Towards an application of fourth-order shear statistics

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 ap n ⟩, to the shear n PCF 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 ap 4 ⟩ 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 ap 2 ⟩+⟨ M ap 3 ⟩ joint analysis for a DES-Y3-like setup, using non-tomographic equal-scale aperture statistics.