Gravitational lensing by massive objects along the line of sight to the source causes distortions to gravitational wave (GW) signals; such distortions may reveal information about fundamental physics, cosmology, and astrophysics. In this work, we have extended the search for lensing signatures to all binary black hole events from the third observing run of the LIGO-Virgo network. We search for repeated signals from strong lensing by (1) performing targeted searches for subthreshold signals, (2) calculating the degree of overlap among the intrinsic parameters and sky location of pairs of signals, (3) comparing the similarities of the spectrograms among pairs of signals, and (4) performing dual-signal Bayesian analysis that takes into account selection effects and astrophysical knowledge. We also search for distortions to the gravitational waveform caused by (1) frequency-independent phase shifts in strongly lensed images, and (2) frequency-dependent modulation of the amplitude and phase due to point masses. None of these searches yields significant evidence for lensing. Finally, we use the nondetection of GW lensing to constrain the lensing rate based on the latest merger-rate estimates and the fraction of dark matter composed of compact objects.

LISA is considered to be launched alongside the Athena to probe the energetic astrophysical processes. LISA can determine the direction of sources for Athena’s follow-up observation. As another space gravitational wave mission, TAIJI is expected to be launched in the 2030s. The LISA-TAIJI network would provide abundant merits for sources understanding. In this work, we simulate the joint LISA-TAIJI observations for gravitational waves from coalescing supermassive black hole binaries and monochromatic sources. By using the numerical mission orbits, we evaluate the performances of sky localization for various time-delay interferometry channels. For 30 days observation until coalescence, the LISA-TAIJI network in optimal operation can localize all simulated binary sources, $({10}^7,3.3\times {10}^6)M_{\odot }$, $({10}^6,3.3\times {10}^5)M_{\odot }$, and $({10}^5,3.3\times {10}^4)M_{\odot }$ at redshift $z=2$, in $0.4{\mathrm{deg}}^2$ (field of view of Wide Field Imager on Athena). The angular resolution can be improved by more than ten times comparing to LISA or TAIJI single detector at a given percentage of population. The improvements for monochromatic sources at 3 and 10 mHz are relatively moderate in one year observation. The precision of sky localization could be improved by a factor of 2 to 4 comparing to single LISA at a given percentage of sources. For a simulated 90 days observation for monochromatic waves, the LISA-TAIJI network still represents a considerable localization advantage which could be more than ten times better.

We report the results of the first joint observation of the KAGRA detector with GEO 600. KAGRA is a cryogenic and underground gravitational-wave detector consisting of a laser interferometer with 3 km arms, located in Kamioka, Gifu, Japan. GEO 600 is a British–German laser interferometer with 600 m arms, located near Hannover, Germany. GEO 600 and KAGRA performed a joint observing run from April 7 to 20, 2020. We present the results of the joint analysis of the GEO–KAGRA data for transient gravitational-wave signals, including the coalescence of neutron-star binaries and generic unmodeled transients. We also perform dedicated searches for binary coalescence signals and generic transients associated with gamma-ray burst events observed during the joint run. No gravitational-wave events were identified. We evaluate the minimum detectable amplitude for various types of transient signals and the spacetime volume for which the network is sensitive to binary neutron-star coalescences. We also place lower limits on the distances to the gamma-ray bursts analyzed based on the non-detection of an associated gravitational-wave signal for several signal models, including binary coalescences. These analyses demonstrate the feasibility and utility of KAGRA as a member of the global gravitational-wave detector network.

The space-based laser interferometers, LISA, Taiji and TianQin, are targeting to observe milliHz gravitational waves (GWs) in the 2030s. The joint observations from multiple space-based detectors yield significant advantages. In this work, we recap the studies and investigations for the joint space-based GW detector networks to highlight: 1) the high precision of sky localization for the massive binary black hole (BBH) coalescences and the GW sirens in the cosmological implication, 2) the effectiveness to test the parity violation in the stochastic GW background observations, 3) the efficiency of subtracting galactic foreground, 4) the improvement in stellar-mass BBH observations. We inspect alternative networks by trading off massive BBH observations and stochastic GW background observation.