  Theories of dark energy and modified gravity can be strongly constrained by
astrophysical or cosmological observations, as illustrated by the recent
observation of the gravitational wave event GW170817 and of its electromagnetic
counterpart GRB 170817A, which shows that the speed of gravitational waves,
$c_g$, is the same as the speed of light, within deviations of order
$10^{-15}$. This observation implies very severe restrictions on scalar-tensor
theories, in particular theories whose action depends on second derivatives of
a scalar field. Working in the very general framework of Degenerate
Higher-Order Scalar-Tensor (DHOST) theories, which encompass Horndeski and
Beyond Horndeski theories, we present the DHOST theories that satisfy $c_g=c$.
We then examine, for these theories, the screening mechanism that suppresses
scalar interactions on small scales, namely the Vainshtein mechanism, and
compute the corresponding gravitational laws for a non-relativistic spherical
body. We show that it can lead to a deviation from standard gravity inside
matter, parametrized by three coefficients which satisfy a consistency relation
and can be constrained by present and future astrophysical observations.
