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    In this study, we investigate the impact of microlensing on gravitational wave (GW) signals in the LIGO−Virgo sensitivity band. Microlensing caused by an isolated point lens, with (redshifted) mass ranging from MLz ∈ (1,  105) M⊙ and impact parameter y ∈ (0.01,  5), can result in a maximum mismatch of $\sim 30~{{\ \rm per\ cent}}$ with their unlensed counterparts. When y < 1, it strongly anticorrelates with the luminosity distance enhancing the detection horizon and signal-to-noise ratio (SNR). Biases in inferred source parameters are assessed, with in-plane spin components being the most affected intrinsic parameters. The luminosity distance is often underestimated, while sky-localization and trigger times are mostly well-recovered. Study of a population of microlensed signals due to an isolated point lens primarily reveals: (i) using unlensed templates during the search causes fractional loss (20 per cent to 30 per cent) of potentially identifiable microlensed signals; (ii) the observed distribution of y challenges the notion of its high improbability at low values (y ≲ 1), especially for y ≲ 0.1; (iii) Bayes factor analysis of the population indicates that certain region in MLz − y parameter space have a higher probability of being detected and accurately identified as microlensed. Notably, the microlens parameters for the most compelling candidate identified in previous microlensing searches, GW200208_130117, fall within a 1σ range of the aforementioned higher probability region. Identifying microlensing signatures from MLz < 100 M⊙ remains challenging due to small microlensing effects at typical SNR values. Additionally, we also examined how microlensing from a population of microlenses influences the detection of strong lensing signatures in pairs of GW events, particularly in the posterior-overlap analysis.

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    When travelling from their source to the observer, gravitational waves can get deflected by massive objects along their travel path. For a massive lens and a good source-lens alignment, the wave undergoes strong lensing, leading to several images with the same frequency evolution. These images are separated in time, magnified, and can undergo an overall phase shift. Searches for strongly lensed gravitational waves look for events with similar masses, spins, and sky location and linked through so-called lensing parameters. However, the agreement between these quantities can also happen by chance. To reduce the overlap between background and foreground, one can include lensing models. When doing realistic searches, one does not know which model is the correct one to be used. Using an incorrect model could lead to the non-detection of genuinely lensed events. In this work, we investigate how one can reduce the false alarm probability when searching for strongly lensed events. We focus on the impact of the addition of a model for the lens density profile and investigate the effect of potential errors in the modelling. We show that the risks of false alarm are high without the addition of a lens model. We also show that slight variations in the profile of the lens model are tolerable, but a model with an incorrect assumption about the underlying lens population causes significant errors in the identification process. We also suggest some strategies to improve confidence in the detection of strongly lensed gravitational waves.

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    Since the first detection of gravitational waves in 2015, gravitational-wave astronomy has emerged as a rapidly advancing field that holds great potential for studying the cosmos, from probing the properties of black holes to testing the limits of our current understanding of gravity. One important aspect of gravitational-wave astronomy is the phenomenon of gravitational lensing, where massive intervening objects can bend and magnify gravitational waves, providing a unique way to probe the distribution of matter in the Universe, as well as finding applications to fundamental physics, astrophysics, and cosmology. However, current models for gravitational-wave millilensing—a specific form of lensing where small-scale astrophysical objects can split a gravitational wave signal into multiple copies—are often limited to simple isolated lenses, which is not realistic for complex lensing scenarios. In this paper, we present a novel phenomenological approach to incorporate millilensing in data analysis in a model-independent fashion. Our approach enables the recovery of arbitrary lens configurations without the need for extensive computational lens modelling, making it a more accurate and computationally efficient tool for studying the distribution of matter in the Universe using gravitational-wave signals. When gravitational-wave lensing observations become possible, our method could provide a powerful tool for studying complex lens configurations in the future.

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    As the number of detected gravitational wave sources increases with increased sensitivity of the gravitational wave observatories, observing strongly lensed pairs of events will become a real possibility. Lensed gravitational wave (GW) events will have very accurately measured time delays and magnification ratios. Suppose we identify the lens system corresponding to a GW event in the electromagnetic domain and also measure the redshifts of the lens and the host galaxy; in that case, we can use the GW event to constrain important astrophysical parameters of the lens system. As most lensing events have image separations that are significantly smaller than the GW event localization uncertainties, we must develop diagnostics that will aid in the robust identification of such lensed events. We define a new statistic based on the joint probability of lensing observables that can be used to discriminate lensed pairs of events from the unlensed ones. To this end, we carry out simulations of lensed GW events to infer the distribution of the relative time delays and relative magnifications subdivided by the type of lensed images. We compare this distribution to a similar one obtained for random unlensed event pairs. Our statistic can improve the search pipelines’ existing ranking approach to down-select event pairs for joint parameter estimates. The distributions we obtain can further be used to define more informative priors in joint parameter estimation analyses for candidate lensed events.

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