Kantowski-Sachs Einstein-{\ae}ther perfect fluid models

TL;DR

This paper analyzes Kantowski-Sachs models within Einstein-{ extae}ther theory, revealing rich cosmological behaviors including inflationary phases, anisotropic attractors, and solutions with extreme physical properties, using analytical and numerical methods.

Contribution

It provides a comprehensive dynamical systems analysis of Kantowski-Sachs Einstein-{ extae}ther models, exploring new parameter regimes and identifying novel cosmological solutions.

Findings

Identification of inflationary sources and sinks at early and late times.

Discovery of solutions with infinite shear and matter energy density.

Existence of stiff-like and anisotropic late-time attractors.

Abstract

We investigate Kantowski-Sachs models in Einstein-{\ae}ther theory with a perfect fluid source using the singularity analysis to prove the integrability of the field equations and dynamical system tools to study the evolution. We find an inflationary source at early times, and an inflationary sink at late times, for a wide region in the parameter space. The results by A. A. Coley, G. Leon, P. Sandin and J. Latta (JCAP 12, 010, 2015), are then re-obtained as particular cases. Additionally, we select other values for the non-GR parameters which are consistent with current constraints, getting a very rich phenomenology. In particular, we find solutions with infinite shear, zero curvature, and infinite matter energy density in comparison with the Hubble scalar. We also have stiff-like future attractors, anisotropic late-time attractors, or both, in some special cases. Such results are developed analytically, and then verified by numerics. Finally, the physical interpretation of the new critical points is discussed.