Towards an application of fourth-order shear statistics I. The information content of $⟨M_{\mathrm{ap}}^4⟩$

Abstract

Higher-order shear statistics contain part of the non-Gaussian information of the projected matter field and therefore can provide additional constraints on the cosmological parameters when combined with second-order statistics. 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 forecast the information content of fourth-order aperture statistics. We begin by giving the relation of the $n$-th order aperture statistics, $⟨M_{\mathrm{ap}}^n⟩$, to the shear $n$PCF and to the convergence polyspectra. We then focus on the fourth-order case, where we derive the functional form of their filters and test the behavior of these filters by numerically integrating over the 4PCF of a Gaussian random shear field (GRF). Finally, we perform a Fisher forecast on the constraining power of $\langle M_\mathrm{ap}^4\rangle_\rm{c}$, where we develop a novel method to estimate derivatives from a simulation suite with arbitrarily distributed cosmological sets. 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 $⟨M_{\mathrm{ap}}^2⟩+⟨M_{\mathrm{ap}}^3⟩$ joint analysis for a DES-Y3-like setup, using non-tomographic equal-scale aperture statistics.

arXiv commentSubmitted to A&A. 19 pages, 11 figures

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