Nonlinear Effective Theory of Dark Energy
  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.
