Métrica Bianchi I em uma teoria com derivadas superiores e matéria relativística

Abstract

In the first part of this thesis, results are presented about an anisotropic metric of the type Bianchi I in a cosmological model with described relativistic matter by Reduced Relativistic Gas (RRG) which interpolates between radiation and dust regimes depending on the warmness parameter. We propose a new deduction of the RRG state equation and show that there is the isotropization process in which the solutions are asymptotic to the isotropic universe with dust. In the second part, we trace the similarities of Bianchi I with gravitational waves and we explore the relation between linear and nonlinear stability in a higher derivative gravity theory in which there is a massive and nonphysical ghost. For small enough initial conditions, mathematical theorems ensure that once there is stability at the linear level, then there is perturbative stability. Through numerical calculations for dynamic equations without any approximations, we were to able to show that there is a qualitative equivalence between the solutions in the linear and nonlinear levels.