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arxiv: 2605.13547 · v1 · submitted 2026-05-13 · 🌌 astro-ph.CO

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UNIONS-3500 Weak Lensing: III. 2D Cosmological Constraints in Configuration Space

L. W. K. Goh , S. Guerrini , C. Daley , F. Hervas-Peters , M. Kilbinger , A. Wittje , C. Murray , S. Fabbro
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H. Hildebrandt M. J. Hudson L. van Waerbeke A. H. Wright T. de Boer J.-C. Cuillandre E. Magnier A. W. McConnachie
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Pith reviewed 2026-05-14 18:12 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords cosmic shearweak lensingtwo-point correlation functionS_8 parametercosmological constraintsUNIONS surveyLCDM modelsystematics mitigation
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The pith

Cosmic shear from the UNIONS-3500 catalogue yields S_8 = 0.831^{+0.067}_{-0.078} in a flat LCDM model, consistent with Planck within 1 sigma.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes the first 2D cosmological constraints from cosmic shear using the UNIONS-3500 weak lensing galaxy catalogue across 3500 square degrees of the northern sky. It measures the two-point correlation function in a single tomographic bin after estimating the source redshift distribution, applying shear calibration, and constructing the covariance matrix while mitigating PSF systematics and B-modes. A sympathetic reader would care because this result demonstrates that a large photometric survey can deliver competitive constraints on structure growth that align with cosmic microwave background data. The work also shows the pipeline remains stable under changes in scale cuts, prior ranges, and nonlinear modelling choices.

Core claim

Assuming a flat LCDM model, the 2D cosmic shear analysis of the UNIONS-3500 catalogue yields S_8 = 0.831^{+0.067}_{-0.078}, which is consistent with constraints from Planck CMB measurements and precedent cosmic shear results within 1 sigma. The analysis uses the two-point correlation function statistic together with methodologies for source redshift distribution estimation, shear calibration, and covariance construction while mitigating residual PSF systematics and B-modes.

What carries the argument

The two-point correlation function statistic applied to cosmic shear measurements in a single tomographic bin, with explicit steps for redshift distribution estimation, shear calibration, covariance estimation, and mitigation of PSF systematics and B-modes.

If this is right

  • The S_8 constraint supports the flat LCDM model because it lies within 1 sigma of independent Planck CMB results.
  • The pipeline's stability under varied scale cuts, prior ranges, and nonlinear modelling choices indicates reliable error control.
  • The coordinated data release positions the UNIONS survey as ready to contribute competitive results ahead of Stage IV weak lensing experiments.
  • The single-bin configuration-space measurement provides a baseline that future multi-bin analyses can build upon directly.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Adding multiple tomographic bins to the same catalogue would likely tighten constraints on the dark energy equation of state parameter.
  • Cross-correlating the UNIONS shear catalogue with spectroscopic galaxy samples could test whether the reported S_8 value changes under different tracer selections.
  • Repeating the identical analysis in Fourier space on the same data would allow a direct internal consistency check between configuration-space and power-spectrum approaches.

Load-bearing premise

The analysis assumes that the source redshift distribution, shear calibration, and covariance matrix are accurately estimated and that residual PSF systematics and B-modes have been sufficiently mitigated.

What would settle it

A new cosmic shear measurement on the same or larger area that returns an S_8 value lying well outside the reported 1-sigma interval while using an otherwise identical flat LCDM setup would falsify the claimed consistency.

Figures

Figures reproduced from arXiv: 2605.13547 by A. H. Wright, A. Wittje, A. W. McConnachie, C. Daley, C. Murray, E. Magnier, F. Hervas-Peters, H. Hildebrandt, J.-C. Cuillandre, L. van Waerbeke, L. W. K. Goh, M. J. Hudson, M. Kilbinger, S. Fabbro, S. Guerrini, T. de Boer.

Figure 1
Figure 1. Figure 1: Real space 2PCF data vectors estimated from the data in black (left: 𝜉+, right: 𝜉−) as a function of angular separation 𝜃, with error bars computed from the diagonals of the covariance matrix. The grey sections denote the fiducial scale cuts employed in this analysis. The solid orange line shows the best-fit model to the data obtained in this analysis, which includes both the cosmological and PSF-leakage 𝜉… view at source ↗
Figure 2
Figure 2. Figure 2: The PSF systematic statistics 𝜏0,+ ( 𝜃 ) (left panel) and 𝜏2,+ ( 𝜃 ) (right) statistics estimated based on Eqs. (9) and (10), as a function of angular separation 𝜃, along with their error bars calculated from the semi-analytic covariance matrix. We also include the 𝜏0 and 𝜏2 best-fit obtained from the inference. with the PSF. Residual terms can only be evaluated at the positions of the stars. The PSF-PSF a… view at source ↗
Figure 3
Figure 3. Figure 3: Normalised redshift distribution, 𝑛(𝑧). defined as 𝑤 SOM 𝑖 = ∑︁ 𝑗 𝑤𝑗 ⟨𝑅𝛾⟩bin( 𝑗) ∑︁ 𝑘 𝑤 prior 𝑘 , (14) where the numerator sums the weighted counts of UNIONS galaxies 𝑗 assigned to cell𝑖, and the denominator is the sum of the prior volume weights 𝑤 prior 𝑘 of spectroscopic calibration galaxies 𝑘 in that cell (Wright et al. 2025b). This definition ensures that the spectroscopic sample is reweighted to match… view at source ↗
Figure 5
Figure 5. Figure 5: Ratio of the total covariance matrix with and without the survey mask, for both the auto-covariance and cross-covariance of the 𝜉± ( 𝜃 ) corre￾lation functions (top) and their diagonals (bottom), over 𝜃 ∈ [1, 250] arcmin. the lensing power spectrum likelihood, as we currently lack a pre￾scription for the cross-correlation in the covariance matrix between cosmic shear and lensing data. 3.6.2 Baryonic Acoust… view at source ↗
Figure 6
Figure 6. Figure 6: Marginalised posteriors of 𝛼PSF and 𝛽PSF obtained from the PSF inference step (see Sect. 4.3), which are subsequently adopted as priors when they are sampled in the cosmological inference analysis. We include the results for both sets of ellipticities: the object-wise leakage corrected one (gold) and the non-leakage corrected one (pink). The catalogue-level object￾wise leakage correction effectively remove… view at source ↗
Figure 8
Figure 8. Figure 8: Histogram of the difference in best-fit 𝑆8 values obtained from the 341 mocks, when run with the configuration space versus harmonic space pipelines (harmonic − configuration). The orange histogram and correspond￾ing fitted KDE distribution are that of the weighted means, while the blue histogram represents the 2D marginalised mode values. We mark out the null value with the black dashed vertical line. 𝜃 ∈… view at source ↗
Figure 7
Figure 7. Figure 7: 2D heatmap of the ratio of the 2PCF signal as a function of wavenumber 𝑘 and angular separation 𝜃 (upper: 𝜉+; lower: 𝜉−). The red contours mark the boundary beyond which smaller scales (i.e. larger 𝑘 values) contribute less than 10% of the total signal. White vertical dashed lines mark the fiducial scale cuts: a 12 arcmin lower bound for 𝜉+ would signify that wavenumbers no larger than 𝑘max = 0.43 ℎ Mpc−1 … view at source ↗
Figure 9
Figure 9. Figure 9: Whisker plot of the best-fit 𝑆8, 𝜎8, and Ωm parameters, along with their 68% confidence interval (CI), for the various observables (orange for configuration space and blue for harmonic space as presented in Paper IV), comparison with external surveys (written in pink for Planck and black for the rest of the weak lensing surveys), and changes in analysis setup (in green). For 𝑆8 and Ωm, we report the 2D mar… view at source ↗
Figure 10
Figure 10. Figure 10: 2D marginalised contour plot of 𝑆8, 𝜎8 and Ωm of our fiducial results (orange), including those obtained in harmonic space (blue, see Paper IV), as well as results from external surveys (red unfilled: KiDS-Legacy 𝜉±; green unfilled: HSC-Y3 𝜉±; purple filled: Planck CMB). of clustering would then be required to compensate for it, leading to a strong linear relationship between these two parameters. This is… view at source ↗
Figure 12
Figure 12. Figure 12: 2D marginalised contour plot of 𝑆8, Ωm and 𝐴IA comparing the effects of modelling intrinsic alignment: using a Gaussian prior on the amplitude parameter 𝐴IA (orange), using a flat prior (blue unfilled) and not including intrinsic alignment (green). resultant posterior distributions, demonstrating that even without the additional step of first fitting for 𝛼 and 𝛽 (as outlined in Sect. 4.3), we are still ab… view at source ↗
Figure 11
Figure 11. Figure 11: Histogram of 𝜒 2 values when considering the combined cosmo￾logical and systematic signals (top, in green), and when only considering the cosmological signal (bottom, pink). The red vertical line denotes the fiducial 𝜒 2 . We find an effective degree of freedom of 14.4, and PTE of 0.39 for the 𝜉± signal, and an effective degree of freedom of 40.4 with a PTE of 5.9 × 10−3 for the 𝜏0,2 statistics. this has … view at source ↗
Figure 15
Figure 15. Figure 15: Plot of the best-fit 𝜉+ data vector for the two scale cuts considered: in the fiducial analysis when 𝜃 ∈ [12, 83] arcmin (orange), and when 𝜃 ∈ [5, 83] arcmin (cyan). We also include the 𝜉+ vector computed from the best￾fit values of the harmonic space analysis in dotted blue. The light grey vertical bands denote the fiducial scale cuts, while the darker grey band on the left demarcates the 5 arcmin cut, … view at source ↗
Figure 13
Figure 13. Figure 13: 2D marginalised contour plot of 𝑆8, Ωm and Δ𝑧 comparing the effects of modelling redshift uncertainty parameter Δ𝑧: using a Gaussian prior (orange), using a flat prior (blue unfilled), and not accounting for redshift uncertainties (pink). 0.8 1.0 S8 0.6 0.8 1.0 βPSF 0.01 0.02 αPSF 0.2 0.4 0.6 Ω m 0.2 0.4 0.6 Ωm 0.006 0.023 αPSF 0.7 1.0 βPSF Gaussian α and β priors Flat α and β priors No ξ sys included No … view at source ↗
Figure 14
Figure 14. Figure 14: 2D marginalised contour plot of 𝑆8, Ωm, 𝛼PSF and 𝛽PSF comparing the effects of modelling PSF: using Gaussian priors on the leakage parameters 𝛼PSF and 𝛽PSF (orange), using flat priors (blue unfilled), not including 𝜉sys in the data vector during inference (pink), and using the set of objects in the catalogue whose ellipticities were not leakage-corrected (grey). The black ‘x’ marks the best-fit values of … view at source ↗
Figure 16
Figure 16. Figure 16: 2D marginalised contour of 𝑆8 and Ωm derived from UNIONS-3500 𝜉± (orange), UNIONS-3500 + Planck (blue), and UNIONS￾3500 + Planck + DESI DR2 BAO (black) data sets, comparing them to the Planck 2018 results that we have run using the plik_lite likelihood (green dashed unfilled). The grey band marks the fiducial 1𝜎 CI of Ωm from DESI BAO, as reported in Abdul Karim et al. (2025b). one, which are themselves n… view at source ↗
read the original abstract

We present the first cosmological constraints from the cosmic shear analysis of the UNIONS-3500 weak lensing galaxy catalogue in configuration space. The Ultraviolet Near Infrared Optical Northern Survey (UNIONS) is the largest and deepest photometric survey of the northern hemisphere to date, with the UNIONS-3500 catalogue using high-quality $r$-band imaging across 3500 deg2 of the sky. We perform a 2D cosmic shear analysis with a single tomographic bin, using the two-point correlation function (2PCF) statistic. Assuming a flat LCDM model, we obtain constraints on the clustering amplitude of S_8 = 0.831^{+0.067}_{-0.078}, which is consistent with constraints from Planck CMB measurements and precedent cosmic shear results within 1sigma. We outline the construction of our cosmological inference pipeline, including the estimation of the source redshift distribution, shear calibration, and covariance matrix, and describe methodologies for the mitigation of systematic effects arising from PSF systematics and B-modes. We demonstrate that our results are robust to variations in analysis choices, including scale cuts, prior ranges, and nonlinear modelling. This paper is part of a coordinated release which collectively demonstrates the maturity and readiness of UNIONS to deliver competitive cosmological results, positioning it as a key stepping stone towards the forthcoming era of Stage IV weak lensing experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript presents the first cosmological constraints from a 2D cosmic shear analysis of the UNIONS-3500 weak lensing catalogue in configuration space. Using the two-point correlation function in a single tomographic bin under a flat ΛCDM model, the authors derive S_8 = 0.831^{+0.067}_{-0.078}. The result is reported to be consistent with Planck CMB measurements and prior cosmic shear constraints within 1σ. The paper outlines the full inference pipeline, including source n(z) estimation, shear calibration, covariance construction, PSF mitigation, and B-mode null tests, along with explicit robustness checks against scale cuts, prior ranges, and nonlinear modeling choices.

Significance. If the central result holds, this work delivers an independent northern-hemisphere constraint on the clustering amplitude S_8 from one of the largest photometric surveys to date. The explicit demonstration of robustness to analysis choices and the detailed treatment of systematics (PSF, B-modes) strengthen the reliability of the measurement and position UNIONS as a mature precursor to Stage-IV weak-lensing experiments. The consistency with Planck within 1σ and the reproducibility-oriented pipeline description are notable strengths.

minor comments (3)
  1. The abstract states that results are robust to scale cuts, priors, and nonlinear modeling; a concise summary table listing the S_8 shifts under each variation would improve readability and allow readers to assess the impact at a glance.
  2. In the description of the covariance matrix construction, the treatment of the survey mask and shape noise should be cross-referenced to the specific equations or appendices where the analytic or simulation-based form is defined.
  3. Figure captions for the 2PCF measurements and model fits should explicitly state the scale range used and whether the plotted error bars include the full covariance or only diagonal elements.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending acceptance. We are pleased that the work is recognized for its robust pipeline, detailed systematics treatment, and value as an independent northern-hemisphere S_8 constraint from UNIONS-3500. No major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; standard parameter fit from data

full rationale

The paper's central result is the posterior on S_8 obtained by fitting the measured 2PCF under flat LCDM. This is a direct likelihood evaluation against observed correlation functions, with n(z), shear calibration, covariance, and systematics mitigation serving as external inputs rather than outputs derived from the same equations. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain. The analysis is self-contained against external benchmarks (Planck consistency is a post-hoc comparison, not an input).

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The result rests on the assumption of a flat LCDM cosmology and on the accuracy of the estimated redshift distribution, shear calibration, and covariance matrix. No new particles or forces are introduced.

free parameters (1)
  • S_8
    The clustering amplitude parameter that is directly constrained by the fit to the observed 2PCF; its central value and errors are the primary output.
axioms (1)
  • domain assumption flat LCDM cosmology
    The model is assumed throughout the inference; the reported S_8 constraint is conditional on this choice.

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