Euclid Preparation. XXVIII. Forecasts for ten different higher-order weak lensing statistics

TL;DR

This paper evaluates ten higher-order weak lensing statistics using Euclid-like simulations, demonstrating they outperform traditional two-point methods in constraining cosmological parameters, and highlights their combined potential for future analyses.

Contribution

It provides a comprehensive comparison of ten different higher-order weak lensing statistics and demonstrates their superior constraining power over two-point statistics for Euclid-like data.

Findings

Each HOS outperforms two-point statistics by a factor of about two in forecast precision.

Combining all HOS yields a 4.5 times improvement in constraining cosmological parameters.

Forecasts show significant potential for HOS in Euclid cosmic shear analyses.

Abstract

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set of $Euclid$-like mocks, derived from N-body simulations. In this first paper of the HOWLS series, we computed the nontomographic ($\Omega_{\rm m}$, $\sigma_8$) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a $4.5$ times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses with $Euclid$. The data used in this analysis are publicly released with the paper.