Effective Field Theory of Cosmological Perturbations

TL;DR

The paper develops the effective field theory of cosmological perturbations to describe inflation and dark energy in a model-independent way, by treating cosmological perturbations as the light degrees of freedom around a FRW background with spontaneously broken time translations. It constructs a universal unitary-gauge action built from $f(t)R$, $\Lambda(t)$, $c(t)g^{00}$ plus higher-order operators, and uses the Stueckelberg trick to reintroduce the scalar $\pi$, connecting to Horndeski theories via a covariant top-down map. An ADM analysis yields a controlled, second-order quadratic action for the curvature perturbation $\zeta$, with explicit expressions for the background constraints, stability parameter $\alpha>0$, and sound speed $c_s^2=\beta/\alpha$, and shows how higher spatial derivatives modify dispersion as $\omega^2=c_s^2 k^2 + k^4/M^2$. The framework provides clear routes to observable consequences, including the modified growth of structure via $G_{ m eff}(t,k)$ and the gravitational slip $\gamma$, while revealing open issues such as screening mechanisms and precise mass-scale mappings of the EFT operators. Overall, the EFT of cosmological perturbations offers a compact, versatile toolkit for exploring inflation and modified gravity with a small set of time-dependent functions and a structured derivative expansion.

Abstract

The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry---that allows to write down the most general Lagrangian---and of the Stueckelberg "trick"---that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy.