Effective Field Theory of Cosmological Perturbations

TL;DR

This paper develops an effective field theory framework for cosmological perturbations, unifying inflation and dark energy modeling through a gauge-invariant formalism based on symmetry breaking.

Contribution

It introduces a systematic, gauge-invariant effective field theory approach for cosmological perturbations applicable to both inflation and dark energy.

Findings

Unified formalism for inflation and dark energy perturbations

Explicit construction of the most general Lagrangian with broken symmetry

Application of the formalism to ADM variables and cosmological models

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.