  Gravitational wave propagation encounters a spacetime friction from a running
Planck mass in modified gravity, causing the luminosity distance to deviate
from that in general relativity (or given by the photon luminosity distance to
the source), thus making it a valuable cosmological probe. We present the exact
expression for the cosmological distance deviation in Horndeski gravity
including theories that have a $G_5$ term yet propagate at the speed of light.
An especially simple result ensues for coupled Gauss-Bonnet gravity, which we
use to show it does not give a viable cosmology. We also generalize such
coupling, and review the important connection of gravitational wave
cosmological distance deviations to growth of cosmic structure measured by
redshift space distortions.
