Essential Building Blocks of Dark Energy

TL;DR

This paper develops a unified effective field theory framework for single field dark energy and modified gravity models, simplifying their description and linking theoretical parameters to observable cosmological perturbations.

Contribution

It introduces a minimal set of operators for linear perturbations, maps existing models into this framework, and derives observable quantities in terms of these parameters.

Findings

Seven key Lagrangian operators identified for second-order equations.

Most existing models, including Horndeski theories, can be described with six operators.

Provides explicit formulas for the effective Newton constant and gravitational potential ratios.

Abstract

We propose a minimal description of single field dark energy/modified gravity within the effective field theory formalism for cosmological perturbations, which encompasses most existing models. We start from a generic Lagrangian given as an arbitrary function of the lapse and of the extrinsic and intrinsic curvature tensors of the time hypersurfaces in unitary gauge, i.e. choosing as time slicing the uniform scalar field hypersurfaces. Focusing on linear perturbations, we identify seven Lagrangian operators that lead to equations of motion containing at most two (space or time) derivatives, the background evolution being determined by the time dependent coefficients of only three of these operators. We then establish a dictionary that translates any existing or future model whose Lagrangian can be written in the above form into our parametrized framework. As an illustration, we study Horndeski's-or generalized Galileon-theories and show that they can be described, up to linear order, by only six of the seven operators mentioned above. This implies, remarkably, that the dynamics of linear perturbations can be more general than that of Horndeski while remaining second order. Finally, in order to make the link with observations, we provide the entire set of linear perturbation equations in Newtonian gauge, the effective Newton constant in the quasi-static approximation and the ratio of the two gravitational potentials, in terms of the time-dependent coefficients of our Lagrangian.