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

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

Problem and Context
This paper presents the first cosmological constraints derived from the cosmic shear analysis of the UNIONS-3500 weak lensing galaxy catalogue in configuration space. As the largest and deepest photometric survey of the northern hemisphere to date, UNIONS (Ultraviolet Near Infrared Optical Northern Survey) aims to probe the large-scale structure (LSS) of the Universe, specifically the properties of dark energy and dark matter. The analysis addresses the "S8 tension," a persistent discrepancy where low-redshift weak lensing surveys typically infer a lower clustering amplitude ($S_8 \equiv \sigma_8 \sqrt{\Omega_m/0.3}$) than high-redshift Cosmic Microwave Background (CMB) measurements. While previous Stage III surveys (e.g., KiDS, DES, HSC) have largely relied on southern sky data, this work provides a critical independent constraint from the northern hemisphere to test the robustness of these tensions against systematics and sky coverage.

Methodology
The analysis utilizes a 2D cosmic shear approach using a single tomographic bin, as the current UNIONS-3500 catalogue lacks the multi-band colour information required for multiple redshift bins. The core observable is the two-point correlation function (2PCF), $\xi_{\pm}(\theta)$, measured in configuration space over angular scales of 1–250 arcmin.

Key methodological components include:

• Data Processing: The shear catalogue comprises over 61 million galaxies across 3500 deg² (2894 deg² effective area) with an effective number density of 4.96 arcmin⁻². Shapes were measured using ngmix and calibrated via Metacalibration.
• Systematic Mitigation:
  • PSF Systematics: The analysis employs a joint inference framework where Point Spread Function (PSF) leakage parameters ($\alpha, \beta$) are sampled alongside cosmological parameters. These parameters are constrained by fitting $\tau$-statistics (galaxy-PSF correlations) derived from the data. Scale cuts are applied to ensure PSF systematics contribute less than 10% of the total signal.
  • B-modes: Scale cuts are further informed by $B$-mode null tests (using COSEBIs and pure-mode correlation functions) to ensure residual systematics are below detection thresholds.
  • Redshift Calibration: The source redshift distribution, $n(z)$, is estimated using a Self-Organizing Map (SOM) trained on a spectroscopic sample (DEEP2, VVDS, VIPERS) and weighted by the UNIONS photometry. A prior volume weighting scheme corrects for selection biases between the spectroscopic and wide-field samples.
  • Intrinsic Alignments (IA): Due to the single redshift bin, the IA amplitude ($A_{IA}$) cannot be tightly constrained by the shear data alone. A data-driven Gaussian prior is applied, derived from direct measurements of red and blue galaxy populations in the W3 field.
• Inference Pipeline: Bayesian inference is performed using CosmoSIS with Polychord (and Nautilus for consistency checks). The likelihood includes Gaussian terms for the 2PCF data vectors and the PSF statistics. The covariance matrix accounts for Gaussian, non-Gaussian, and Super Sample Covariance (SSC) contributions, with specific corrections for the survey mask.
• Validation: The pipeline was validated against 341 mock catalogues generated with GLASS, ensuring internal consistency between configuration and harmonic space pipelines and verifying the recovery of fiducial cosmology. A blinded analysis strategy was employed, with shifts applied to the $n(z)$ distributions to prevent confirmation bias.

Key Contributions

• First Northern Hemisphere 2D Constraints: This work delivers the first configuration-space cosmological constraints from the largest northern hemisphere weak lensing dataset, offering a crucial cross-check for southern hemisphere surveys.
• Integrated Systematic Modeling: The paper outlines a robust pipeline that jointly fits cosmological parameters and PSF leakage systematics, utilizing $\tau$-statistics to inform priors on nuisance parameters rather than relying solely on theoretical models.
• Data-Driven Priors: The methodology derives priors for redshift bias ($\Delta z$) and intrinsic alignment ($A_{IA}$) directly from the data and simulations, rather than adopting purely theoretical or external constraints, thereby maximizing the constraining power while remaining conservative.
• Pipeline Validation: The study demonstrates a novel approach to unblinding by validating the consistency between independent configuration and harmonic space pipelines on mock data prior to unblinding the real data.

Results
Assuming a flat $\Lambda$CDM model, the fiducial analysis yields the following constraints:

• Clustering Amplitude: $S_8 = 0.831^{+0.067}_{-0.078}$
• Matter Density: $\Omega_m = 0.265^{+0.130}_{-0.075}$
• Amplitude of Clustering: $\sigma_8 = 0.782^{+0.206}_{-0.144}$

These results are consistent with Planck CMB measurements and previous Stage III cosmic shear results (KiDS-Legacy, DES Y6, HSC-Y3) within $1\sigma$. The analysis finds no significant tension between early- and late-time measurements of the clustering amplitude.

The paper notes a $\sim 0.6\sigma$ difference between the configuration space result ($S_8 \approx 0.831$) and the concurrent harmonic space analysis ($S_8 \approx 0.891$). This discrepancy is attributed to the different scale ranges probed; the configuration space analysis excludes small scales ($\theta < 12$ arcmin) due to systematics, where the data exhibits stronger clustering.

Robustness tests indicate that the results are sensitive to:

• Intrinsic Alignment Modeling: Using a flat prior on $A_{IA}$ broadens $S_8$ uncertainties significantly, while fixing $A_{IA}=0$ shifts $S_8$ by $-0.71\sigma$.
• Redshift Calibration: Adopting a flat prior on the redshift shift $\Delta z$ increases $S_8$ uncertainty, though fixing $\Delta z=0$ yields consistent results given the small magnitude of the bias.
• Scale Cuts: Including smaller scales ($\theta \in [5, 83]$ arcmin) increases the best-fit $S_8$ to $0.886$, aligning more closely with the harmonic space result but at the cost of a poorer fit ($\chi^2_{red} = 1.34$) due to a localized feature at 10 arcmin.

Significance
The paper positions UNIONS as a mature Stage III survey capable of delivering competitive cosmological results. The consistency of the UNIONS-3500 constraints with other major surveys and the Planck CMB suggests that the $S_8$ tension may not be driven by unaccounted-for systematics in the northern hemisphere or by the specific analysis choices of this survey. The work serves as a key stepping stone for Stage IV experiments (e.g., Euclid, Rubin/LSST), demonstrating the readiness of the UNIONS collaboration to handle complex systematic modeling and providing a validated framework for future tomographic and 3x2-point analyses. The authors emphasize that while current constraints are limited by nuisance parameter degeneracies (particularly IA and redshift uncertainties), future releases with spectroscopic overlap and tomographic binning will significantly enhance constraining power.