标题： 减缩霍恩德斯基理论中的引力波随机背景 显示英文标题

标题： Gravitational wave stochastic background in reduced Horndeski theories

摘要： 我们推广到简化的霍恩德斯基引力理论，其中引力波（GWs）以光速传播，得出统计同质且非偏振的随机引力波背景（SGWB）信号的表达式，该信号作为两个任意配置的干涉仪检测到的单独信号之间的相关性进行测量。 我们还讨论了文献中关于修改理论中的宇宙学距离的一些结果，即对于GW信号，双极距关系的同时有效性，以及基于能量通量的引力波光度距离与从波幅推导出的距离之间的重合。 这种讨论使我们得出结论，天体物理SGWB信号的单位立体角谱能密度与每个发射源的光度具有相同的函数依赖关系，正如广义相对论（GR）中一样。 利用GW能量-动量张量的广义表达式和张量模式的修改传播定律，我们得出结论，只要修改理论在给定的常时间超曲面中与GR一致，SGWB的能量密度与尺度因子之间的函数关系与GR中相同。 然而，检测到的信号与谱能密度之间的关系被全局因子$G_4(\varphi(t_0))$所改变，因此可能作为探测修改引力理论的工具。 显示英文摘要

摘要： We generalize to reduced Horndeski theories of gravity, where gravitational waves (GWs) travel at the speed of light, the expression of a statistically homogeneous and unpolarized stochastic gravitational wave background (SGWB) signal measured as the correlation between the individual signals detected by two interferometers in arbitrary configurations. We also discuss some results found in the literature regarding cosmological distances in modified theories, namely, the simultaneous validity of a duality distance relation for GW signals and of the coincidence between the gravitational wave luminosity distance, based on the energy flux, and the distance inferred from the wave amplitude. This discussion allows us to conclude that the spectral energy density per unit solid angle of an astrophysical SGWB signal has the same functional dependency with the luminosity of each emitting source as in General Relativity (GR). Using the generalized expression of the GW energy-momentum tensor and the modified propagation law for the tensor modes, we conclude that the energy density of a SGWB maintains the same functional relation with the scale factor as in GR, provided that the modified theory coincides with GR in a given hypersurface of constant time. However, the relation between the detected signal and the spectral energy density is changed by the global factor $G_4(\varphi(t_0))$, thus potentially serving as a probe for modified gravity theories.