Cosmological perturbation theory in Generalized Einstein-Aether models

TL;DR

This paper explores the evolution of cosmological perturbations in Generalized Einstein-Aether models, providing a comprehensive framework for understanding their background dynamics and perturbation behavior in the context of dark energy and modified gravity.

Contribution

It introduces a detailed analysis of perturbations in Generalized Einstein-Aether models, including background modeling, equations of state, and elimination of extra degrees of freedom for linear perturbations.

Findings

Only one form of the model matches $\\Lambda$CDM at background level.

Derived differential equations for $\\mathcal{F}(\ ext{K})$ for general $w$CDM.

Expressed perturbation variables solely in terms of fluid and metric perturbations.

Abstract

We investigate the evolution of cosmological perturbations in models of dark energy described by a time-like unit normalized vector field specified by a general function $\mathcal{F}(\mathcal{K})$, so-called Generalized Einstein-Aether models. First we study the background dynamics of such models via a designer approach in an attempt to model this theory as dark energy. We find that only one specific form of this designer approach matches $\Lambda$CDM at background order and we also obtain a differential equation which $\mathcal{F}(\mathcal{K})$ must satisfy for general $w$CDM cosmologies. We also present the equations of state for perturbations in Generalized Einstein-Aether models, which completely parametrize these models at the level of linear perturbations. A generic feature of modified gravity models is that they introduce new degrees of freedom. By fully eliminating these we are able to express the gauge invariant entropy perturbation and the scalar, vector, and tensor anisotropic stresses in terms of the perturbed fluid variables and metric perturbations only. These can then be used to study the evolution of perturbations in the scalar, vector, and tensor sectors and we use these to evolve the Newtonian gravitational potentials.