Towards an application of fourth-order shear statistics

I. The information content of ⟨M_ap⁴⟩

¹ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
² University of Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
³ Astronomy Centre, Department of Physics and Astronomy, University of Sussex, Brighton BN1 9RH, UK

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 8 September 2025
Accepted: 16 December 2025

Abstract

Context. Higher-order shear statistics contain part of the non-Gaussian information of the projected matter field and can therefore provide additional constraints on the cosmological parameters when combined with second-order statistics.

Aims. We aim to provide the theoretical framework for studying shear four-point correlation functions (4PCF) using fourth-order aperture statistics and develop a numerical integration pipeline to compute them. Finally, we aim to forecast the information content of fourth-order aperture statistics.

Methods. We began by giving the relation of the n-th order aperture statistics, ⟨M_apⁿ⟩, to the shear nPCF and to the convergence polyspectra. We then focused on the fourth-order case, where we derived the functional form of their filters and tested the behavior of these filters by numerically integrating over the 4PCF of a Gaussian random shear field (GRF). Finally, we performed a Fisher forecast on the constraining power of ⟨M_ap⁴⟩_c, where we developed a novel method to estimate derivatives from a simulation suite with arbitrarily distributed cosmological sets.

Results. By analyzing and mitigating numerical effects within the integration pipeline, we achieve a two-percent-level precision on the fourth-order aperture statistics for a GRF, which remains well below the noise budget of Stage IV surveys. We report a minimal improvement in the constraining power of the aperture statistics when including fourth-order statistics to a ⟨M_ap²⟩+⟨M_ap³⟩ joint analysis for a DES-Y3-like setup, using non-tomographic equal-scale aperture statistics.