Youjun Lu

The gravitational lensing of multimessenger signals from binary neutron star (BNS) mergers, including gravitational waves (GWs), short γ -ray bursts (sGRBs), kilonovae, and afterglows, can serve as a unique probe to constrain the mass of the graviton and cosmological parameters. In this paper, we estimate the detection rates of lensed electromagnetic counterparts associated with lensed BNS GW events detected by Cosmic Explorer and Einstein Telescope. For kilonovae and afterglows, we further consider a complementary pointed follow-up strategy targeting preidentified galaxy-scale lens candidates within the GW localization region. By utilizing both numerical and observational constraints on BNS mergers, we find the following: (1) Future γ -ray telescopes, even with a sensitivity more than 10 times better than that of the Fermi γ -ray Burst Monitor, may only detect lensed sGRB prompt emission at a rate ∼ 0.1 yr ⁻¹ , corresponding to ∼2 × 10 ⁻³ detectable lensed BNS GW events. (2) For the known-lens pointed strategy, the identifiable lensed-host fraction is approximately 0.15–0.30 for the fiducial deep-lens-catalog case considered, suggesting a possible gain in per-lens sensitivity for faint kilonovae and afterglows. (3) A Nancy Grace Roman Space Telescope–like near-infrared facility could detect lensed kilonovae at rates of approximately ∼ 0.4 5 − 0.34 + 0.81 , 0.5 5 − 0.41 + 0.98 , and 0.07 8 − 0.059 + 0.139 yr ⁻¹ in the F106, F158, and F213 bands, respectively. (4) Lensed afterglows remain difficult to detect in the optical and radio bands, while ATHENA-like X-ray observations may detect 0.5–5 events over 10 yr.

The discovery of the gravitational-wave event GW170817 from a binary neutron star merger, together with its multi-wavelength electromagnetic counterparts, marks the beginning of the era of multi-messenger gravitational-wave astronomy. Observations of gravitational-wave signals from compact binary mergers enable an independent measurement of the luminosity distance to the source. This implies that gravitational-wave sources can serve as “standard sirens” to probe the expansion history of the Universe, providing a new approach to constrain cosmological parameters. In this paper, we review the basic principles of using gravitational-wave standard sirens to constrain cosmology. We discuss various methods for determining the source distance and redshift, as well as the capabilities of second- and third-generation ground-based detectors and space-based detectors in constraining cosmological parameters, especially the Hubble constant and dark energy parameters. By examining three types of standard sirens—binary neutron star mergers with electromagneticc ounterparts as bright sirens, stellar-mass binary black hole mergers as dark sirens, and the dark lensed sirens— we illustrate the methodology, challenges, and future prospects of the standard siren approach.

Aims. The microlensing of lensed quasars presents a promising avenue for understanding the structure of accretion disks around supermassive binary black holes (SMBBHs). We investigated the microlensing signatures in multiband (optical, UV, and X-ray) light curves of active SMBBH systems, focusing on how these signatures depend on the mass ratio, separation, and accretion rate. Methods. We analyzed the periodic fluctuations in microlensing light curves induced by the orbital motion of SMBBHs. We examined the relation between the mass ratio and the period of variations in light curves across optical, UV, and X-ray bands. Results. We find that the periodic fluctuations in the light curves depend on the mass ratio of the black holes: for nearly equal masses, variations occur at half the orbital period, whereas for low mass ratios, the period corresponds to the orbital period influenced by the secondary mini-disk. Furthermore, all optical, UV, and X-ray light curves exhibit the same period and phase, but the amplitude of variation is greater in the UV and X-ray bands than in the optical bands. These light curves provide insights into the motion and radiation regions of the disks through wavelength-dependent periodic variations, although they yield limited constraints on the system’s black hole mass or Eddington ratio, which can instead be derived from the spectral energy distribution (SED). Integrating microlensing data with SED observations is crucial for accurately constraining the parameters of SMBBH systems.

Gravitational Waves (GWs) emitted from distant astrophysical sources can be gravitationally lensed by objects or systems encountered along their propagation paths. Strong astrophysical GW sources include inspiralling and merging stellar-mass compact binaries (stellar-mass binary black holes and binary neutron stars), intermediate- and supermassive-binary-black-holes. Lenses range from stars, primordial black holes, dark matter halos to galaxies and galaxy clusters. Depending on the ratio of the GW wavelength to the lensing scale, GW lensing can occur in two regimes: geometric-optics, which produces multiple images of a single lensed event with relative time delays and magnifications, and wave-optics, which produces frequency-dependent amplifications and phase shifts in the observed waveform. Lensed GW signals can be identified either by overlap of inferred parameters between event pairs followed by joint Bayesian model comparison or by characteristic frequency-dependent amplification and phase modulation in the waveform that distinguish them from unlensed signals. The detection rates for different classes of lensed GW events are set by the redshift distributions of source populations and of intervening lenses, together with the lenses' mass and spatial distributions, of which the predictions are quite promising for future detection. Once confirmed, lensed GW events can be used as powerful probes to astrophysical processes, fundamental physics and cosmology: they can constrain the nature and abundance of dark matter (including compact-object candidates), the mass function and internal structure of lensing galaxies and subhalos, the Hubble constant, and other cosmological parameters. In this paper, we provide a concise overview of the gravitational lensing of GWs, covering the theoretical framework, predicted detection rates for lensed inspirals and mergers, search strategies for lensed GW events, and their astrophysical and cosmological applications. We conclude with prospects and future directions for observing and exploiting the lensing of astrophysical GW events.

This study aims to test whether a supermassive binary black hole (SMBBH) system with a triple-disk accretion structure can explain the observed ~173-day periodic microlensing variations and spectral energy distribution (SED) of the gravitationally lensed quasar Q J0158-4325. We construct a triple-disk model for the SMBBH system, incorporating realistic accretion disk structures, orbital motion, and microlensing effects. The model is used to simulate optical and X-ray microlensing light curves and SEDs, which are compared with long-term optical monitoring, X-ray observations, and UV-optical spectra from HST and XSHOOTER. Bayesian analysis and MCMC fitting are applied to constrain model parameters. The model successfully reproduces the periodic microlensing variations. Combined light curve and SED fitting favor a high mass ratio (q > 0.5) SMBBH system with total mass ~109.5M⊙, and nearly equal-mass binaries (q ~ 1) provides the best agreement with both the optical/UV spectrum and the microlensing signal. This model predicts larger X-ray microlensing amplitudes than in the optical, but, the available X-ray observations lack the precision needed to place strong constraints. We emphasize the need for future high-cadence monitoring to resolve remaining uncertainties. This study demonstrates the effectiveness of combining multi-wavelength microlensing signatures with spectral modeling to provide robust constraints on SMBBH systems, with the developed framework applicable to other lensed quasars for identifying and characterizing candidate SMBBHs.

Stellar-mass binary black holes (sBBHs) formed in globular clusters (GCs) are promising sources for multiband gravitational-wave (GW) observations, particularly with low- and middle-frequency detectors. These sBBHs can retain detectable eccentricities when they enter the sensitivity bands of low-frequency GW observatories. We study multiband GW observations of eccentric sBBHs that escape from GC models simulated with the MOCCA code, focusing on how low- and middle-frequency detectors can constrain their eccentricities and other parameters. Using Monte Carlo simulations, we generate 10 realizations of cosmic sBBHs by combining the MOCCA sample with a cosmological model for GC formation and evolution. We then assess their detectability and the precision of parameter estimation. Our results show that LISA, Taiji, the LISA-Taiji (LT) network, and AMIGO could detect 0.8 ± 0.7, 11.6 ± 2.0, 15.4 ± 2.7, and 7.9 ± 1.3 escaping sBBHs, respectively, over 4 yr, while LT-AMIGO could detect 20.6 ± 3.0 multiband sBBHs in the same period. LT and AMIGO can measure initial eccentricities with relative errors of approximately 10 ⁻⁶ –2 × 10 ⁻⁴ and 10 ⁻³ –0.7, respectively. Joint LT-AMIGO observations have a similar ability to estimate eccentricities as LT alone.