Einstein-Aether Cosmological Scalar Field Models

Abstract

The so-called Einstein-Aether theory is General Relativity coupled (at second derivative order) to a dynamical time-like unit vector field (the "Aether"). It is a Lorentz-violating theory and has gained much attention in recent years. We study two classes of Einstein-Aether cosmological scalar field models using dynamical systems techniques. In particular, we are interested in exploring the impact of Lorentz violation on the inflationary scenario. We study the local stability of the equilibrium points of the dynamical system corresponding to physically realistic solutions and find that there are always ranges of values of the parameters of the models for which there exists an inflationary attractor.

In the first application, we investigate the qualitative behaviour of a class of spatially homogeneous Einstein-Aether models with a scalar field. Particularly, we study two models; an isotropic model and an anisotropic model. In both models there always exists a range of the values of the parameters in which there is an attractor which corresponds to an inflationary universe at late times.

In the second application, we study spherically symmetric cosmological models with a scalar field. Particularly, we consider a special case of spatially homogeneous Kantowski-Sachs models using appropriate normalized bounded variables. In this special case, we found that there always exists a range of values in the parameters in which there is one inflationary attractor solution which corresponds to an inflationary of the Universe at late times.