[论文解读] Tests of General Relativity with the Stochastic Gravitational-Wave Background

T. A. Callister, A. S. Biscoveanu+8 more|arXiv (Cornell University)|Apr 26, 2017

Pulsars and Gravitational Waves Research被引用 1

一句话总结

本文提出一种贝叶斯方法，利用先进LIGO和Virgo探测器检测并表征随机引力波背景的偏振特性，从而对广义相对论之外的矢量和标量偏振模式施加约束。尽管增加先进Virgo并未显著提升检测灵敏度，但其极大增强了对混合偏振背景的参数估计能力。

ABSTRACT

The direct observation of gravitational waves with Advanced LIGO and Advanced Virgo offers novel opportunities to test general relativity in strong-field, highly dynamical regimes. One such opportunity is the measurement of gravitational-wave polarizations. While general relativity predicts only two tensor gravitational-wave polarizations, general metric theories of gravity allow for up to four additional vector and scalar modes. The detection of these alternative polarizations would represent a clear violation of general relativity. The LIGO-Virgo detection of the binary black hole merger GW170814 has recently offered the first direct constraints on the polarization of gravitational waves. The current generation of ground-based detectors, however, is limited in its ability to sensitively determine the polarization content of transient gravitational-wave signals. Observation of the stochastic gravitational-wave background, in contrast, offers a means of directly measuring generic gravitational-wave polarizations. The stochastic background, arising from the superposition of many individually unresolvable gravitational-wave signals, may be detectable by Advanced LIGO at design-sensitivity. In this paper, we present a Bayesian method with which to detect and characterize the polarization of the stochastic background. We explore prospects for estimating parameters of the background, and quantify the limits that Advanced LIGO can place on vector and scalar polarizations in the absence of a detection. Finally, we investigate how the introduction of new terrestrial detectors like Advanced Virgo aid in our ability to detect or constrain alternative polarizations in the stochastic background. We find that, although the addition of Advanced Virgo does not notably improve detection prospects, it may dramatically improve our ability to estimate the parameters of backgrounds of mixed polarization.

研究动机与目标

• 开发一种贝叶斯框架，用于检测和表征随机引力波背景的偏振特性。
• 评估先进LIGO和Virgo对矢量和标量引力波偏振模式的敏感度。
• 在未检测到随机引力波背景的情况下，量化对替代偏振模式的限制。
• 评估增加如先进Virgo等地面探测器如何提升对混合偏振背景的参数估计能力。

提出的方法

• 开发了一种贝叶斯推断框架，用于分析多个探测器中的随机引力波背景信号。
• 该方法将随机背景建模为具有任意偏振态的引力波叠加，包括张量、矢量和标量模态。
• 引入针对每种偏振类型的探测器响应函数，以模拟信号在不同激光干涉仪中的表现。
• 基于探测器数据的功率谱构建似然函数，以计算偏振振幅的后验分布。
• 采用马尔可夫链蒙特卡洛采样方法进行参数估计，以全面探索后验空间。
• 在先进LIGO达到设计灵敏度及增加先进Virgo的现实灵敏度假设下对方法进行了测试。

实验结果

研究问题

• RQ1 随机引力波背景能否用于探测替代引力理论所预测的非张量偏振模式？
• RQ2 当前地面探测器对随机背景中的矢量和标量引力波偏振模式的敏感度如何？
• RQ3 增加先进Virgo在多大程度上提升了对混合偏振背景的约束或测量能力？
• RQ4 在未检测到背景的情况下，对矢量和标量偏振振幅的定量限制是什么？
• RQ5 探测器网络配置如何影响偏振参数估计的精度？

主要发现

• 增加先进Virgo并未显著提升对随机引力波背景的检测前景。
• 先进Virgo显著提升了对具有混合偏振成分背景的参数估计精度。
• 即使在未检测到信号的情况下，该方法在先进LIGO达到设计灵敏度运行时仍能对矢量和标量偏振模式施加稳健约束。
• 贝叶斯框架支持对随机背景偏振振幅与谱参数的联合推断。
• 研究表明，当背景可检测时，未来的多探测器网络能够以高保真度区分不同偏振模态。
• 结果表明，探测器网络中偏振特异性响应模式对于分离随机背景中的非张量成分至关重要。