DESI-DR1 $3 \times 2$-pt analysis: consistent cosmology across weak lensing surveys

This paper, titled "DESI-DR1 3 × 2-PT Analysis: Consistent Cosmology Across Weak Lensing Surveys," presents a joint cosmological analysis combining spectroscopic galaxy clustering from the Dark Energy Spectroscopic Instrument (DESI) with weak gravitational lensing data from three major surveys.

1. The Problem

Modern cosmology faces several "tensions," most notably the disagreement between the local expansion rate and the Cosmic Microwave Background (CMB) predictions, as well as debates regarding the amplitude of matter fluctuations ($S_8$). To resolve these, cosmologists must combine different probes (spectroscopic and photometric) to break parameter degeneracies and mitigate systematic errors.

However, combining datasets from different surveys is technically challenging because each survey has unique systematic errors (e.g., photometric redshift uncertainties, shape measurement biases, and baryonic effects). There is a need for a unified analysis framework that can self-consistently determine both cosmological and astrophysical parameters across multiple, overlapping datasets.

2. Methodology

The authors employ a $3 \times 2$-point (3x2pt) correlation function approach. This involves cross-correlating three distinct statistics:

1. Cosmic Shear ($\xi_{\pm}$): The correlation of galaxy shapes induced by weak lensing.
2. Galaxy Clustering ($w_p$): The correlation of galaxy positions.
3. Galaxy-Galaxy Lensing ($\gamma_t$): The tangential shear of background galaxies around foreground lens galaxies.

Key Technical Components:

• Data Integration: They use DESI-DR1 (spectroscopic) as the "lens" sample to provide high-precision redshifts, which is then cross-correlated with the "source" samples from three weak lensing (WL) surveys: DES-Y3, KiDS-1000, and HSC-Y3.
• Modeling: They assume flat $\Lambda$CDM and $w$CDM models. They model non-linear matter power spectra using HMCODE2020 (including baryonic feedback) and account for Intrinsic Alignments (IA) using the Non-Linear Alignment (NLA) and Tidal Alignment and Tidal Torquing (TATT) models.
• Covariance & Blinding: They developed an analytical covariance matrix that includes cross-covariances between different probes. To prevent confirmation bias, they implemented a data-vector blinding procedure that shifts cosmological parameters during the analysis, only unblinding once robustness tests are passed.
• Scale Cuts: To avoid modeling uncertainties at small scales (where baryonic physics and non-linear bias are complex), they applied rigorous scale cuts validated through "contamination" tests.

3. Key Contributions

• Unified Pipeline: The creation of a single, tailored pipeline that can handle the specific requirements and nuisance parameters of DES, KiDS, and HSC simultaneously.
• Spectroscopic Lensing: By using DESI's spectroscopic redshifts for the lens sample, they significantly improve the signal-to-noise ratio of the galaxy-galaxy lensing measurements compared to purely photometric methods.
• Analytical Framework: They extended the analytical covariance framework to include the projected correlation function ($w_p$), which is more precise for spectroscopic samples than the traditional angular correlation function ($w(\theta)$).

4. Results

The study provides highly consistent constraints on the matter fluctuation parameter $S_8 = \sigma_8(\Omega_m/0.3)^{0.5}$:

• DESI-DR1 $\times$ DES-Y3: $S_8 = 0.786^{+0.022}_{-0.019}$
• DESI-DR1 $\times$ KiDS-1000: $S_8 = 0.760^{+0.020}_{-0.018}$
• DESI-DR1 $\times$ HSC-Y3: $S_8 = 0.771^{+0.026}_{-0.027}$

Major Findings:

• Consistency: The results are mutually consistent across all three weak lensing surveys.
• CMB Comparison: The results are consistent with the Planck CMB datasets, though they sit $1.5–2\sigma$ lower in the $S_8-\Omega_m$ plane (a common feature in weak lensing studies).
• Dark Energy: In the $w$CDM model, the results are consistent with a cosmological constant ($w = -1$).
• Robustness: The analysis proved robust against changes in modeling (e.g., switching from NLA to TATT) and variations in lens redshift bins.

5. Significance

This paper represents a major step toward Stage-IV cosmology. It demonstrates that large-scale spectroscopic surveys (like DESI) can be successfully integrated with wide-field imaging surveys to provide a powerful, self-consistent check on the standard cosmological model. The methodology established here provides the blueprint for future, even more precise analyses using DESI Data Release 2 (DR2) and upcoming missions like Euclid, which will aim to further scrutinize the nature of dark energy and the evolution of the universe.