Modelo cosmológico do tipo Kantowski-Sachs com fluidos de radiação, poeira e fantasma

Abstract

In this dissertation we study the dynamics of a Universe described by a cosmological model of the Kantowski-Sachs type where the material content is the fluids of dust, radiation and phantom. The latter representing dark energy. The study was done separately for each fluid and then for all of them together. The results obtained from the studies with dust and radiation fluids show that the universe is not expansive due to the presence of these fluids. For the phantom fluid we have that the scale factors, a(t) and b(t), go to infinite values in a finite time, resulting in the Big Rip type of singularity. Due to the domination of the phantom fluid over the radiation and dust fluids, in the model with all the three fluids, called complete fluid, we observed an expansion of the universe with the scale factors going to the Big Rip singularity. Being homogeneous and anisotropic, the Kantowski-Sachs metric allowed us to study the model’s anisotropy through the expansion anisotropy parameter (∆). Through the analysis for various values of the initial conditions and model parameters, we concluded that by the time the universe tends to the singularity the model becomes isotropic. Finally, inspired by the Misner’s parameterization, we rewrote the metric in terms of a scale factor a(t) and another function β(t), which describes the anisotropy. Through the study of this cosmological model with that new parameterization and the complete fluid, we concluded that the scale factor a(t) tends to the Big Rip singularity and the function β(t) tends to a constant, when the time tends to the singularity instant. This behavior confirms the isotropization of the model.