Gravitational waves (GWs) have opened a new window on fundamental physics in a number of important ways. The next generation of GW detectors may reveal more information about the polarization structure of GWs. Additionally, there is growing interest in theories of gravity beyond general relativity (GR). One such theory which remains viable within the context of recent measurements of the speed of propagation of GWs is the teleparallel analog of Horndeski gravity. In this work, we explore the polarization structure of this newly proposed formulation of Horndeski theory. In curvature-based gravity, Horndeski theory is almost synonymous with extensions to GR since it spans a large portion of these possible extensions. We perform this calculation by taking perturbations about a Minkowski background and consider which mode propagates. The result is that the polarization structure depends on the choice of model parameters in the teleparallel Horndeski Lagrangian with a maximum of seven propagating degrees of freedom. While the curvature-based Horndeski results follows as a particular limit within this setup, we find a much richer structure of both massive and massless cases which produce scalar-vector-tensor propagating degrees of freedom. We also find that the GW polarization that emerges from the teleparallel analog of Horndeski gravity results in analogous massive and massless modes which take on at most four polarizations in the massless sector and two scalar ones in the massive sector. In none of the cases do we find vector polarizations.

中文翻译：

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Horndeski 引力的远平行模拟中的引力波传播和极化

引力波 (GW) 在许多重要方面为基础物理学打开了一扇新窗口。下一代引力波探测器可能会揭示更多关于引力波极化结构的信息。此外，人们对超越广义相对论 (GR) 的引力理论越来越感兴趣。在最近测量 GW 传播速度的背景下仍然可行的一种这样的理论是 Horndeski 重力的远平行模拟。在这项工作中，我们探索了这种新提出的 Horndeski 理论公式的极化结构。在基于曲率的引力中，Horndeski 理论几乎与 GR 的扩展同义，因为它涵盖了这些可能扩展的大部分。我们通过对 Minkowski 背景进行扰动并考虑哪种模式传播来执行此计算。结果是极化结构取决于具有最大七个传播自由度的远程平行 Horndeski Lagrangian 中模型参数的选择。虽然基于曲率的 Horndeski 结果遵循此设置中的特定限制，但我们发现有质量和无质量情况的更丰富的结构产生标量矢量张量传播自由度。我们还发现，从 Horndeski 引力的远平行模拟中出现的 GW 极化导致类似的有质量和无质量模式，在无质量部门中最多采用四个极化，在质量部门中采用两个标量极化。在任何一种情况下，我们都没有发现矢量极化。