Dark Energy Survey Year 6 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing

Abstract: We present cosmology results combining galaxy clustering and weak gravitational lensing measured in the full six years (Y6) of observations by the Dark Energy Survey (DES) covering $\sim$5000 deg$^2$. We perform a large-scale structure analysis using three two-point correlation functions (3$\times$2pt): (i) cosmic shear from 140 million source galaxy shapes, (ii) galaxy clustering of 9 million lens galaxy positions, and (iii) galaxy-galaxy lensing from their cross-correlation. We model the data in flat $Λ$CDM and $w$CDM cosmologies. The combined analysis yields $S_8\equiv σ8 (Ω{\rm m}/0.3)^{0.5} = 0.789^{+0.012}_{-0.012}$ and matter density $Ω{\rm m} = 0.333^{+0.023}{-0.028}$ in $Λ$CDM (68\% CL), where $σ8$ is the clustering amplitude. These constraints show a (full-space) parameter difference of 1.8$σ$ from a combination of cosmic microwave background (CMB) primary anisotropy datasets from Planck 2018, ACT-DR6, and SPT-3G DR1. Projected only into $S_8$ the difference is $2.6σ$. In $w$CDM the Y6 3$\times$2pt results yield $S_8 = 0.782^{+0.021}{-0.020}$, $Ω{\rm m} = 0.325^{+0.032}{-0.035}$, and dark energy equation-of-state parameter $w = -1.12^{+0.26}_{-0.20}$. For the first time, we combine all DES dark-energy probes: 3$\times$2pt, SNe Ia, BAO and Clusters. In $Λ$CDM this combination yields a $2.8σ$ parameter difference from the CMB. When combining DES 3$\times$2pt with other low-redshift datasets (DESI DR2 BAO, DES SNe Ia, SPT clusters), we find a 2.3$σ$ parameter difference with CMB. A joint fit of Y6 3$\times$2pt, CMB, and those low-redshift datasets produces the tightest $Λ$CDM constraints to date: $S_8 = 0.806^{+0.006}_{-0.007}$, $Ω{\rm m} = 0.302^{+0.003}{-0.003}$, $h = 0.683^{+0.003}_{-0.002}$, and $\sum m_ν< 0.14$ eV (95\% CL). In $w$CDM, this combination yields $w = -0.981^{+0.021}_{-0.022}$.

• The paper presents a joint 3×2pt analysis combining galaxy clustering and weak lensing to yield tight constraints on key parameters like S8 and Ωm.
• It employs advanced photometric redshift calibration, tomographic binning, and rigorous marginalization techniques to control astrophysical systematics.
• The study improves previous analyses with a doubled figure-of-merit and detailed cross-checks against CMB and other external datasets.

Cosmological Constraints from DES Year 6: Joint Galaxy Clustering and Weak Lensing Analysis

Survey Scope and Data Products

Year 6 of the Dark Energy Survey (DES Y6) delivers a significant cosmological analysis combining galaxy clustering and weak gravitational lensing using six years of data covering approximately 5000 deg² of the southern sky. The survey employed the DECam instrument, resulting in $>76,000$ exposures across five optical bands and generating refined "Gold" object catalogs, high-fidelity lensing shear catalogs, and advanced photometric redshift calibration for over 140 million source galaxies and 9 million lens galaxies. The lens and source samples were carefully separated for optimal tomographic binning, and redshift distributions were calibrated using hybrid methodologies derived from SOM-based photometry and clustering cross-correlations.

Figure 2: The DES Y6 footprint in equatorial coordinates, showing the $\sim$5000 deg$^2$ wide survey area, supernova fields, and relevant overlap with other sky surveys.

Figure 4: Estimated redshift distributions of lens (bottom) and source (top) galaxies in DES Y6, along with the lensing efficiency kernel.

Methodology: The Three Two-point Analysis (3×2pt)

The analysis jointly models three two-point projected correlation functions: galaxy clustering auto-correlation $w(\theta)$, galaxy-galaxy lensing tangential shear $\gamma_t(\theta)$, and cosmic shear correlation functions $\xi_{\pm}(\theta)$. Nuisance and astrophysical systematics are controlled via point-mass marginalization, scale cuts motivated by baryonic feedback uncertainties, flexible photometric redshift parameterization via mode decomposition, analytic marginalization over observational weights, and a TATT (tidal alignment and tidal torquing) model for intrinsic alignments.

Figure 6: Angular auto-correlation functions $w(\theta)$ for lens bins, compared to best-fit $\Lambda$CDM and $w$CDM models with both linear and nonlinear galaxy bias assumptions.

Figure 8: Galaxy-galaxy lensing correlation functions $\gamma_\mathrm{t}(\theta)$ for different source-lens bin pairs, with model residuals and excluded angular scales.

Figure 10: Cosmic shear correlation functions $\xi_+(\theta)$ and $\xi_-(\theta)$ for source bin pairs, illustrating agreement with various bias models and highlighting theoretical scale cuts.

Parameter inference is conducted via the CosmoSIS framework, sampled with the Nautilus nested sampler, and all chains were blinded during analysis up to the final stage to safeguard against confirmation bias and ensure robustness of null and internal consistency tests.

Baseline Cosmological Results

The joint 3×2pt dataset achieves a total signal-to-noise ratio of $S/N = 110$ post-scale cuts and yields cosmological constraints under both flat $\Lambda$CDM and $w$CDM paradigms.

• $\Lambda$CDM constraints (68% CL):
  • $$S_8 \equiv \sigma_8 (\Omega_\mathrm{m}/0.3)^{0.5} = 0.789^{+0.012}_{-0.012}$$
  • $\Omega_\mathrm{m} = 0.333^{+0.023}_{-0.028}$
  • $\sigma_8 = 0.751^{+0.034}_{-0.036}$
• $w$CDM constraints (68% CL):
  • $S_8 = 0.782^{+0.021}_{-0.020}$
  • $\Omega_\mathrm{m} = 0.325^{+0.032}_{-0.035}$
  • $w = -1.12^{+0.26}_{-0.20}$

These constraints represent a $\sim2\times$ increase in figure-of-merit in the $(\Omega_\mathrm{m},\sigma_8)$ plane over the previous DES Y3, primarily due to greater source density, expanded redshift reach, and improved systematics mitigation. In both models, no statistically significant preference for deviation from $w = -1$ is found.

Figure 12: Marginalized constraints in the $(\Omega_{\rm m}, \sigma_8, S_8)$ space for DES Y6 cosmic shear, galaxy-galaxy lensing+clustering, and their 3×2pt combination. Included are the results for nonlinear galaxy bias and CMB constraints for comparison.

Figure 1: A summary of marginalized constraints on $S_8$, $\Omega_\mathrm{m}$, and $\sigma_8$ for DES Y6 (and previous) analyses, CMB, and various data combinations.

Inter-survey and Probe Tension Metrics

The Y6 3×2pt constraints are compared with combined primary CMB datasets from Planck, ACT, and SPT. The results are:

• Full-parameter difference: $1.8\sigma$ between DES Y6 3×2pt and the combined CMB posterior.
• In $S_8$ projection: $2.6\sigma$ difference, with DES favoring a lower $S_8$.

Incorporating additional DES datasets (BAO, type Ia SNe, galaxy clusters), the multi-probe DES constraint further tightens $S_8$ to $0.794^{+0.009}_{-0.012}$ and $\Omega_\mathrm{m}$ to $0.322^{+0.012}_{-0.011}$, with a residual $2.8\sigma$ full-parameter difference from the CMB. No single DES probe dominates the tension with the CMB, and consistency tests between probes yield high internal concordance ($<2\sigma$ across all main DES sub-combinations).

Figure 3: Combined parameter constraints from all DES probes (3×2pt, clusters, SNe Ia, BAO) in $\Lambda$CDM (left) and $w$CDM (right), compared with CMB contours.

External Cross-Checks and Extension to Other Probes

DES Y6 is integrated with contemporary BAO measurements (DESI, DES BAO excl. overlap), external cluster constraints (SPT), and late-universe SNIa to produce the tightest low-$z$ constraint:

• $S_8=0.799^{+0.009}_{-0.010}$, $\Omega_\mathrm{m}=0.308^{+0.006}_{-0.006}$.

When further combined with the CMB, the constraints reach $S_8 = 0.806^{+0.006}_{-0.007}$ and $\Omega_\mathrm{m} = 0.302^{+0.003}_{-0.003}$. The upper bound on the sum of neutrino masses tightens to $<0.14\,\mathrm{eV}$ (95% CL), although the marginalized posterior is prior-dominated, confirming the degeneracy with $\Omega_{\rm m}$ persists.

Figure 5: Combined $\Lambda$CDM (left) and $w$CDM (right) constraints for DES Y6 3×2pt with external low-redshift and CMB probes.

Figure 7: Constraints on the sum of neutrino masses from DES Y6 3×2pt and combinations with external probes, with all chains capped at $[0.06, 0.6]$ eV for $\sum m_\nu$.

Figure 9: Joint marginalized constraints on $h$ and $\Omega_{\rm m}$ from various probe combinations, including DES 3×2pt, BAO, and CMB.

An independent determination of the Hubble parameter $h$ based purely on DES+BBN is $h = 0.715^{+0.021}_{-0.019}$, consistent with local TRGB-based and time-delay strong lensing measurements, and distinguishable from the lower values inferred from CMB-only analyses.

Robustness and Cross-Survey Comparison

Multiple robustness checks are performed, including varying nuisance models (IA, galaxy bias, magnification, baryonic feedback), redshift parameterizations, and data vector splits (e.g., excluding problematic tomographic bins, high-$z$/low-$z$ splits). The cosmological posteriors are found to be insensitive to all such decisions within $<0.5\sigma$ shifts for $S_8$ and negligible degradation in constraining power.

Comparisons with KiDS-Legacy and HSC Y3 3×2pt/cosmic shear analyses are performed in the $S_8-\Omega_\mathrm{m}$ plane, all yielding mutually consistent marginalized posteriors, although lensing experiments continue to find $S_8$ slightly lower than CMB values (but never exceeding $3\sigma$ discrepancy).

Implications, Theoretical Consistency, and Future Outlook

The DES Y6 results reinforce the internal consistency of the $\Lambda$CDM model, with no evidence for deviation in $w$ at the several percent level. Parameter shifts with respect to the CMB—particularly in $S_8$—hover around the $2-3\sigma$ regime, persisting into the most tightly constrained, data-rich multi-probe combinations. The origin of these parameter differences remains a salient target of further investigation, especially with respect to systematic modeling in lensing calibration and astrophysical modeling (e.g., baryonic feedback, redshift distributions).

These results set a new standard for parameter estimation using photometric imaging surveys, both in terms of internal systematic control and the statistical power achieved. They also define a methodological template for LSST, Euclid, and Roman, especially with respect to photometric redshift calibration, internal cross-checks, and probe integration.

Conclusion

The analysis of DES Y6 provides precise constraints on cosmic structure growth, matter density, and the dark energy equation-of-state from photometric data, with an unprecedented level of self-consistency and multiple avenues for internal and external validation. While the results remain in mild but notable tension with CMB-inferred parameters, particularly in $S_8$, these differences do not yet reach a level meriting claims of new physics given current methodological and systematic uncertainties. The limitations and systematic controls developed herein form a baseline for cosmological analysis pipelines in next-generation weak lensing surveys.