Research

Time-delay Cosmography & the Hubble Constant

Gravitational lensing sometimes produces multiple mirage images of the same background object. This is illustrated below, where a foreground massive galaxy is lensing a background quasar.

Illustration of strong gravitational lensing: a foreground galaxy deflects light from a background quasar, producing multiple mirage images

As the path taken by photons in the different images can be a bit shorter or a bit longer, they reach the observer at different time. In the video below, you can see the variation of the lensed quasar WFI2033-4723 over more than 15 years. The same luminosity variations arrive in the different multiple images, but delayed in time. By shifting the light curves, we can measure the time delay, which is inversely proportional to the Hubble Constant.

Light curves of the four images of lensed quasar WFI2033-4723, monitored over 15 years. The same brightness variations appear in each image, but shifted in time — these time delays are the key observable we measure.

To measure the Hubble constant, we need :
  1. A measurement of the time delays. This can be obtained from long-term monitoring of the lensed quasars with small telescopes
  2. The distribution of the mass of the lensing galaxy, that can be reconstructed from high-resolution images
  3. An estimate of the external convergence, i.e. the matter density along the line of sight
  4. An estimate of the stellar velocity dispersions of the lensing galaxy, which provide a second estimate of its mass.

Combining these four ingredients, we have recently measured H0 = 73.7+1.4-1.5 km.s-1.Mpc-1, using 7 gravitationally lensed quasars. This is in good agreement with the distance ladder method, using pulsating stars and Supernovae Ia, but in tension with the CMB measurement of Planck. This discrepancy — known as the Hubble tension — is one of the most debated puzzles in modern cosmology, and independent measurements like ours are key to understanding whether it points to new physics or unaccounted systematic errors.

Posterior distributions of H0 from 7 TDCOSMO time-delay lenses assuming ΛCDM
H0 posterior distributions from the 7 TDCOSMO time-delay lenses, assuming Λ CDM

Using weaker assumptions on the mass profile of the lens galaxy but better stellar kinematic data, we found H0 = 71.6+3.9-3.3 km.s-1.Mpc-1, with the 8 time-delay lenses. We are currently gathering more and more stellar kinematic observations to keep improving the precision of our measurement.

In October 2024, we discovered the first Einstein zig-zag lens , where the light from the background quasar is deflected by two different galaxies at different redshifts. The optical path taken by the photons forms a zig-zag between the two deflecting galaxies as illustrated below. This rare configuration opens a new window for cosmography, as it provides additional constraints on the mass distribution along the line of sight.

Image configuration of the Einstein zig-zag lens PSJ1721+8842, showing the zig-zag light path between two deflecting galaxies
Image configuration of the Einstein zig-zag lens, PSJ1721+8842

Selected publications

Black holes and accretion disks

Microlensing is a unique tool to probe the structure of accretion disks around supermassive black holes. It occurs in strongly lensed quasars when a star in the foreground galaxy passes in front of one of the quasar's multiple images. The star is not massive enough to produce detectable lensed images itself, but it slightly changes the apparent brightness of the quasar. As the alignment between the star and the quasar changes over time, the magnification varies. There is a remarkable coincidence: the caustics produced by the star are a few nano-arcseconds in size — comparable to the angular size of an accretion disk at cosmological distances. This makes microlensing sensitive to structures the size of our solar system in galaxies several billion light-years away, which is far beyond the resolution of any existing telescope.

We have used the microlensing signal to measure the physical size of accretion disks — finding them to be larger than predicted by standard thin-disk models (e.g. Cornachione et al. 2020). In the future, multiband observations from the Rubin Observatory will also constrain the temperature profile of accretion disks, providing a powerful test of black hole accretion physics.

Recently, we have found unexpected periodic variations in the microlensing signal of lensed quasar J0158-4325, with a period of 172.6 days. This signal is only observed in the flux ratios of this lensed quasars, i.e. once the time delay is corrected and the intrinsic variations of the quasar are subtracted. The periodicity of this signal is best explained in the context of Supermassive Binary Black Hole. The animation below shows how the gradient of magnification produced by the microlense leaves a detectable periodic signal in the microlensing light curves.

Animation showing the periodic microlensing signal of lensed quasar J0158-4325, consistent with a supermassive binary black hole
Animation of the microlensing magnification map for J0158-4325. As the caustic sweeps across the accretion disk, it produces a periodic signal (period: 172.6 days) that is best explained by a supermassive binary black hole system.

Selected publications

Galaxies and Quasars co-evolution

In the local Universe, there is a tight correlation between the mass of a galaxy and the mass of its central supermassive black hole. This is interpreted as evidence for co-evolution: the central quasar (AGN) regulates its host galaxy's growth through a mechanism called AGN feedback, where the energy it radiates is injected back into the galaxy and suppresses star formation. By tracing this correlation across cosmic time, we can test galaxy evolution models and understand how the galaxies we see today came to be.

Doing this in the distant Universe requires precise mass estimates — but standard techniques become increasingly less reliable at high redshift due to projection effects and model assumptions. Strong gravitational lensing offers a clean geometric solution: it directly measures the projected mass of the lensing object, independent of its internal dynamics.

Lens model of the quasar acting as a gravitational lens SDSS J0919+2720
Lens model of the quasar acting as a gravitational lens SDSS J0919+2720.

We have pioneered the use of quasars acting as gravitational lenses to precisely weigh their host galaxies. These systems are extraordinarily rare — only a handful are known — but they provide uniquely clean mass measurements. In a study published in Nature Astronomy, we presented the first strong lensing analysis of such a system, obtaining a precise mass for the quasar's host galaxy that would be inaccessible by any other means. We are now building a statistical sample: we have already identified 7 new candidates in DESI DR1, and the upcoming Euclid survey is expected to uncover many more.

Selected publications

Image processing and deconvolution

All of my research depends on extracting precise measurements from astronomical images — and images from ground-based telescopes suffer from blurring caused by turbulence in the Earth's atmosphere. This blurring can be partially corrected if we can measure the Point Spread Function (PSF). Recovering a sharp image from a blurred, noisy one is an ill-posed problem: many different sharp images are mathematically consistent with the same blurred data, so additional constraints are needed to find the right one. To address this, we developed STARRED, a novel deconvolution algorithm based on three principles:

  1. the image is reconstructed in two separate channels — one for point sources (stars, quasar images) and one for extended emission (the host galaxy) — avoiding contamination between the two
  2. rather than fully removing the PSF (which amplifies noise), the image is brought to a higher but well-controlled resolution with a known Gaussian PSF
  3. starlet wavelets are used to regularise the problem — they efficiently represent smooth astrophysical structures while suppressing noise

Image deconvolution of lensed quasar DES0408-5354 using STARRED, comparing ground-based input and deconvolved output
Image deconvolution of the lensed quasar DES0408-5354. Ground-based images were taken at the ESO/MPG 2.2m telescope in La Silla, Chile.

STARRED is implemented in JAX, enabling fast execution on GPUs. It is used directly in my other research: sharper images lead to more precise lens models, which in turn improve our measurement of the Hubble constant. The code is general enough for a wide range of imaging problems beyond gravitational lensing. To learn more, watch this presentation on YouTube or explore the GitLab repository and its example notebooks.

Selected publications