The Effective Field Theory of Dark Energy

TL;DR

The paper introduces a universal EFT framework for dark energy and modified gravity with a single scalar degree of freedom, formulated in unitary gauge and anchored by three background functions f(t), Λ(t), and c(t). By organizing operators by perturbative order, it isolates background evolution from perturbations, and shows how mixing between the scalar and gravity arises and can be de-mixed, with explicit stability and sound-speed criteria. It then demonstrates how a broad class of DE/modified gravity models (Quas Quintessence, k-essence, DGP/galileon, kinetic braiding, ghost condensate, khronon, F(R)) map into specific EFT coefficients, providing a practical dictionary for model embedding and data-driven constraints. An Einstein-frame formulation complements the Jordan-frame description, clarifying frame-dependent interpretations and enabling covariant reconstructions of the same dynamics. Overall, the EFT of DE offers a concise, testable, and covariant-compatible platform to compare and constrain single-field DE and modified gravity theories against cosmological observations.

Abstract

We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write in terms of it the most general unitary gauge action consistent with the residual unbroken symmetries of spatial diffeomorphisms. Our action is particularly suited for cosmological perturbation theory: the background evolution depends on only three operators. All other operators start at least at quadratic order in the perturbations and their effects can be studied independently and systematically. In particular, we focus on the properties of a few operators which appear in non-minimally coupled scalar-tensor gravity and galileon theories. In this context, we study the mixing between gravity and the scalar degree of freedom. We assess the quantum and classical stability, derive the speed of sound of fluctuations and the renormalization of the Newton constant. The scalar can always be de-mixed from gravity at quadratic order in the perturbations, but not necessarily through a conformal rescaling of the metric. We show how to express covariant field-operators in our formalism and give several explicit examples of dark energy and modified gravity models in our language. Finally, we discuss the relation with the covariant EFT methods recently appeared in the literature.