Nonlinear Effective Theory of Dark Energy

TL;DR

This paper develops a nonlinear parametrization framework for cosmological perturbations in dark energy and modified gravity models, focusing on Horndeski theories, and derives the nonlinear Poisson equation up to cubic order.

Contribution

It introduces a comprehensive nonlinear effective theory for dark energy, extending linear perturbation analysis to cubic order and exploring the Vainshtein regime.

Findings

Six relevant operators in the nonlinear regime.

Nonlinear modifications to the Poisson equation.

Analysis of the Vainshtein screening mechanism.

Abstract

We develop an approach to parametrize cosmological perturbations beyond linear order for general dark energy and modified gravity models characterized by a single scalar degree of freedom. We derive the full nonlinear action, focusing on Horndeski theories. In the quasi-static, non-relativistic limit, there are a total of six independent relevant operators, three of which start at nonlinear order. The new nonlinear couplings modify, beyond linear order, the generalized Poisson equation relating the Newtonian potential to the matter density contrast. We derive this equation up to cubic order in perturbations and, in a companion article, we apply it to compute the one-loop matter power spectrum. Within this approach, we also discuss the Vainshtein regime around spherical sources and the relation between the Vainshtein scale and the nonlinear scale for structure formation.