AI 中文总结
利用 LIGO-Virgo-KAGRA 网络探测引力波，研究外尔规范引力理论的极化模式。通过将测地线偏差方程转换到外尔几何，在德西特背景下计算极化模式，发现除张量模式外还有矢量模式，为外尔规范对称性提供证据。
AI 中文摘要
随着全球 LIGO-Virgo-KAGRA（LVK）探测器网络在引力波（GW）探测方面的进展，现在可以在强场区域对引力进行更灵敏的测试。这使得人们能够测试超越爱因斯坦 - 希尔伯特作用的规范理论，比如外尔规范引力理论。唯一无反常（量子）的超越庞加莱时空对称性的规范理论基于外尔规范群（伸缩和庞加莱对称性），其基础几何是外尔共形几何。该规范理论具有外尔规范对称性自发破缺到爱因斯坦 - 希尔伯特和普罗卡作用，以及一个正宇宙学常数。我们研究了外尔几何中引力的外尔（二次）规范理论的引力波极化模式，并将结果与最新实验数据对比。展示了黎曼几何中的测地线偏差方程如何转换到外尔几何，并解释了为何在德西特背景（外尔二次引力的正确低能极限）附近进行分析对于不改变引力波内容并计算极化模式至关重要。除了爱因斯坦 - 希尔伯特作用预测的两个横无迹张量模式外，我们还发现了由外尔规范场横向涨落诱导的另外两个矢量模式。若被探测到，这些矢量模式将是外尔规范对称性的重要证据。
英文摘要
With current advances in gravitational wave (GW) detection made by the worldwide LIGO-Virgo-KAGRA (LVK) network of detectors, ever-more sensitive tests of gravity in the strong-field regime are now possible. This enables one to test gauge theories beyond Einstein-Hilbert action, such as Weyl gauge theories of gravity. The only anomaly-free (quantum) gauge theory of a space-time symmetry beyond Poincaré is based on Weyl gauge group (of dilatations and Poincaré symmetry) with Weyl conformal geometry as its natural underlying geometry. This gauge theory has spontaneous breaking of Weyl gauge symmetry to Einstein-Hilbert and Proca actions, plus a positive cosmological constant. We investigate the GW polarisation modes of Weyl (quadratic) gauge theory of gravity in Weyl geometry and compare our findings to the most recent experimental data. We show how the geodesic deviation equation from Riemannian geometry translates to Weyl geometry, and explain why it is crucial to perform the analysis around de Sitter background, which is the correct low-energy limit of Weyl quadratic gravity, to not alter the GW content, and then compute the polarisation modes. In addition to the two transverse-traceless tensor modes predicted by Einstein-Hilbert action, we find two additional vector modes induced by the transverse fluctuations of the Weyl gauge field. If detected, these vectors modes would be important evidence for Weyl gauge symmetry.
Comments28 pages, 2 figures. One figure has been updated, and the discussion of the experimental tests has been expanded
