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We present a simulated cosmology analysis using the second and third momentsof the weak lensing mass (convergence) maps. The analysis is geared towards thethird year (Y3) data from the Dark Energy Survey (DES), but the methodology canbe applied to other weak lensing data sets. The second moment, or variances, ofthe convergence as a function of smoothing scale contains information similarto standard shear 2-point statistics. The third moment, or the skewness,contains additional non-Gaussian information. We present the formalism forobtaining the convergence maps from the measured shear and for obtaining thesecond and third moments of these maps given partial sky coverage. We estimatethe covariance matrix from a large suite of numerical simulations. We test ourpipeline through a simulated likelihood analyses varying 5 cosmologicalparameters and 10 nuisance parameters. Our forecast shows that the combinationof second and third moments provides a 1.5 percent constraint on $S_8 \equiv\sigma_8 (\Omega_{\rm m}/0.3)^{0.5}$ for DES Y3 data. This is 20 percent betterthan an analysis using a simulated DES Y3 shear 2-point statistics, owing tothe non-Gaussian information captured by the inclusion of higher-orderstatistics. The methodology developed here can be applied to current and futureweak lensing datasets to make use of information from non-Gaussianity in thecosmic density field and to improve constraints on cosmological parameters.

Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps -- validation on simulations