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

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 $\xi_{\pm}$ 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 $\xi_\pm$ and $\langle M_{\rm ap}^3\rangle$ measured from DES Y3 data with a $\Lambda$CDM model, we find $S_8=0.780\pm0.015$ and $\Omega_{\rm m}=0.266^{+0.039}_{-0.040}$, yielding 111% of figure-of-merit improvement in $\Omega_m$-$S_8$ plane relative to $\xi_{\pm}$ 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 $2.3\sigma$. 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.