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arXiv 2103.00155gr-qcastro-ph.COhep-th
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标量-张量引力理论中的引力波宇宙学距离

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

Gianmassimo Tasinato, Alice Garoffolo, Daniele Bertacca, Sabino Matarrese

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22 pages plus technical appendixes. 3 figures. V2: version published in JCAP
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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GW测量中推断出的宇宙学距离的性质。通过使用对称性原理，我们首先确定GW线性化方程和GW能量动量张量的最一般结构，假设GW以光速移动。修改后的引力效应被编码在少量参数中，我们研究了在协变设置中确保引力子数守恒的条件。然后，我们将我们的一般性研究结果的情况下，GW通过扰动宇宙时空传播，推导出的GW光度距离$d_L^{({\rm GW})}$和GW角距离$d_A^{({\rm GW})}$的表达式。本文首次在标量-张量框架下证明了扰动宇宙中Etherington互易律$d_L^{({\rm GW})}\,=\,(1+z)^2\,d_A^{({\rm GW})}$的有效性。我们发现，除了GW的光度距离，也可以修改GW角距离相对于广义相对论。我们讨论了这一结果的影响，引力透镜，聚焦于时间延迟的透镜GW和透镜光子同时发射的多信使事件。我们明确地显示了如何修改重力效应之间的补偿不同系数的GW的时间延迟公式：透镜GW到达的同时，他们的透镜电磁对应，在协议的因果关系约束。

英文摘要：

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.

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