In 1919, during a solar eclipse, light from distant stars bent near the Sun — the first confirmation of Einstein field equations prediction that massive objects warp spacetime curvature. A century later, in 2015, the LIGO detectors caught gravitational waves from a black hole merger — another triumph of general relativity. The intersection of these phenomena opens up an exotic possibility: the waves themselves could undergo gravitational lensing — being bent and focused by intervening masses. When the wavelength is comparable to the lens size, diffraction kicks in, and the signal isn't just copied but reshapes — it's the microlensing regime with diffraction, like a funhouse mirror reflection. In the autumn of 2023, LIGO registered event GW231123: if unlensed, it's a record black hole merger with anomalously high masses and spins. But perhaps it's a mirage: a lighter merger, amplified and distorted by a lens made of dark matter, a concept Fritz Zwicky already pondered in the 1930s. Solving the puzzle required Bayesian inference comparison of hypotheses with the prior rarity (optical depth) — how often objects of the right mass appear along the line of sight as a function of the source's redshift. To do this, astrophysicists built numerical simulation models of different lens types, from point masses to extended halos, and ran them through signal processing of actual interferometry data, accounting for the large-scale structure of the universe.
The authors applied Bayesian inference to open LIGO data, using numerical simulation templates of lensed signals. They compared the unlensed hypothesis with three lens models: point mass (an intermediate-mass black hole), a power-law profile (gSIS, describing gravothermally collapsed halos of self-interacting dark matter), and a cored isothermal sphere (CIS). For each model, a frequency-dependent amplification factor F(f) was computed, accounting for diffraction (wave optics), and then nested sampling was used to estimate posterior parameter distributions. The key departure from previous work is the inclusion of astrophysical priors: mass, spin, and distance distributions for merging black holes from the GWTC-5 catalog, along with the optical depth of lenses, derived from the halo mass function and observational constraints on black hole abundances. This turned the Bayes factor into posterior odds that directly account for the rarity of both source and lens.
Without prior information, all lensed models showed a better fit to the data (log-likelihood increased by several units). The component masses shifted from extreme values (137 and 101 solar masses) to more typical ones (~100 and 50 M⊙), while spins decreased. The time delay between leading images was ~22 ms. However, after accounting for the probability of encountering a lens, support for the hypotheses changed dramatically. For a point lens — an intermediate-mass black hole — using the predicted mass function of star clusters gave posterior odds of 10^−5 in favor of the unlensed scenario. For cold dark matter halos (NFW profile), the odds dropped below 10^−6, because such halos are not dense enough. Only for self-interacting dark matter with gravothermal core collapse did the odds come out around 1, but even then the expected observation rate of such an event is minuscule (<10^−3).
This work shows that in the era of growing gravitational-wave statistics, one cannot rely on fit quality alone: the prior rarity of the lensing hypothesis can outweigh even a noticeable model improvement. This calls for rethinking candidate selection criteria and advancing Bayesian inference methods that fully account for population properties. For GW231123, the most likely interpretation still involves unaccounted systematics — possibly flaws in signal processing or shortcomings in waveform models.
The next generation of interferometry (Einstein Telescope, Cosmic Explorer) will boost event samples by orders of magnitude, enabling precise measurements of population tails and optical depth. In parallel, progress in numerical simulation of gravothermal collapse in dark matter will refine predictions for lens profiles. Developing dedicated algorithms to pick out diffraction distortions will make the search for lensed waves more sensitive.
The findings impact the search strategy for lensed gravitational waves and the interpretation of exceptional events, bridging black hole astrophysics, cosmology of large-scale structure, and dark matter physics.
Future work should explore more realistic lens models embedded in external gravitational fields (for example, within galaxy halos), as well as refine the mass function of intermediate-mass black holes and collapsing halos.
The work touches on the nature of dark matter (is it self-interacting?), the origin of intermediate-mass black holes, and the completeness of our understanding of systematics in detectors and signal models — all key open questions in modern physics.
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What the work does
You analyzed event GW231123, comparing hypotheses of an unlensed merger of massive black holes versus lensing of a lighter pair. Using Bayesian inference and numerical lens models, you accounted for prior probabilities, including optical depth, and showed that the self-interacting dark matter model (gSIS) yields the highest posterior odds.
Where its strength is
The strength of this work lies in moving from a simple calculation of the magnification factor to a full Bayesian model comparison with realistic astrophysical priors, allowing a quantitative assessment of the lensing likelihood given the rarity of configurations.
Where it could go next
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If GW231123 were truly lensed, its 22 ms time delay would match the period of the gravitational wave at merger peak — such a coincidence is very unlikely and suggests that "lensing" might be a fitting artifact.
In Carl Sagan's novel 'Contact', aliens use gravitational lensing to amplify a signal; here, however, the lens confuses the picture, masking the true nature of the source.