Spherically Symmetric Einstein-Aether Kantowski-Sachs Cosmological Models with Scalar Field

Abstract

In this thesis we first give a brief introduction to the application of dynamical systems to cosmology. This enables us to study spherically-symmetric cosmological models in Einstein-aether theory with a scalar field. The models depend on the time-like aether vector field through the expansion and shear scalars, and we focus on some special cases of the models. This leads to a compact phase space. From the evolution equations we obtain a three-dimensional dynamical system in terms of expansion-normalized variables. The aim of studying this system is to find the local stability of the equilibrium points of the dynamical system corresponding to physically realistic solutions. As an application we study spherically symmetric Einstein-aether Kantowski-Sachs cosmological models with a scalar field using the dynamical systems theory.