An Anisotropic Kantowski-Sachs Universe with Radiation, Dust and a Phantom Fluid

In the present work, we study the dynamical evolution of a 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 a 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 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.

Automated summary

In this study, we investigated the dynamical evolution of a homogeneous and anisotropic cosmological model, considering general relativity and three different perfect fluids in the matter sector. We found that the universe tends to become isotropic during its expansion, suggesting an initial anisotropic stage that later became isotropic.