Cosmic structures and gravitational waves in ghost-free scalar-tensor
  theories of gravity
  We study cosmic structures in the quadratic Degenerate Higher Order Scalar
Tensor (qDHOST) model, which has been proposed as the most general
scalar-tensor theory (up to quadratic dependence on the covariant derivatives
of the scalar field), which is not plagued by the presence of ghost
instabilities. We then study a static, spherically symmetric object embedded in
de Sitter space-time for the qDHOST model. This model exhibits breaking of the
Vainshtein mechanism inside the cosmic structure and Schwarzschild-de Sitter
space-time outside, where General Relativity (GR) can be recovered within the
Vainshtein radius. We then look for the conditions on the parameters on the
considered qDHOST scenario which ensure the validity of the Vainshtein
screening mechanism inside the object and the fulfilment of the recent
GW170817/GRB170817A constraint on the speed of propagation of gravitational
waves. We find that these two constraints rule out the same set of parameters,
corresponding to the Lagrangians that are quadratic in second-order derivatives
of the scalar field, for the shift symmetric qDHOST.
