Non-Gaussian statistics in galaxy weak lensing: compressed three-point correlations and cosmological forecasts

Abstract: Building on previous developments of a harmonic decomposition framework for computing the three-point correlation function (3PCF) of projected scalar fields over the sky, this work investigates how much cosmological information is contained in these higher-order statistics. We perform a forecast to determine the number of harmonic multipoles required to capture the full information content of the 3PCF in the context of galaxy weak lensing, finding that only the first few multipoles are sufficient to capture the additional cosmological information provided by the 3PCF. This study addresses a critical practical question: to what extent can the high-dimensional 3PCF signal be compressed without significant loss of cosmological information? Since the different multipoles contain highly redundant information, we apply a principal component analysis (PCA) which further reduces its dimensionality and preserving information. We also account for non-linear parameter degeneracies using the DALI method, an extension of Fisher forecasting that includes higher-order likelihood information. Under optimistic settings, we find that the 3PCF considerably improves the constraining power of the 2PCF for $\Omega_m$, reaching a 20% improvement. Other parameters also benefit, mainly due to their degeneracy with the matter abundance. For example, with our chosen scale cuts for galaxy sources at $z = 0.5$, we find that $\sigma_8$ is more tightly constrained, whereas $S_8$ and $w_0$ are not. Finally, we construct analytical Gaussian covariance matrices that can serve as a first step toward developing semi-analytical, semi-empirical alternatives to sample covariances.