matter-dominated and asymptotically homogeneous, and another vacuum-dominated with diverse asymptotic behaviors.

Contribution

It introduces a new class of self-similar cosmological models with particular symmetry constraints and analyzes their spatial and dynamical properties.

Findings

Two classes of well-behaved models identified

One class is asymptotically matter-dominated and homogeneous

Another class is vacuum-dominated with diverse asymptotics

Abstract

We consider a class of inhomogeneous self-similar cosmological models in which the perfect fluid flow is tangential to the orbits of a three-parameter similarity group. We restrict the similarity group to possess both an Abelian $G_{2}$, and a single hypersurface orthogonal Killing vector field, and we restrict the fluid flow to be orthogonal to the orbits of the Abelian $G_{2}$. The temporal evolution of the models is forced to be power law, due to the similarity group, and the Einstein field equations reduce to a three-dimensional autonomous system of ordinary differential equations which is qualitatively analysed in order to determine the spatial structure of the models. The existence of two classes of well-behaved models is demonstrated. The first of these is asymptotically spatially homogeneous and matter dominated, and the second is vacuum dominated and either asymptotically spatially homogeneous or acceleration dominated, at large spatial distances.