Anisotropic Matter in Cosmology: Locally Rotationally Symmetric Bianchi $I$ and $VII_o$ Models

TL;DR

This paper explores exact solutions for anisotropic cosmological models with anisotropic matter, revealing complex behaviors near singularities and expanding understanding of matter's role in early universe anisotropies.

Contribution

It provides new exact solutions for Bianchi I and VII_o models with anisotropic pressures, highlighting the impact of different matter sources on anisotropic cosmological evolution.

Findings

Existence of solutions with anisotropic matter that differ from isotropic models.

Identification of matter types like magnetic fields and cosmic strings influencing anisotropy.

More complex matter effects near singularities than previously understood.

Abstract

We examine the behaviour of homogeneous, anisotropic space-times, specifically the locally rotationally symmetric Bianchi types $I$ and $VII_o$ in the presence of anisotropic matter. By finding an appropriate constant of the motion, and transforming the equations of motion we are able to provide exact solutions in the presence perfect fluids with anisotropic pressures. The solution space covers matter consisting of a single perfect fluid which satisfies the weak energy condition and is rich enough to contain solutions which exhibit behaviour which is qualitatively distinct from the isotropic sector. Thus we find that there is more `matter that matters' close to a homogeneous singularity than the usual stiff fluid. Example metrics are given for cosmologies whose matter sources are magnetic fields, relativistic particles, cosmic strings and domain walls.