Theories beyond general relativity (GR) modify the propagation of gravitational waves (GWs). In some, inhomogeneities (aka. gravitational lenses) allow interactions between the metric and additional fields to cause lens-induced birefringence (LIB): a different speed of the two linear GW polarisations ($+$ and $\times$). Inhomogeneities then act as non-isotropic crystals, splitting the GW signal into two components whose relative time delay depends on the theory and lens parameters. Here we study the observational prospects for GW scrambling, i.e when the time delay between both GW polarisations is smaller than the signal's duration and the waveform recorded by a detector is distorted. We analyze the latest LIGO-Virgo-KAGRA catalog, GWTC-3, and find no conclusive evidence for LIB. The highest log Bayes factor that we find in favour of LIB is $3.21$ for GW$190521$, a particularly loud but short event. However, when accounting for false alarms due to (Gaussian) noise fluctuations, this evidence is below 1-$σ$. The tightest constraint on the time delay is $<0.51$ ms (90% C.L.) from GW$200311\_115853$. From the non-observation of GW scrambling, we constrain the optical depth for LIB, accounting for the chance of randomly distributed lenses (eg. galaxies) along the line of sight. Our LIB constraints on a (quartic) scalar-tensor Horndeski theory are more stringent than solar system tests for a wide parameter range and comparable to GW170817 in some limits. Interpreting GW190521 as an AGN binary (i.e. taking an AGN flare as a counterpart) allows even more stringent constraints. Our results demonstrate the potential and high sensitivity achievable by tests of GR, based on GW lensing.
Probing globular clusters parameters through gravitational wave lensing with stellar-mass black hole binaries
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（尼古拉·哥白尼天文学中心，波兰科学院）；INFN Sezione di Ferrara（费拉拉意大利国家核物理研究所分部）；National Centre for Nuclear Research（国家核研究中心）；SUPA, School of Physics and Astronomy, University of Glasgow（格拉斯哥大学物理与天文学院，苏格兰粒子物理与天文学联盟）；Center for Cosmology, Particle Physics and Phenomenology-CP3, Université Catholique de Louvain（宇宙学、粒子物理与现象学中心-CP3，天主教鲁汶大学）；Royal Observatory of Belgium（比利时皇家天文台）
Probing the spin of compact objects with gravitational microlensing of gravitational waves
The Inter-University Centre for Astronomy and Astrophysics（大学间天体物理中心）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（理论科学国际中心，塔塔基础研究所）；Indian Association for the Cultivation of Science（印度科学培养协会）
