Dark Energy Survey Year 3 Results: Cosmological constraints from second and third-order shear statistics

TL;DR

This work demonstrates the power of higher-order weak-lensing statistics by jointly analyzing DES Year 3 two-point and third-order statistics, specifically using $\langle\mathcal{M}_{\rm ap}^3\rangle$ as a compressed proxy for the shear 3PCF. Leveraging a CosmoGrid covariance and a neural-network emulator for the MAP3 signal, the authors achieve substantial improvements in cosmological constraints under both $Λ$CDM and $w$CDM, with a notable reduction in the $Ω_m$–$S_8$ degeneracy. The results remain in tension with Planck by about $2.3\sigma$, highlighting potential systematics or new physics, while the analysis shows robustness to baryonic effects and enables self-calibration of redshift uncertainties. Overall, the paper underscores the practical utility of higher-order lensing statistics for current surveys and sets the stage for their use in upcoming data sets.

Abstract

We present a cosmological analysis of the third-order aperture mass statistic using Dark Energy Survey Year 3 (DES Y3) data. We perform a complete tomographic measurement of the three-point correlation function of the Y3 weak lensing shape catalog with the four fiducial source redshift bins. Building upon our companion methodology paper, we apply a pipeline that combines the two-point function $ξ_{\pm}$ with the mass aperture skewness statistic $\langle M_{\rm ap}^3\rangle$, which is an efficient compression of the full shear three-point function. We use a suite of simulated shear maps to obtain a joint covariance matrix. By jointly analyzing $ξ_\pm$ and $\langle M_{\rm ap}^3\rangle$ measured from DES Y3 data with a $Λ$CDM model, we find $S_8=0.780\pm0.015$ and $Ω_{\rm m}=0.266^{+0.039}_{-0.040}$, yielding 111% of figure-of-merit improvement in $Ω_m$-$S_8$ plane relative to $ξ_{\pm}$ alone, consistent with expectations from simulated likelihood analyses. With a $w$CDM model, we find $S_8=0.749^{+0.027}_{-0.026}$ and $w_0=-1.39\pm 0.31$, which gives an improvement of $22\%$ on the joint $S_8$-$w_0$ constraint. Our results are consistent with $w_0=-1$. Our new constraints are compared to CMB data from the Planck satellite, and we find that with the inclusion of $\langle M_{\rm ap}^3\rangle$ the existing tension between the data sets is at the level of $2.3σ$. We show that the third-order statistic enables us to self-calibrate the mean photometric redshift uncertainty parameter of the highest redshift bin with little degradation in the figure of merit. Our results demonstrate the constraining power of higher-order lensing statistics and establish $\langle M_{\rm ap}^3\rangle$ as a practical observable for joint analyses in current and future surveys.

Figures (15)

• Figure 1: The third moment of the mass aperture statistic Y3 data vector. The panels show the aperture mass statistic as a function of filter radii $\theta$ for different redshift-bin combinations $(i,j,k)$ indicated on the upper right corner of each panel. The error bars are estimated from our simulation-based covariance. The theoretical prediction at our joint best fit cosmology, as described in Section \ref{['sec:result']}, is shown by the continuous green line, which indicates the prediction with our 3PCF scale cut at 8 arcmin. The green dotted line shows the theoretical prediction with no scale cuts on the 3PCF. This is not expected to match the data (which does have scale cuts applied) but it shows that only a modest amount of the signal is lost by the scale cuts (difference between continuous and dotted lines).
• Figure 2: Mass aperture statistic Y3 data, as in Figure \ref{['fig:meas']}, but with aperture filters at small scales. The green continuous line shows the theoretical prediction at best fit cosmology with our 3PCF scale cut at 8 arcmin. The dark-matter-only theoretical prediction is an adequate fit to the small scale data, with no systematic departure present across most of the redshift bin combinations.
• Figure 3: Measurement of the isosceles three-point correlation function on DES Y3 data. We performed the measurement without redshift tomography, and present the results for scales below 18 arcmin (right panel) and between 18 and 80 arcmin (left panel). Both panels show the characteristic shape and zero crossing of the shear 3PCF. The error bars are estimated from the jackknife covariance. To provide a comparison with theoretical expectations, the dotted curve shows our simulation measurements, rescaled to account for the difference between cosmological parameters. The $1\sigma$ intervals around our $\langle\mathcal{M}_{\rm ap}^3\rangle$ best fit cosmology is shown by the gray shaded region.
• Figure 4: Parameter constraints from DES-Y3 data from separate and joint analyses of $\xi_{\pm}$ and $\langle\mathcal{M}_{\rm ap}^3\rangle$ within $\Lambda$CDM. The cosmological parameters shift less then 1$\sigma$ when moving from $\xi_{\pm}$ to a joint 2PCF and 3PCF analysis. We find an improvement of 111% in the $\Omega_m$-$S_8$ figure-of-merit. This improvement is driven in part by the difference between the degeneracy directions for $\xi_{\pm}$ alone and $\langle\mathcal{M}_{\rm ap}^3\rangle$ alone. Here $A_1$ is the intrinsic alignment amplitude (see Eq. \ref{['eq:f-IA']})
• Figure 5: The $\chi^2$ distribution estimated from noisy mock simulations for the DES joint $\xi_{\pm}$+$\langle\mathcal{M}_{\rm ap}^3\rangle$ analysis. The value from the analysis with Y3 data is represented by the dashed red line. Our data $\chi^2$ is consistent with its expected distribution, with a probability of 14% of a random realization having higher $\chi^2$. Our distribution average is 73.3, which is sufficiently close to our effective number of degrees of freedom ($N=89$).