Joint cosmological fits to DESI-DR1 full-shape clustering and weak gravitational lensing in configuration space

Technical Summary: Joint Cosmological Fits to DESI-DR1 Full-Shape Clustering and Weak Gravitational Lensing in Configuration Space

Problem and Motivation
The Dark Energy Spectroscopic Instrument (DESI) has entered the "Stage IV" era of cosmological surveys, providing datasets orders of magnitude larger than predecessors. A primary goal is to understand dark energy and resolve tensions in cosmological parameters (e.g., $S_8$) observed between different probes like the Cosmic Microwave Background (CMB) and large-scale structure (LSS). While galaxy clustering and weak gravitational lensing are naturally complementary—clustering tracing visible matter and lensing tracing total matter distribution—performing a joint analysis is non-trivial. It requires reconciling different modeling prescriptions (perturbative theories for clustering vs. halo models for lensing) and handling scale-dependent systematics. Previous joint analyses often either projected clustering data (losing Redshift Space Distortion, RSD, information) or used uniform models that might not optimally fit the full range of scales for both probes. This work aims to perform a joint "3 $\times$ 2-pt" analysis in configuration space, retaining the full anisotropic clustering information (RSD) from DESI while combining it with shear and galaxy-galaxy lensing from overlapping weak lensing surveys.

Methodology
The analysis utilizes the DESI Data Release 1 (DR1) Bright Galaxy Survey (BGS) and Luminous Red Galaxy (LRG) samples as lens tracers, cross-correlated with weak lensing shear measurements from KiDS-1000, DES-Y3, and HSC-Y3.

• Data Vectors: The study combines three correlation statistics:
  1. Cosmic Shear ($\xi_{\pm}$): Auto-correlations of source galaxy shapes.
  2. Galaxy-Galaxy Lensing ($\gamma_t$): Cross-correlations between DESI lens positions and source shapes.
  3. Clustering Multipoles ($\xi_\ell$): Auto-correlations of DESI lens positions, specifically the monopole ($\ell=0$) and quadrupole ($\ell=2$), measured over the full DESI-DR1 footprint.
• Modeling:
  • Clustering: The authors employ a configuration-space emulator based on the Fourier-space comet emulator, which uses Effective Field Theory (EFT). To handle non-linear Redshift Space Distortions (RSD) and the "Fingers-of-God" effect without diverging Fourier transforms, they utilize the Velocity Difference Generating function at infinity ($VDG_\infty$) approach. This involves damping the power spectrum with an effective function $W_\infty$ before transforming to configuration space.
  • Weak Lensing: The shear and galaxy-galaxy lensing are modeled using a halo-model-based power spectrum prescription (following Porredon et al. 2025), incorporating the Non-Linear Alignment (NLA) model for intrinsic alignments and magnification bias.
  • Covariance: An analytical Gaussian covariance is used, including cross-correlations between lensing and clustering. However, the auto-covariance for clustering multipoles is replaced with a semi-analytical determination from the RascalC code to better account for survey geometry and non-Gaussianity.
• Inference: Bayesian inference is performed using the cosmosis framework with the nautilus sampler. The analysis focuses on the physical parameter space (avoiding dependence on the Hubble parameter $h$ in the definition of parameters), constraining $\omega_m$, $\omega_{DE}$, $\sigma_{12}$ (amplitude of the linear density field variance on 12 Mpc scales), and $\ln(10^{10}A_s)$.

Key Contributions

• First Full-Shape Configuration-Space Analysis: This paper presents the first full-shape analysis of DESI measurements in configuration space, fitting the full shape of the two-point correlation function multipoles rather than projected clustering.
• Joint "Same-Sky" Analysis: It is the first to consider the full set of three two-point correlation functions for multiple weak lensing surveys (KiDS, DES, HSC) combined with DESI clustering in a unified pipeline.
• Hybrid Modeling Approach: The study employs distinct, traditional modeling approaches for each probe (perturbative EFT for clustering, halo models for lensing) rather than forcing a single uniform model, allowing access to the full range of scales traditionally used in flagship analyses for each specific observable.
• Validation: The pipeline is validated using Abacus lightcone mocks, demonstrating the ability to recover fiducial cosmology parameters, though noting specific biases in amplitude parameters due to projection effects.

Results

• Cosmological Constraints: The joint analysis yields constraints on the matter density ($\Omega_m \approx 0.30$) and dark energy density ($\Omega_{DE} \approx 0.34$) that are consistent with DESI's Fourier-space full-shape analysis and Planck CMB constraints.
• Amplitude Parameters: The addition of weak lensing information improves the precision of the power spectrum amplitude parameters compared to clustering-only fits:
  • $\ln(10^{10}A_s)$ improves by 15%.
  • $\sigma_{12}$ improves by 36%.
  • Linear bias ($b_1$) measurements improve by 15–20%.
• $S_8$ Tension: The measured weak lensing amplitude $S_8$ values are:
  • $S_8^{\text{DESI}\times\text{HSC}} = 0.787 \pm 0.020$
  • $S_8^{\text{DESI}\times\text{DES}} = 0.791 \pm 0.016$
  • $S_8^{\text{DESI}\times\text{KiDS}} = 0.771 \pm 0.017$
    These values are $1.9\sigma - 2.9\sigma$ below the $S_8$ value preferred by Planck, consistent with tensions found in other weak lensing surveys.
• Consistency: The results show excellent consistency across the different weak lensing surveys and are consistent with the companion paper (Porredon et al. 2025) which uses projected clustering, as well as with the DESI Collaboration's fiducial Fourier-space analysis.
• Projection Effects: Mock analyses reveal that amplitude parameters ($\sigma_{12}$ and $\ln(10^{10}A_s)$) can be biased low by $\sim 1.5-1.8\sigma$ in combined fits due to projection effects in the multi-dimensional parameter space, even within $\Lambda$CDM. The authors note that the BGS tracer specifically shows larger deviations in mock fits, potentially due to the Halo Occupation Distribution (HOD) model used.

Significance and Claims
The paper claims to pave the way for future "same-sky" cross-correlation analyses between upcoming DESI data releases and overlapping shear datasets. It serves as an important consistency test for current observations, demonstrating that joint galaxy clustering and weak lensing fits in configuration space provide precise and consistent cosmological constraints. The authors emphasize that while they observe some indications of projection effects and biases in amplitude parameters (particularly in mocks), the overall framework is robust. They conclude that weak lensing is a promising probe for mitigating projection effects in spectroscopic surveys by breaking degeneracies with galaxy bias. The work is presented as a benchmark analysis for the constraining power of joint probes, limiting its scope to $\Lambda$CDM fits to establish a baseline before exploring dark energy extensions or more complex systematics in future work (e.g., DESI-DR2).