Vainshtein regime in Scalar-Tensor gravity: constraints on DHOST
  theories
  We study the screening mechanism in the most general scalar-tensor theories
that leave gravitational waves unaffected and are thus compatible with recent
LIGO/Virgo observations. Using the effective field theory of dark energy
approach, we consider the general action for perturbations beyond linear order,
focussing on the quasi-static limit. When restricting to the subclass of
theories that satisfy the gravitational wave constraints, the fully nonlinear
effective Lagrangian contains only three independent parameters. One of these,
$\beta_1$, is uniquely present in degenerate higher-order theories. We compute
the two gravitational potentials for a spherically symmetric matter source and
we find that for $\beta_1 \ge 0$ they decrease as the inverse of the distance,
as in standard gravity, while the case $\beta_1 < 0$ is ruled out. For $\beta_1
> 0$, the two potentials differ and their gravitational constants are not the
same on the inside and outside of the body. Generically, the bound on anomalous
light bending in the Solar System constrains $\beta_1 \lesssim 10^{-5}$.
Standard gravity can be recovered outside the body by tuning the parameters of
the model, in which case $\beta_1 \lesssim 10^{-2}$ from the Hulse-Taylor
pulsar.
