Effective theory for the Vainshtein mechanism from the Horndeski action
  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.
