Effective theory for the Vainshtein mechanism from the Horndeski action

TL;DR

This work develops a general effective theory for scalar perturbations around flat space derived from the Horndeski action to describe the Vainshtein mechanism. By enforcing Galilean symmetry and expanding around a background, the authors obtain an action with Galileon interactions up to L5 and tensor-scalar couplings controlled by seven parameters, providing a unified framework for screening. They show that vacuum configurations become unstable if the β coupling is nonzero, while suitable matter density profiles can stabilize fluctuations inside the Vainshtein radius; this implies strong constraints on the G5 sector and on the viability of such models. The analysis connects to decoupling limits of other theories like massive gravity and DGP and outlines directions for non-spherical configurations and the role of pressure in stability.

Abstract

Starting from the general Horndeski action, we derive the most general effective theory for scalar perturbations around flat space that allows us to screen fifth forces via the Vainshtein mechanism. The effective theory is described by a generalization of the Galileon Lagrangian, which we use to study the stability of spherically symmetric configurations exhibiting the Vainshtein effect. In particular, we discuss the phenomenological consequences of a scalar-tensor coupling that is absent in the standard Galileon Lagrangian. This coupling controls the superluminality and stability of fluctuations inside the Vainshtein radius in a way that depends on the density profile of a matter source. Particularly we find that the vacuum solution is unstable due to this coupling.