Data analysis

Discovering lensed signals

Lensing signatures are usually subtle. Most lensed gravitational waves will arrive looking like ordinary signals carrying a small distortion, and the question is whether that distortion is better explained by a lens than by detector noise, by missing physical effects, or by inaccuracies in the waveform model. The first step towards an answer is to analyze the same data under the lensed and the unlensed hypotheses and compare the results, which is what the animation above is a picture of, each sample in it being a lens configuration in its own right.

An uncontested discovery is challenging, for several reasons. First, lensing enlarges the parameter space, introducing degeneracies with physical effects such as spin-induced precession, which then have to be disentangled. Second, non-Gaussian noise transients and model inaccuracies can mimic some lensing signatures, so the significance of a candidate has to account for the probability of a false positive. Third, the astrophysical chance of a particular lensing configuration has to be folded in, which introduces uncertainties of its own. Finally, realistic lenses need models that do not yet exist.

The search for lensed gravitational waves has become a core pursuit of the LIGO–Virgo–KAGRA collaboration.^[1] But lensing signatures are varied and subtle, and a claim of this kind carries much further when more than one group arrives at it. GLOW will provide that independent analysis: a different team, different methods, different assumptions, and the infrastructure for anyone to reproduce the results.

An effective microlensing theory

Stochastic lenses such as stellar fields cannot be fitted directly: no method will ever measure the particular arrangement of objects that produced a given distortion. The project will develop an effective description instead. A well-tempered basis of functions reduces a seemingly random lens to a handful of free coefficients, and the distribution of those coefficients across simulated realizations gives them a physically motivated prior: the reduced-order model developed for microlensing. These methods extend inference beyond the simple lens models (a point lens with external shear, for instance, the model behind the analysis of GW231123) that are currently within reach through the GLoW code.

The significance of a lensing claim then comes from the posteriors of those coefficients rather than from a template match. This has a useful property: the model is agnostic about what the lenses are, so the same fit serves stars and dark-matter objects, and the distinction between them is drawn afterwards, from the population the coefficients imply.

Global evidence for lensing

Not every question is answered by a single loud event. It is far more likely that near-term detectors deliver many lensed events, none of them carrying much evidence on its own. Searching the catalog as a whole is therefore essential: beyond the wave-optics distortions in individual signals, lensing changes the distribution of apparent masses and distances across the population.

Population analyses also discipline the single-event claims. An astrophysical prior on how often lensing should occur, and on what the lenses are likely to be, is what turns a well-fitting lensed model into a credible one. New population methods may also be able to fold in information from sources that form multiple images.

The need for speed

Lensing searches face a growing computational challenge. Inference of wave-optics distortions enlarges the parameter space of every event analyzed, and improving detector sensitivity will bring thousands of events per year.^[2] Analyses that take days or weeks per event become prohibitive at that rate, and the cost grows sharply again for searches over pairs of events, where multiply-imaged candidates have to be compared with one another.

Accelerated inference is the way through. A network trained to map data directly to posteriors amortizes the cost: the expense moves into training, and each subsequent event is analyzed in seconds. The project builds on DINGO for this, a simulation-based inference tool^[3] already demonstrated for an isolated point lens.^[4] At a later stage the same machinery can run real-time searches for lensed neutron stars, so that telescopes can follow up a potential multi-messenger observation while there is still something to see.

References

1. LIGO Scientific, Virgo and KAGRA Collaborations, A. G. Abac et al., GWTC-4.0: searches for gravitational-wave lensing signatures arXiv preprint (2025)
2. LIGO Scientific Collaboration, LIGO–Virgo–KAGRA observing plan Observing capabilities documentation
3. K. Cranmer, J. Brehmer, G. Louppe, The frontier of simulation-based inference (2019)
4. M. Caldarola, S. Goyal, N. Gupte, S. R. Green, M. Zumalacárregui, Accelerated inference of microlensed gravitational waves with machine learning Phys. Rev. D 113, 104073 (2026)

Where this is done

Work packages

Microlensing searches · Accelerated inference

Papers

Across the Universe: GW231123 as a magnified and diffracted black hole merger · Effective description of lensed gravitational waves diffracted by stellar fields