  Using conformal invariance of gravitational waves, we show that for a luminal
modified gravity theory, the gravitational-wave propagation and luminosity
distance are the same as in general relativity. The relation between the
gravitational-wave and electromagnetic-wave luminosity distance gets however
modified for electromagnetism minimally coupled to the Jordan frame metric.
Using effective field theory we show that the modified relation obtained for
luminal theories is also valid for non-luminal theories with Jordan frame
matter-gravity coupling.We generalise our analysis to a time-dependent speed of
gravitational waves with matter minimally coupled to either the Jordan or
Einstein frame metrics.
