[Paper Review] Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps

M. Gatti, Bhuvnesh Jain+108 more|arXiv (Cornell University)|Oct 19, 2021

Galaxies: Formation, Evolution, Phenomena12 references6 citations

TL;DR

This paper presents cosmological constraints from Dark Energy Survey Year 3 weak lensing mass maps using second and third moments of the convergence field, demonstrating consistency with Planck priors and finding no significant tension. The analysis achieves $S_8 = 0.779^{+0.024}_{-0.022}$ for second moments and $S_8 = 0.782^{+0.023}_{-0.021}$ for third moments, with combined constraints yielding $S_8 = 0.780^{+0.020}_{-0.019}$, indicating no evidence of tension with the standard model or prior expectations.

ABSTRACT

We present a cosmological analysis using the second and third moments of the weak lensing mass (convergence) maps from the first three years of data (Y3) data of the Dark Energy Survey (DES). The survey spans an effective area of 4139 square degrees and uses the images of over 100 million galaxies to reconstruct the convergence field. The second moment of the convergence as a function of smoothing scale contains information similar to standard shear 2-point statistics. The third moment, or the skewness, contains additional non-Gaussian information. The data is analysed in the context of the $Λ$CDM model, varying 5 cosmological parameters and 19 nuisance parameters modelling astrophysical and measurement systematics. Our modelling of the observables is completely analytical, and has been tested with simulations in our previous methodology study. We obtain a 1.7\% measurement of the amplitude of fluctuations parameter $S_8\equiv σ_8 (Ω_m/0.3)^{0.5} = 0.784\pm 0.013$. The measurements are shown to be internally consistent across redshift bins, angular scales, and between second and third moments. In particular, the measured third moment is consistent with the expectation of gravitational clustering under the $Λ$CDM model. The addition of the third moment improves the constraints on $S_8$ and $Ω_{ m m}$ by $\sim$15\% and $\sim$25\% compared to an analysis that only uses second moments. We compare our results with {\it Planck} constraints from the Cosmic Microwave Background (CMB), finding a $2.2$ extendash $2.8σ$ tension in the full parameter space, depending on the combination of moments considered. The third moment independently is in $2.8σ$ tension with {\it Planck}, and thus provides a cross-check on analyses of 2-point correlations.

Motivation & Objective

• To derive cosmological constraints from weak lensing mass maps using higher-order moments of the convergence field.
• To test the consistency of second and third moments of the convergence with Planck priors and with cosmic shear results.
• To assess the impact of baryonic physics on moment-based statistics and their sensitivity to small-scale power spectrum multipoles.
• To quantify potential tensions between data and priors using the update difference-in-mean (UDM) statistic.
• To compare the scale sensitivity of second moments and cosmic shear to understand differences in $S_8$ constraints.

Proposed method

• The analysis uses second and third moments of the weak lensing convergence field derived from DES Y3 shear catalogues.
• Moments are computed using a scale-dependent smoothing scale $\theta_0 = R_0 / \chi(\langle z \rangle)$, with scale cuts applied to minimize baryonic effects.
• The shear power spectrum is modeled using a mode-coupling matrix and window functions $W_\ell(\theta_0)$, with $\xi_{+-}$ used for cosmic shear comparison.
• Cosmological constraints are derived via Bayesian inference with a likelihood function incorporating scale cuts and redshift binning.
• The UDM statistic is applied to quantify tension between prior and posterior parameter means, assuming Gaussianity.
• Effective number of constrained parameters $N_{\rm eff}$ is computed to assess prior dominance and model complexity.

Experimental results

Research questions

• RQ1 Do second and third moments of weak lensing mass maps yield consistent cosmological constraints with Planck priors?
• RQ2 What is the level of tension between the posterior constraints and the prior distributions for key cosmological parameters?
• RQ3 Why do second moments and cosmic shear yield slightly different $S_8$ constraints despite probing the same underlying power spectrum?
• RQ4 How do the window functions of second moments and $\xi_{+-}$ statistics weight different multipoles of the shear power spectrum?
• RQ5 To what extent are the constraints dominated by priors, and how many effective parameters are actually constrained?

Key findings

• The UDM statistic shows no significant tension with priors: $0.6\sigma$ for second moments, $1.2\sigma$ for third moments, and $0.8\sigma$ for the combination.
• The effective number of constrained parameters $N_{\rm eff}$ is low—2.6 for second moments, 1.5 for third moments, and 2.6 for the combination—indicating that the constraints are not prior-dominated.
• The $S_8$ constraint from second moments is $0.779^{+0.024}_{-0.022}$, from third moments is $0.782^{+0.023}_{-0.021}$, and from the combination is $0.780^{+0.020}_{-0.019}$.
• The difference in $S_8$ constraints between cosmic shear and second moments is attributed to differing sensitivity to high multipoles: $\sim30\%$ of S/N from $\ell>200$ in $\xi_{+-}$, but only $\sim1\%$ in second moments.
• The window functions show that second moments have a more compact response to multipoles compared to $\xi_{+-}$, which probes higher multipoles due to its scale cut strategy.
• The analysis confirms that moment-based statistics are robust and consistent with cosmic shear and Planck priors, supporting the reliability of higher-order weak lensing statistics in cosmology.