The future ground- and space-based gravitational wave (GW) detectors offer unprecedented opportunities to test general relativity (GR) with greater precision. In this work, we investigate the capability of future ground-based GW detectors, the Einstein Telescope (ET) and the Cosmic Explorer (CE), and space-based GW detectors, LISA, Taiji, and TianQin, for constraining parity and Lorentz violations in gravity. We inject several typical GW signals from compact binary systems into GW detectors and perform Bayesian inferences with the modified waveforms with parity and Lorentz-violating effects. These effects are modeled in the amplitude and phase corrections to the GW waveforms with their frequency-dependence described by factors $β_ν$, $β_μ$, $β_{\bar ν}$, and $β_{\bar μ}$. Our results show that the combined observations of ET and CE will impose significantly tighter bounds on the energy scale of parity and Lorentz violations ($M_{\rm PV}$ and $M_{\rm LV}$) compared to those given by LIGO-Virgo-KAGRA (LVK) detectors. For cases with positive values of $β_ν$, $β_μ$, $β_{\bar ν}$, and $β_{\bar μ}$, the constraints on $M_{\rm PV}$ and $M_{\rm LV}$ from ground-based detectors are tighter than those from the space-based detectors. For the $β_μ = -1$ case, space-based GW detectors provide constraints on $M_{\rm PV}$ that are better than current LVK observations and comparable to those from ET and CE. Additionally, space-based detectors exhibit superior sensitivity in constraining $M_{\rm LV}$ for $β_{\bar μ} = -2$ case, which is approximately three orders of magnitude tighter than those from ground-based GW detectors. This scenario also enables bounds on the graviton mass at $m_g \lesssim 10^{-35}\; {\rm GeV}$. These findings highlight the promising role of future GW observatories in probing fundamental physics beyond GR.
Testing Lorentz Invariance Using an Odd-Parity Asymmetric Optical Resonator
我们提出了第一个实验测试的洛伦兹不变性使用之间的频率差的非对称奇宇称光学谐振腔中的反向传播模式。这种类型的测试是$\sim10^{4}$更敏感的奇宇称和各向同性（标量）违反洛伦兹不变性比等效的传统偶宇称实验，由于光学谐振腔的不对称性。奇宇称谐振器的缺点已经通过使用反向传播模式来消除，从而对环境波动提供高水平的免疫力。与非旋转实验，我们的结果限制各向同性洛伦兹违反参数$\tildeκ_{tr}$为3.4 $\pm$ 6.2 x $10^{-9}$，最好的报告约束从直接测量。使用这种技术的奇宇称和标量违反洛伦兹不变性的界限可以提高许多数量级。
Constraints on parity and Lorentz violations from gravitational waves: a comparison between single-parameter and multi-parameter analysis
Zhejiang University of Technology（浙江工业大学）；Institute for theoretical physics & cosmology, Zhejiang University of Technology（浙江工业大学理论物理与宇宙学研究所）；United Center for Gravitational Wave Physics, Zhejiang University of Technology（浙江工业大学引力波物理联合中心）
Constraining primordial non-Gaussianity and parity-violation through Scalar-Induced Gravitational Waves with next-generation ground-based interferometers
Università di Pisa（比萨大学）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；Università degli Studi di Padova（帕多瓦大学）；Istituto Nazionale di Astrofisica (INAF)（意大利国家天体物理研究所）
Constraining Lorentz symmetry breaking in bumblebee gravity with extreme mass-ratio inspirals
Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院）；Hunan Normal University（湖南师范大学）；Beijing Normal University（北京师范大学）；Yangzhou University（扬州大学）
Constraining Lorentz and parity violations in gravity with multiband gravitational wave observations
Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Science（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology（浙江工业大学理论物理与宇宙学研究所）；United Center for Gravitational wave Physics (UCGWP), Zhejiang University of Technology（浙江工业大学引力波物理学联合中心）；Department of Astronomy, Beijing Normal University（北京师范大学天文系）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学天文与前沿物理研究所）
