Nonlinear effective theory of dark energy

Abstract

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