Theoretical Physics Department, CERN, CH-1211 Geneva 23, Switzerland.
ICRANet, Piazza della Repubblica 10, I-65122 Pescara, Italy.
Phys Rev Lett. 2023 Jun 9;130(23):231401. doi: 10.1103/PhysRevLett.130.231401.
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.
利用引力波的共形不变性，我们表明对于光传播修正引力理论，引力波的传播和光度距离与广义相对论相同。然而，对于与乔丹框架度量最小耦合的电磁作用，引力波和电磁波的光度距离之间的关系会发生变化。我们利用有效场论表明，对于具有乔丹框架物质-引力耦合的非光传播理论，我们得到的修正关系也是有效的。我们将我们的分析推广到与乔丹或爱因斯坦框架度量最小耦合的物质的时变引力波速度。
