Healthy theories beyond Horndeski
  We introduce a new class of scalar-tensor theories that extend Horndeski, or
"generalized galileon", models. Despite possessing equations of motion of
higher order in derivatives, we show that the true propagating degrees of
freedom obey well-behaved second-order equations and are thus free from
Ostrogradski instabilities, in contrast to the standard lore. Remarkably, the
covariant versions of the original galileon Lagrangians-obtained by direct
replacement of derivatives with covariant derivatives-belong to this class of
theories. These extensions of Horndeski theories exhibit an uncommon,
interesting phenomenology: the scalar degree of freedom affects the speed of
sound of matter, even when the latter is minimally coupled to gravity.
