SBi3PCF: cosmology with Dark Energy Survey Year 3 cosmic shear

We present the first cosmic shear data analysis of the integrated 3-point correlation function (i3PCF), a higher-order weak lensing statistic, and the first simulation-based inference (SBI) analysis of a three-point cosmic shear correlation function on survey data. Using SBi3PCF, our previously developed SBI framework for the i3PCF, we jointly constrain the $w$CDM parameter space with the cosmic shear 2-point correlation functions $ξ_\pm$ (2PCFs) and the i3PCFs $ζ_\pm$ from the Dark Energy Survey Year 3 (DES Y3) weak lensing shape catalogue, from which we detect $ζ_\pm$ with a signal-to-noise ratio of 12.8. Our forward model is built on the CosmoGridV1 N-body simulations and includes the survey mask, shape noise, intrinsic alignment, baryonic feedback, photometric redshift uncertainty and shear calibration bias. The analysis was carried out blind, with all choices frozen, and only unblinded once coverage tests, tests of the accuracy of the learned likelihoods, and internal consistency tests had been passed. For the joint $ξ_\pm$ + $ζ_\pm$ analysis we obtain $Ω_m = 0.272^{+0.038}_{-0.033}$, $S_8 = 0.784^{+0.024}_{-0.021}$ and $w_0 = -1.04^{+0.25}_{-0.19}$. Adding $ζ_\pm$ improves the figure of merit in the $Ω_m$-$S_8$-$w_0$ parameter space by a factor of $1.59$ over $ξ_\pm$ alone, as predicted by simulated i3PCF analyses. This gain comes from third-order information on angular scales $\geq 15'$ and aperture radii $\geq 50'$, a regime where baryonic effects are subdominant. The constraints are consistent with the other DES Y3 analyses of the same catalogue and with independent lensing analyses, and differ by at most $2.4σ$ from CMB and BAO data (Planck 2018 + BAO, in $Ω_m$-$S_8$-$w_0$). This shows that $ζ_\pm$ can be analysed on cosmological survey data with a fully simulation-based approach, an important step towards Stage-IV surveys.