在任意偏振引力波背景中基于相关性的谐波分析
Harmonic Analysis on Correlation for Gravitational-Wave Backgrounds of Arbitrary Polarization from Interfering Sources in Generic Dispersion Relation
AI总结：
本文研究了引力波背景中任意偏振和通用色散关系下的源干涉对空间相关性的影响，揭示了多极矩特征的保持与更高阶截断机制，指出单宇宙现实对区分修改引力与广义相对论的理论限制。
摘要：
Hellings-Downs（HD）相关性是检测脉冲星定时阵列（PTAs）中引力波背景（GWB）在广义相对论（GR）中的基本基准。然而，这一经典特征依赖于连续源的理想化假设。在由超大质量黑洞双星（SMBHBs）主导的真实天体物理场景中，离散源之间的干涉会在空间相关性中引入固有偏差，这可能会模拟或掩盖修改引力的特征。在本工作中，我们推导了在存在源干涉的情况下，具有任意偏振和通用引力波色散关系的引力波背景的空间相关函数的闭合形式。通过严格的谐波分析，我们证明源干涉会改变相关性形状，但严格保持每种偏振的最低非零多极矩特征，即张量的四极矩、向量的偶极矩和标量的单极矩。更高阶多极矩的截断由脉冲星距离和色散效应的相互作用决定。此外，我们量化了干涉引起的变异性与修改引力特征之间的统计退化性。我们得出结论，仅访问宇宙的一个单一现实会对使用空间相关性来区分修改引力与GR施加了根本性的理论限制。
英文摘要：
The Hellings-Downs (HD) correlation serves as the fundamental benchmark for detecting the gravitational-wave background (GWB) in pulsar timing arrays (PTAs) within General Relativity (GR). However, this canonical signature relies on the idealization of a continuum of sources without interference. In realistic astrophysical scenarios dominated by supermassive black hole binaries (SMBHBs), interference between discrete sources induces intrinsic deviations in the spatial correlation, which may mimic or obscure signatures of modified gravity. In this work, we derive the closed-form spatial correlation functions for a GWB with arbitrary polarization and generic GW dispersion relations, in the presence of source interference. Through a rigorous harmonic analysis, we demonstrate that source interference modifies the correlation shape but strictly preserves the lowest non-vanishing multipole moment characteristic of each polarization, specifically the quadrupole for tensor, dipole for vector, and monopole for scalar modes. The truncation at higher-order multipoles is governed by the interplay between pulsar distances and dispersion effects. Furthermore, we quantify the statistical degeneracy between interference-induced variation and modified gravity signatures. We conclude that access to only a single realization of the Universe imposes a fundamental theoretical limit on distinguishing modified gravity from GR using spatial correlations alone.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
