Extended Scalar-Tensor Theories of Gravity
  We study new consistent scalar-tensor theories of gravity recently introduced
by Langlois and Noui with potentially interesting cosmological applications. We
derive the conditions for the existence of a primary constraint that prevents
the propagation of an additional dangerous mode associated with higher order
equations of motion. We then classify the most general, consistent
scalar-tensor theories that are at most quadratic in the second derivatives of
the scalar field. In addition, we investigate the possible connection between
these theories and (beyond) Horndeski through conformal and disformal
transformations. Finally, we point out that these theories can be associated
with new operators in the effective field theory of dark energy, which might
open up new possibilities to test dark energy models in future surveys.
