Horndeski under the quantum loupe
  With recent constraints on the propagation speed of gravitational waves, the
class of scalar-tensor theories has significantly been reduced. We consider one
of the surviving models still relevant for cosmology and investigate its
radiative stability. The model contains operators with explicit breaking of the
Galileon symmetry and we study whether they harm the re-organization of the
effective field theory. Within the regime of validity we establish a
non-renormalization theorem and show explicitly that the quantum corrections,
to one-loop, do not detune the classical Lagrangian generating suppressed
counterterms. This is striking since the non-renormalization theorem is
established in the presence of a genuine Galileon symmetry breaking term.
