标题： 标量-张量引力理论中的引力波宇宙学距离 显示英文标题

标题： Gravitational-wave cosmological distances in scalar-tensor theories of gravity

摘要： 我们分析了标量-张量引力理论中高频引力波（GW）的传播，目的是研究从引力波测量推断出的宇宙距离性质。 通过使用对称性原理，我们首先确定了引力波线性方程和引力波能动张量的最一般结构，假设引力波以光速传播。 修正引力效应被编码在少量参数中，并且我们研究了在我们的协变设定下确保引力子数守恒的条件。 然后我们将一般发现应用于引力波通过扰动的宇宙时空传播的情况，导出了引力波光度距离 $d_L^{({\rm GW})}$ 和引力波角距离 $d_A^{({\rm GW})}$ 的表达式。 我们首次证明了在标量-张量框架内，对于扰动宇宙，以太顿互易定律 $d_L^{({\rm GW})}\,=\,(1+z)^2\,d_A^{({\rm GW})}$ 是有效的。 我们发现，除了引力波光度距离外，引力波角距离也可以相对于广义相对论发生改变。 我们讨论了这一结果对引力透镜的影响，重点关注在多信使事件中同时发射的透镜化引力波和透镜化光子的时间延迟。 我们明确展示了如何在引力波时间延迟公式中的不同系数之间补偿修正引力效应：透镜化的引力波与它们的透镜化电磁对应物同时到达，符合因果约束。 显示英文摘要

摘要： We analyze the propagation of high-frequency gravitational waves (GW) in scalar-tensor theories of gravity, with the aim of examining properties of cosmological distances as inferred from GW measurements. By using symmetry principles, we first determine the most general structure of the GW linearized equations and of the GW energy momentum tensor, assuming that GW move with the speed of light. Modified gravity effects are encoded in a small number of parameters, and we study the conditions for ensuring graviton number conservation in our covariant set-up. We then apply our general findings to the case of GW propagating through a perturbed cosmological space-time, deriving the expressions for the GW luminosity distance $d_L^{({\rm GW})}$ and the GW angular distance $d_A^{({\rm GW})}$. We prove for the first time the validity of Etherington reciprocity law $d_L^{({\rm GW})}\,=\,(1+z)^2\,d_A^{({\rm GW})}$ for a perturbed universe within a scalar-tensor framework. We find that besides the GW luminosity distance, also the GW angular distance can be modified with respect to General Relativity. We discuss implications of this result for gravitational lensing, focussing on time-delays of lensed GW and lensed photons emitted simultaneously during a multimessenger event. We explicitly show how modified gravity effects compensate between different coefficients in the GW time-delay formula: lensed GW arrive at the same time as their lensed electromagnetic counterparts, in agreement with causality constraints.