A unifying description of dark energy
  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.
