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.

中文翻译：

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流明修正引力波传播的海市蜃楼

利用引力波的共形不变性，我们证明了对于光腔修正引力理论，引力波传播和光度距离与广义相对论中的相同。然而，引力波和电磁波光度距离之间的关系会被修改，因为电磁力与乔丹框架度量的耦合程度最低。使用有效场理论，我们表明，针对光速理论获得的修正关系对于具有乔丹框架物质重力耦合的非光速理论也有效。我们将我们的分析推广到与时间相关的引力波速度，其中物质与乔丹或爱因斯坦框架度量最小耦合。