Cosmological evolution of Einstein-Aether models with power-law-like potential

Abstract

The so-called Einstein-Aether theory is General Relativity coupled (at second derivative order) to a dynamical unit time-like vector field (the aether). It is a Lorentz-violating theory, and gained much attention in the recent years. In the present work, we study the cosmological evolution of Einstein-Aether models with power-law-like potential, by using the method of dynamical system. In the case without matter, there are two attractors which correspond to an inflationary universe in the early epoch, or a de Sitter universe in the late time. In the case with matter but there is no interaction between dark energy and matter, there are only two de Sitter attractors, and no scaling attractor exists. So, it is difficult to alleviate the cosmological coincidence problem. Therefore, we then allow the interaction between dark energy and matter. In this case, several scaling attractors can exist under some complicated conditions, and hence the cosmological coincidence problem could be alleviated.

Spontaneous Color Polarization as A Modus Originis of the Dynamic Aether

“…We speak about extensions of the Einstein-aether theory, when one already has the unit vector field U i , and one adds new terms into the action functional, which describe the scalar, pseudoscalar, electromagnetic, gauge, etc., fields. The scalar extension of the Einstein-aether theory was motivated by cosmological applications, (see, e.g., [44][45][46][47][48][49]), in particular, to precise some details of inflation, dynamics of perturbations, and the large-scale structure formation. In order to describe the impact of the scalar field ϕ on the unit vector field U k , the authors of [44] suggested to modify the constitutive tensor K ab mn (2) by introduction of the functions…”

Integrability and cosmological solutions in Einstein-æther-Weyl theory

“…The Einstein-aether action is the most general second-order theory which is defined by the spacetime metric and the aether field involving no more than two derivatives [6] (not including total derivatives). There are several gravitational and cosmological applications for both a e-mail: anpaliat@phys.uoa.gr b e-mail: genly.leon@ucn.cl (corresponding author) of these theories in the literature, for instance see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and references therein.…”

New application of the Killing vector field formalism: modified periodic potential and two-level profiles of the axionic dark matter distribution

“…The extension of the potential was prompted by the analogy with the Einstein-aether theory [34][35][36], which is based on the introduction of a timelike dynamic vector field U i normalized by unity (g ik U i U k = 1). In the framework of the Einstein-aether theory one can introduce into the potential V four auxiliary scalars based on the decomposition of the covariant derivative ∇ m U n (see, e.g., [37][38][39][40] for details and references). The first scalar is the divergence of the vector field (ξ (1)…”