An anisotropic Kantowski-Sachs universe with radiation, dust and a phantom fluid

TL;DR

This study models an anisotropic universe with radiation, dust, and phantom fluid, showing it evolves towards isotropy over time and ends in a Big Rip, suggesting a possible initial anisotropic state of our universe.

Contribution

It introduces a numerical analysis of an anisotropic Kantowski-Sachs universe with multiple fluids, demonstrating isotropization and the potential link to our universe's initial conditions.

Findings

Universe becomes isotropic over time

Model ends in a Big Rip singularity

Initial anisotropic state may evolve into an isotropic universe

Abstract

In the present work, we study the dynamical evolution of an homogeneous and anisotropic KS cosmological model, considering general relativity as the gravitational theory, such that there are three different perfect fluids in the matter sector. They are radiation, dust and phantom fluid. Our main motivation is determining if the present model tends to an homogeneous and isotropic FRW model, during its evolution. Also, we want to establish how the parameters and initial conditions of the model, quantitatively, influence the isotropization of the present model. In order to simplify our task, we use the Misner parametrization of the KS metric. In terms of that parametrization the KS metric has two metric functions: the scale factor $a(t)$ and $\beta(t)$, which measures the spatial anisotropy of the model. We solve, numerically, the Einstein's equations of the model and find a solution where the universe starts to expand from a, small, initial size and continues to expand until it ends in a {\it Big Rip} singularity. We explicitly show that for the expansive solution, after same time, the universe becomes isotropic. Based on that result, we can speculate that the expansive solution may represent an initial, anisotropic, stage of our Universe, that later, due to the expansion, became isotropic.