Towards an application of fourth-order shear statistics I. The information content of $\langle M_\mathrm{ap}^4 \rangle $
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arXiv
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| Format: | Preprint |
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2025
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| author | Silvestre-Rosello, Elena Porth, Lucas Schneider, Peter Linke, Laila Krueger, Jonas Grandis, Sebastian Oel, Jonathan |
| author_facet | Silvestre-Rosello, Elena Porth, Lucas Schneider, Peter Linke, Laila Krueger, Jonas Grandis, Sebastian Oel, Jonathan |
| contents | 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, $\langle M_\mathrm{ap}^n\rangle$, 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 $\langle M_\mathrm{ap}^2\rangle + \langle M_\mathrm{ap}^3\rangle$ joint analysis for a DES-Y3-like setup, using non-tomographic equal-scale aperture statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07973 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards an application of fourth-order shear statistics I. The information content of $\langle M_\mathrm{ap}^4 \rangle $ Silvestre-Rosello, Elena Porth, Lucas Schneider, Peter Linke, Laila Krueger, Jonas Grandis, Sebastian Oel, Jonathan Cosmology and Nongalactic Astrophysics 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, $\langle M_\mathrm{ap}^n\rangle$, 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 $\langle M_\mathrm{ap}^2\rangle + \langle M_\mathrm{ap}^3\rangle$ joint analysis for a DES-Y3-like setup, using non-tomographic equal-scale aperture statistics. |
| title | Towards an application of fourth-order shear statistics I. The information content of $\langle M_\mathrm{ap}^4 \rangle $ |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2509.07973 |