Vainshtein regime in scalar-tensor gravity: Constraints on degenerate higher-order scalar-tensor 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 the dark energy approach, we consider the general action for perturbations beyond linear order, focusing on the quasistatic 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) >= 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 implies beta(1) less than or similar to 10(-5). Standard gravity can be recovered outside the body by tuning the parameters of the model, in which case beta(1) less than or similar to 10(-2) from the Hulse-Taylor pulsar. Theories conformally related to general relativity admit 0 <= beta(1) less than or similar to 10(-6), at least for a specific choice of conformal couplings.