We investigate the novel features of gravitational wave solutions in f(R) gravity under proper gauge considerations in the shifted Ricci scalar background curvature (R1+ϵ). The solution is further explored to study the modified dispersion relations for massive modes at local scales and to derive constraints on ϵ. Our analysis yields new insights as we scrutinize these dispersion effects on the polarization (modified Newman-Penrose content) and lensing properties of gravitational waves. It is discovered that the existing longitudinal scalar mode, and transverse breathing scalar mode are both independent of the mass parameter for ϵ<<1. Further, by analysing the lensing amplification factor for the point mass lens model, we show that lensing of gravitational wave is highly sensitive to these dispersion effects in the milli-Hertz frequency (wave optics regime). It is expected that ultra-light modes, having mass about O(10−15) eV for ϵ<<1(≈10−7) lensed by (103≤MLens≤106)M⊙ compact objects are likely to be detected by the advanced gravitational wave space-borne detectors, particularly within LISA's (The Laser Interferometer Space Antenna) sensitivity band.

中文翻译：

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用透镜引力波探测 f（R） 中的大质量引力子


我们研究了在偏移的 Ricci 标量背景曲率 （R1+ε） 中适当规范考虑下 f（R） 重力引力波解的新特征。进一步探索了该解决方案，以研究局部尺度上大质量模态的修正色散关系，并推导对ε的约束。当我们仔细研究这些色散对引力波的偏振（修正的 Newman-Penrose 含量）和透镜特性的影响时，我们的分析产生了新的见解。研究发现，现有的纵向标量模式和横向呼吸标量模式都与 ε<<1 的质量参数无关。此外，通过分析点质量透镜模型的透镜放大因子，我们表明引力波的透镜对毫赫兹频率（波动光学范围）中的这些色散效应高度敏感。预计，对于由 （103≤MLens≤106）M⊙ 致密物体透镜的 ε<<1（≈10−7） 像素质量约为 O（10−15） eV 的超轻模式可能会被先进的引力波星载探测器探测到，特别是在 LISA（激光干涉仪空间天线）的灵敏度范围内。