Miguel Zumalacárregui

Theory, phenomenology & data interpretation

Research

My research runs in parallel strands: wave-optics lensing of gravitational waves, dark matter, strong-field and multi-messenger lensing, and tests of gravity. All of them rest on a foundation of cosmology, dark energy and gravitational theory. Each strand is described below, with the papers that carry it.

My research encompasses four key predictions of Einstein's theory of general relativity: cosmology (the dynamics and history of the Universe), gravitational waves (ripples in spacetime itself), black holes (regions where gravity is strong enough to trap light) and gravitational lensing (the distortion of signals traveling through the Universe). I use these phenomena to explore astrophysics, dark matter, dark energy and gravity, including general relativity itself: the theory that contains all four.

The research areas drawn as four predictions of general relativity: cosmology, black holes, gravitational lensing and gravitational waves, inside the theory that contains them. GENERAL RELATIVITY Cosmology Black holes Gravitationallensing Gravitationalwaves

Selected work appears below. The research highlights gather the results with the press coverage and data releases behind them, and the complete and current record is on:

INSPIRE-HEP NASA ADS Google Scholar ORCID

Wave-optics lensing phenomena

A gravitational wave that passes near a mass is not simply magnified. When the lens is such that its gravitational radius is comparable to the wavelength, the wave diffracts and interferes with itself: the resulting frequency-dependent pattern encodes the mass, the profile and even the substructure of the lens. The same is true of any phase-coherent signal. That makes lensing a probe of objects that emit no light at all. Because a lens breaks the symmetry of the background, it is also a test of gravity itself. This strand is funded by the GLOW ERC Consolidator Grant.

Time–frequency representation of GW231123 with the modulation expected from a magnified and diffracted signal marked on it.
GW231123 sounds like a magnified and diffracted black-hole merger, lensed by a compact object of 190–850 M☉. (paper)

Geometric optics (the picture of light rays bending around a mass) breaks down when the wavelength becomes comparable to the Schwarzschild radius of the lens. For gravitational waves that happens for lens masses below ~104 M☉ in the LIGO band, and far higher masses for LISA. In this wave-optics regime the amplification factor becomes frequency dependent, producing a characteristic modulation across the signal rather than a simple overall magnification.

That frequency dependence is what makes the effect useful. A lensed event constrains the lens mass distribution because different profiles diffract differently, analogous to diffraction patterns observed in crystallography. It also breaks the magnification–distance degeneracy that plagues lensing in the geometric limit: the modulation is set by the redshifted lens mass, so a diffracted signal carries an absolute mass scale rather than only a relative magnification. The presence of a diffracting object further breaks degeneracies with the external potential, helping constrain the gravitational magnification.

We derived efficient methods for computing these amplification factors, validated them against symmetric lenses where analytic results exist, and extended them to general matter distributions. The resulting machinery is public as the GLoW code. It allowed us to analyze GW231123, which we argue is the first compelling candidate for a magnified and diffracted black-hole merger.

How the wave-optics signature responds to the shape of the lens. As the density slope γ̃ is varied, the microcaustics in the lens plane (left) reorganize, the time-domain arrivals (center) merge and split, and the amplification factor |F(f)| (right) changes its modulation pattern: this is why a single diffracted event constrains the profile and not only the mass. Produced with GLoW; the code and data are in the GW231123 lensing release. (paper)

Selected publications

Dark matter and small-scale structure

Cold dark matter and its alternatives (warm, fuzzy, self-interacting, primordial black holes) agree on large scales and disagree below galactic scales. That is precisely where the observational evidence is thinnest, because sub-galactic halos contain few or no stars. Because lensing responds to mass instead of light, it provides means to probe these elusive halos.

Two complementary handles come out of this. In some cases, diffraction by a single object may be used to constrain the properties of an individual halo. But even when no single lens dominates, the accumulated effect of many small structures along the line of sight leaves a characteristic imprint on the signal: lens stochastic diffraction, which resembles a noise term but has a specific spectral shape and correlations with the underlying signal. For LISA, that imprint would be sensitive to halos of 10–104 M☉, a range that is hard to reach by other means.

Lens stochastic diffraction. Left: cold-dark-matter halos between a gravitational-wave source and the observer. The outline marks the region whose halos affect the signal, which widens as the frequency sweep moves toward long wavelengths. Right: the distortion those halos imprint, an effect that would let LISA detect halos of 10–104 M☉. (paper)

The electromagnetic side of the same argument gave one of the sharpest existing limits on compact dark matter: if a large fraction of dark matter were in stellar-mass black holes, the brightnesses of distant type Ia supernovae would be visibly skewed: most slightly dimmed, a few substantially brighter. The observed distribution shows no such skew, which rules out LIGO-mass black holes as the bulk of dark matter.

Selected publications

See also Lens stochastic diffraction: a signature of compact objects in gravitational-wave data.

Strong-field and multi-messenger lensing

Simulated image of starlight (orange) gravitationally lensed by a supermassive black-hole binary.
Starlight lensed by a supermassive black-hole binary. As the binary orbits, its caustic network sweeps across a background star. (paper)

Black hole binaries are usually studied as sources, but they are also excellent lenses. When a star lies behind a supermassive binary, the orbital rotation of the system produces a quasi-periodic magnification with a distinctive shape. This phenomenon can open a new window into the population of sub-parsec binary systems: the same systems that will dominate the LISA and pulsar-timing signal, and that are otherwise very hard to resolve. Closer to home, we found that continuous gravitational waves from sources behind Sgr A* can be detected well beyond the Einstein radius, and resolved as separate images.

Eight flares per orbit. As an equal-mass binary turns, the caustics it casts sweep repeatedly across a star behind it (left), and the magnification traces a light curve whose flares repeat on the orbital period (right). The number and shape of the flares follow from the separation, the mass ratio and the eccentricity, which is what makes the light curve a measurement of the binary rather than a detection of it. (paper)

Strong fields also change how the wave itself propagates. Near a massive body the standard lensing formalism (weak fields, small deflections, a single flat background) no longer holds: at first order beyond geometric optics the wave's polarization couples to the background curvature, and the two polarizations follow slightly different trajectories. This gravitational spin-Hall effect makes the arrival time depend on both frequency and polarization.

Multi-messenger lensing is the wider frontier. A lensed gravitational wave and a lensed electromagnetic counterpart of the same event constrain the lens far better than either alone, because they probe complementary regimes: gravitational waves are diffracted by stars, but light is described by geometric-optics lensing. Building this into a coherent observational strategy across gravitational interferometers and time-domain electromagnetic surveys is a community-scale effort where wave-optics phenomena may be crucial for discovery.

Lensed electromagnetic sources probe the lens distribution in their own right, and that knowledge feeds back into the gravitational-wave side. Surveys such as Euclid are expected to deliver on the order of a hundred thousand galaxy–galaxy strong lenses, transforming empirical knowledge of the lens population: calibrating the priors that lensed-GW searches rely on, and letting multiply-imaged candidates be cross-matched against lens catalogs, an association that sharpens the localization and opens cosmography applications.

Selected publications

Gravitational-wave propagation and dark energy

Posterior constraints on lens-induced birefringence from 43 gravitational-wave events.
A search for lens-induced birefringence across 43 gravitational-wave events, bounding departures from general relativity. From Goyal, Vijaykumar, Ezquiaga & Zumalacárregui.

Any deviation from Einstein's theory builds up along a gravitational wave's journey, making propagation a clean test of cosmological gravity. My earlier work identified the speed of gravitational waves as a sharp test for many classes of modified theories. GW170817 settled the question: its near-simultaneous electromagnetic counterpart fixed that speed to one part in 1015, which removed large classes of dark-energy theories in a single stroke.

Lensing sharpens and broadens the test, because a lens does what a smooth cosmological background cannot: it breaks the symmetry. In modified theories, this allows the wave to mix with new fields of different spin through couplings that vanish on a homogeneous, isotropic background. The result is birefringence, with the two polarizations propagating differently as if the lens were an anisotropic crystal, and dispersion, with the frequency components spreading like light forming a rainbow. These tests rely on distortions of the waveform, requiring no electromagnetic counterpart and allowing for searches over entire source catalogs.

The program extends this from the high-frequency expansion to a complete wave-optics formalism, and from specific dark-energy models to a theory-agnostic parameterization of lensing beyond Einstein (the analog of the post-Newtonian parameters in the Solar System), delivered as a likelihood module for cosmological analyses.

Selected publications

See also the geometric-optics expansion and lens-induced dispersion, the review Dark energy in light of multi-messenger gravitational-wave astronomy, and Testing modified gravity at cosmological distances with LISA standard sirens.

Methods, inference and public software

Wave-optics lensing is computationally challenging: the amplification factor stems from an oscillatory integral, and a naive evaluation is far too slow to sit inside a parameter-estimation loop. A large part of my work is therefore methodological: finding formulations that are both accurate and fast enough for systematic exploration and Bayesian inference.

The results are public. GLoW implements contour-integration and time-domain methods for general matter distributions (see also Glworia, WOlensing and Microlensing_Wave_Effect). These software tools facilitate the reproducibility of scientific results and the exploration of new ideas.

Speed is not only a convenience. We have adapted machine learning methods to facilitate systematic lensing searches over entire source catalogs: a network trained on microlensed waveforms can perform analyses in minutes rather than days.

Every posterior sample is a lens. Walking up the GW231123 lensing posterior in the (MLz, γ̃) plane (left), each sample predicts a different whitened template in LIGO Livingston (right): the merger stays anchored while the post-merger diffraction echoes move and reshape as the sampler climbs toward the best fit. Samples from the public data release. (paper)

Selected publications

All software GLoW on GitHub

Cosmology and gravity theories

Cosmological tests of dark energy, and the scalar–tensor theories behind them. This line preceded the lensing work and continues alongside it, through collaborations, the hi_class code and its own funding. It is also where much of the theoretical machinery the lensing work relies on came from.

Cosmological tests of gravity and dark energy

Testing the physics behind cosmic acceleration against data, considering mechanisms beyond a simple cosmological constant. Recent work re-examined DESI's evidence for dynamical dark energy by reconstructing the dark-energy density directly from the data, without committing to a parameterization.

Reconstructed change in the dark-energy density relative to its present value, as a function of redshift, with confidence bands that widen with redshift and remain consistent with zero.
The change in dark-energy density with redshift, reconstructed from CMB, BAO and supernova data without assuming a parameterization. A cosmological constant is the flat line at zero. (paper)

Another key goal is what surveys can actually deliver: what forthcoming data will say about scalar–tensor theories, and the individual signatures: cosmic shear, the non-linear shift of the BAO ruler, relativistic effects at ultra-large scales, and obtaining relativistic predictions from standard Newtonian simulations.

Model building and cosmic tensions

Phenomenological parameterizations are useful to test data, but do not map back to fundamental theories. It is therefore essential to build theories from first principles: theories that can be confronted with every dataset at once, and that still have to survive tests from the solar system to the cosmological horizon. A crucial aspect is that the parameters of full theories jointly determine all the predictions: background expansion and large-scale structure are no longer separate levers that can be pulled independently.

The Hubble tension is the sharpest case: the covariant Galileon relieves it through several distinct mechanisms within one theory, and is able to shift H0 without fine-tuned initial conditions. Beyond individual models, theoretical priors chart which regions of Horndeski space survive before any data are involved, and massive gravity raises the prior question of whether cosmic expansion can be accommodated at all.

Parameter space showing how the covariant Galileon shifts the inferred Hubble constant toward distance-ladder values.
Several mechanisms within the covariant Galileon shift H0 toward distance-ladder values. (paper)

hi_class

An Einstein–Boltzmann solver covering the full Horndeski class. It is fast and stable enough for Bayesian inference; flexible and general enough to span quintessence, Horndeski and theories beyond it, specified either by a Lagrangian or by the effective functions that govern linear perturbations; and accurate at the sub-percent level, meeting the requirements of current surveys and checked against independent implementations.

Code details hiclass-code.net
CMB temperature power spectra for Galileon models computed with hi_class, with a lower panel showing relative deviations from an independent implementation below one per cent.
hi_class checked against an independent Galileon implementation (Barreira et al.): the CMB temperature spectra agree to better than one per cent across the whole range of multipoles. (paper)

Scalar–tensor gravity beyond Horndeski

Horndeski's theory is the most general scalar–tensor Lagrangian with second-order equations of motion, which was long taken to be an unavoidable condition to avoid the ghosts that plague higher-derivative theories. It is not: equations of higher order can still be degenerate, and so free of ghosts. Generalized field redefinitions of the metric are how the first explicit examples beyond Horndeski were built.

Hand-drawn map of scalar–tensor theory space, showing labeled regions such as JBD and Horndeski as islands separated by an expanse marked Ostrogradski's Sea.
Theory space drawn as a map: viable scalar–tensor theories are islands in Ostrogradski's sea of instabilities. Field redefinitions extend the coastline beyond Horndeski. (paper)

Disformal transformations

Adding to the metric a term built from derivatives of a scalar field generalizes the conformal rescaling that relates the Einstein and Jordan frames. The consequences are concrete: a disformally coupled scalar becomes a DBI Galileon once written in the Einstein frame, and the same coupling screens fifth forces in dense environments, hiding the scalar where laboratory tests would otherwise have found it.

Diagram relating the Einstein and Jordan frames to Galileon and disformal descriptions through metric field redefinitions.
Disformal field redefinitions connect the Einstein and Jordan frames to Galileon and disformal descriptions of the same theory. (paper)

Scientific coordination and future observatories

Present detectors are the beginning of gravitational-wave astronomy. Much of my community work goes into the observatories and surveys that will follow, and into making sure gravitational lensing has a place in them.

LISA

LISA is where wave-optics lensing stops being a curiosity. At millihertz frequencies the wavelengths are long enough that diffraction by dark-matter halos becomes detectable. Left unmodeled, it could also bias the inferred source parameters. Preparing the mission for that is part of the Cosmology Working Group's remit.

Consortium member since 2018; Council member and Senior Co-Chair of the Cosmology Working Group since 2025. Section coordinator for gravitational-wave lensing in the LISA Cosmology white paper.

Euclid

Euclid maps both the galaxies that host gravitational-wave sources and the structures that lens them, which is what makes the connection worth building: the same survey supplies the redshifts for standard sirens and the lens catalogs for multi-messenger lensing.

Consortium member since 2014; co-lead of the Science Working Group on Gravitational Waves and of its "bright sirens" work package since 2025. Member of the Strong Lensing, Cosmology Theory, and Supernovae & Transients working groups.

GW-Space 2050

The scientific case for ESA's gravitational-wave missions after LISA. Decisions taken now about frequency band and sensitivity determine what is measurable decades from now, so the cosmography case has to be made before the instrument is designed rather than after. The μHz band is a particular opportunity: it reaches sources no other detector will see, and lensed events become more common the further out a detector can reach.

Coordinator for the cosmography section since 2024. The report is expected shortly.

Future detectors and mission concepts

Next-generation ground detectors will see far enough that lensed events stop being rare, which changes what a lensing search has to be able to do. GUEST is a separate concept altogether, detecting gravitational waves by tracking satellites.

Contributor to the science cases below, and coordinator of the microlensing section of the multi-messenger lensing white paper.