Mirage of Luminal Modified Gravitational-Wave Propagation

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 modified, however, 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 nonluminal theories with Jordan frame matter-gravity coupling. We generalize our analysis to a time-dependent speed of gravitational waves with matter minimally coupled to either the Jordan or Einstein frame metrics.

Automated summary

By using the conformal invariance of gravitational waves, it is demonstrated that in luminal modified gravity theories, the propagation and luminosity distance of gravitational waves are the same as those in general relativity. However, the relation between the luminosity distance of gravitational waves and electromagnetic waves is modified for electromagnetism minimally coupled to the Jordan frame metric. The analysis is extended to theories with nonluminal speed of gravitational waves and matter minimally coupled to either the Jordan or Einstein frame metrics using effective field theory.