EXPONENTIAL POTENTIALS IN KANTOWSKI-SACHS EINSTEIN-AETHER SCALAR FIELD COSMOLOGICAL MODELS

Abstract

A class of positive curvature spatially homogeneous but anisotropic cosmological models within an Einstein-aether gravitational framework is investigated. The mat- ter source is assumed to be a scalar field which is coupled to the expansion of the aether field through a generalized (constant plus exponential) potential V = Λ+e −2kφ +a 2 θe −kφ . The evolution equations are expressed in terms of expansion nor- malized variables to produce an autonomous system of ordinary differential equations suitable for a numerical and qualitative analysis. An analysis of the local stability of the equilibrium points leads to the discovery of periodic orbits and we investigate the stability of these solutions as we generalize our model. We will analyze various sets of models in an attempt to investigate some of the underlying features of these models.