A unifying description of dark energy

TL;DR

This paper presents a unified framework for describing various dark energy and scalar-tensor models using an ADM formulation, enabling systematic analysis of linear perturbations and comparison with cosmological data.

Contribution

It introduces a minimal, unified approach that encompasses many existing models and extends to Horava-Lifshitz theories, simplifying the study of dark energy perturbations.

Findings

Unified description of dark energy models

Derivation of perturbation equations in a systematic way

Identification of five key functions governing perturbations

Abstract

We review and extend a novel approach that we introduced recently, to describe general dark energy or scalar-tensor models. Our approach relies on an ADM formulation based on the hypersurfaces where the underlying scalar field is uniform. The advantage of this approach is that it can describe in the same language and in a minimal way a vast number of existing models, such as quintessence models, $F(R)$ theories, scalar tensor theories, their Horndeski extensions and beyond. It also naturally includes Horava-Lifshitz theories. As summarized in this review, our approach provides a unified treatment of the linear cosmological perturbations about a FLRW universe, obtained by a systematic expansion of our general action up to quadratic order. This shows that the behaviour of these linear perturbations is generically characterized by five time-dependent functions. We derive the full equations of motion in the Newtonian gauge, and obtain in particular the equation of state for dark energy perturbations, in the Horndeski case, in terms of these functions. Our unifying description thus provides the simplest and most systematic way to confront theoretical models with current and future cosmological observations.