Constraining cosmology with weak gravitational lensing

Sacha Guerrini, UCL seminar, 9th October 2025

Who am I?

Strasbourg

Who am I?

EC meeting Leiden 2025

My research interest

Main research topics:

• Weak gravitational lensing
  • Point-Spread Function systematics
  • Standard cosmic shear analysis
  • Higher-order statistics
• Forward modelling
  • Simulation-Based Inference
  • Differentiable simulators

Other interests:

• Strong gravitational lensing
• Tests of General Relativity

UNIONS collaboration

• Validation of the weak lensing sample
• Cosmological constraints with cosmic shear
• Constraints with higher-order statistics

Euclid Consortium

• Member of the Weak Lensing Science Working Group
  • Participation in standard cosmic shear analysis (WL1)
  • Higher-Order Statistics Work Package
  • Forward Modelling Work Package
• Validation of PSF modelling and shape measurement in the ground segment

Cosmological context: \(\Lambda\)CDM

Credit: NAOJ

\[\begin{align} \left. \begin{array}{cc} H_0 & \text{Expansion rate}\\ \Omega_m & \text{Matter density}\\ \Omega_b & \text{Baryon density}\\ \sigma_8 & \text{Clumpiness}\\ w & \text{EoS of dark energy} \end{array} \right\} \text{Constrained using Bayesian inference} \end{align}\]

Weak gravitational lensing

Credit: ESA

• Percent-level effect
• Polluted by shape noise
• Requires a large number of galaxies

Cosmology with cosmic shear

Credit: S. Farrens

I. PSF diagnostics

II. Cosmic shear with 2pt-statistics

III. And beyond

I. PSF diagnostics

Credit: Mandelbaum (2018)

Semi-analytical covariance (Guerrini et al. (2025))

Analytical: based on analytical expressions of the covariance

Semi: No theoretical predictions of the \(\rho\)- and \(\tau\)-statistics. Use measurements on data.

Prediction of the systematic additive bias

• Here applied to UNIONS but the pipeline currently runs to validate Euclid data processing.
• Can probe heterogeneous contribution to PSF systematics from galaxies with different properties, e.g. magnitude, size

PSF systematics: Take-home messages

• PSF systematics are essential to understand to perform cosmic shear analysis.
• \(\rho\)- and \(\tau\)-statistics are powerful tools to estimate the bias to the 2PCF.
• Semi-analytical covariance (Guerrini+2025) can speed up comparisons between catalogs.

II. Cosmic shear with 2pt statistics

and other contributors…

Analysis details

• Theoretical prediction: CAMB
• Non-linear power spectrum: HMCode2020
• Shear calibration with MetaCalibration.
• Residual multiplicative bias estimated from image simulations. (Hervas Peters et al., in prep.)
• Cosmology pipeline with CosmoSIS.
• Analysis in real space (Goh et al., in prep.) and harmonic space (Guerrini et al., in prep.).
• PSF systematics accounted for in the inference.

Real CFHT exposure

Simulated exposure

B-modes systematics

Spin-2 shear fields can be decomposed into E-modes, containing the vast majority of lensing information, and B-modes, which are a probe of systematics at UNIONS noise levels.

In the presence of masking, some ambiguous modes usually cannot be cleanly attributed to E or B.

We use three B-mode approaches: pure correlation functions, COSEBIS, and pseudo-\(C_\ell\).

Credit: BICEP2 Collaboration

B-modes in harmonic space

B-modes on the smallest scales. Lower significance after removing the smallest objects from the catalogue. Data points and errorbars obtained with NaMaster.

Covariance (harmonic space)

Gaussian covariance accounting for mask mode-coupling with iNKA (Namaster). Validation against OneCovariance (theory code) and GLASS mocks.

Agreement between the error bars at the \(10\%\) level

Inference

Real space \(\xi_\pm(\vartheta)\)

Harmonic space \(C_\ell\)

\(\sim 2\times\) larger than DES, KiDS or HSC.

Non-tomographic analysis significantly reduces constraining power.

III. Beyond 2pt statistics

Implicit Likelihood Inference (also known as SBI)

UNIONS forward model

Available on GitHub, adapted from DESY3 analysis

JaxILI, a pipeline for Implicit Likelihood Inference

checkpoint_path = ... #Choose the checkpoint path
checkpoint_path = os.path.abspath(checkpoint_path) #Beware, this should be an absolute path.

compressor = Compressor(
    model_class=model_class,
    model_hparams=model_hparams,
)

compressor = compressor.append_simulations(theta=theta, x=x)

metrics, MSE_compression_function = compressor.train(
    checkpoint_path=checkpoint_path
)

inference = NPE()
inference = inference.append_simulations(theta, x)

metrics, density_estimator = inference.train(
    checkpoint_path=checkpoint_path,
)

JaxILI on a cosmological toy model

Cosmological parameters: \(A_\mathrm{s}\), \(n_\mathrm{s}\), \(f_\mathrm{NL}\)

Go here for more

Goal: Obtain constraints on the cosmological parameters using pixel level information.

JaxILI on a cosmological toy model

Cosmological parameters: \(A_\mathrm{s}\), \(n_\mathrm{s}\), \(f_\mathrm{NL}\)

• Implicit contours obtained with MSE compression.
• Loss of information compared to Explicit inference.
• Unbiased constraints obtained.

An application of JaxILI in Euclid

Credit: R. Paviot

• Simulation of realistic redshift distributions using Normalizing Flow.

• \(p(z_\mathrm{noisy} | z_\mathrm{true}, \mathrm{Flux})\) infered with Neural Posterior Esimation

Application to UNIONS data

• CNN optimal compression
• Extract information at the pixel level.
• Cut the footprint in patches.

Credit: M. Maupas

Application to UNIONS data

Project in stand-by due to changes in the fiducial analysis.

Conclusions

• First cosmic shear cosmology results from UNIONS are incoming!
• Allowed to develop tools used in Euclid cosmic shear analysis/validation of the data.
• Exploring advanced Bayesian inference methods to extract more information from the available datasets.

Extra material: UNIONS multi-band coverage

Extra material: MetaCalibration

Credit: F. Hervas Peters

Extra material: Galaxy-PSF correlations

PSF error model: \(\delta \boldsymbol{e}^\mathrm{sys}_\mathrm{PSF} = \alpha \underbrace{\boldsymbol{e}_\mathrm{PSF}}_{\text{Leakage}} + \beta \underbrace{(\boldsymbol{e}_* - \boldsymbol{e}_\mathrm{PSF})}_{\text{Ellipticity error}} + \eta \underbrace{\boldsymbol{e}_\mathrm{PSF} \left(\frac{T_* - T_\mathrm{PSF}}{T_*} \right)}_{\text{Size error}}\). \(\alpha\), \(\beta\) and \(\eta\) free parameters.

\[\begin{equation} \left( \begin{array}{l} \tau_{0,1} \\ \tau_{2,1} \\ \tau_{5, 1} \\ \vdots \\ \tau_{0, n} \\ \tau_{2, n} \\ \tau_{5, n} \end{array} \right) = \left( \begin{array}{llllll} \rho_{0, 1} & \rho_{2, 1} & \rho_{5, 1} \\ \rho_{2, 1} & \rho_{1, 1} & \rho_{4, 1} \\ \rho_{5, 1} & \rho_{4, 1} & \rho_{3, 1} \\ & \ddots & \\ \rho_{0, n} & \rho_{2, n} & \rho_{5, n} \\ \rho_{2, n} & \rho_{1, n} & \rho_{4, n} \\ \rho_{5, n} & \rho_{4, n} & \rho_{3, n} \\ \end{array} \right) \left( \begin{array}{l} \alpha \\ \beta \\ \eta \\ \end{array} \right) \label{eq:tau_matrix} \end{equation}\]

Systematic error: \(\xi^\mathrm{sys}_\mathrm{PSF} = \alpha^2 \rho_0 + \beta^2 \rho_1 + \eta^2 \rho_3 + 2 \alpha \beta \rho_2 + 2 \alpha \eta \rho_5 + 2 \beta \eta \rho_4\)

Constrain with MCMC

Extra material: Scale cuts

Pure B-mode correlation functions

\[ \xi_+^{E/B}(\vartheta) = \frac 1 2 \left[\xi_+(\vartheta) \pm \xi_-(\vartheta) + \int_\vartheta^{\vartheta_\mathrm{max}}\frac{\mathrm{d}\theta}{\theta} \xi_-(\theta) \left(4 - \frac{12\vartheta^2}{\theta^2} \right) \right] - \frac 1 2 \underbrace{[S_+(\vartheta) \pm S_-(\vartheta)]}_{\text{Integrals of $\xi_\pm$ with filter functions}} \]

Credit: C. Daley

B-modes on small scale (\(\sim 3'\) in \(\xi_+\) and \(\sim 30'\) in \(\xi_-\)); large scales are ok.

B-modes with COSEBIS

Pure functions and COSEBIS tell the same story.

Extra material: Best-fit

Extra material: \(S_8\) constraints

Extra material: real space vs harmonic space

Extra material: MSE compression