Effective theory for the Vainshtein mechanism from the Horndeski action

TL;DR

This paper derives a comprehensive effective theory from the Horndeski action to describe scalar perturbations enabling the Vainshtein screening mechanism, analyzing stability and phenomenology of scalar-tensor couplings.

Contribution

It introduces a generalized Galileon-based effective theory from Horndeski gravity, including novel scalar-tensor couplings affecting stability and superluminality inside the Vainshtein radius.

Findings

The effective theory generalizes Galileon Lagrangian for screening.

Scalar-tensor coupling influences superluminality and stability.

Vacuum solutions are unstable due to this coupling.

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.