Cosmic shear data contains a large amount of cosmological information encapsulated in the non-Gaussian features of the weak lensing mass maps. This information can be extracted using non-Gaussian statistics. We compare the constraining power in the $\Omega_{\mathrm{m}} - \sigma_8$ plane of three map-based non-Gaussian statistics with the angular power spectrum, namely; peak/minimum counts and Minkowski functionals. We further analyze the impact of tomography and systematic effects originating from galaxy intrinsic alignments, multiplicative shear bias and photometric redshift systematics. We forecast the performance of the statistics for a stage-3-like weak lensing survey and restrict ourselves to scales $\geq$ 10 arcmin. We find, that in our setup, the considered non-Gaussian statistics provide tighter constraints than the angular power spectrum. The peak counts show the greatest potential, increasing the Figure-of-Merit (FoM) in the $\Omega_{\mathrm{m}} - \sigma_8$ plane by a factor of about 4. A combined analysis using all non-Gaussian statistics in addition to the power spectrum increases the FoM by a factor of 5 and reduces the error on $S_8$ by $\approx$ 25\%. We find that the importance of tomography is diminished when combining non-Gaussian statistics with the angular power spectrum. The non-Gaussian statistics indeed profit less from tomography and the minimum counts and Minkowski functionals add some robustness against galaxy intrinsic alignment in a non-tomographic setting. We further find that a combination of the angular power spectrum and the non-Gaussian statistics allows us to apply conservative scale cuts in the analysis, thus helping to minimize the impact of baryonic and relativistic effects, while conserving the cosmological constraining power. We make the code that was used to conduct this analysis publicly available.

中文翻译：

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大规模弱透镜调查中非高斯统计的宇宙学预测

宇宙剪切数据包含大量宇宙学信息，这些信息封装在弱透镜质量图的非高斯特征中。可以使用非高斯统计提取此信息。我们将三个基于地图的非高斯统计的 $\Omega_{\mathrm{m}} - \sigma_8$ 平面中的约束功率与角功率谱进行比较，即；峰值/最小计数和闵可夫斯基泛函。我们进一步分析了层析成像和系统效应的影响，这些效应源自星系内在排列、倍增剪切偏差和光度红移系统学。我们预测了类似第 3 阶段的弱透镜调查的统计性能，并将我们自己限制在 $\geq$ 10 arcmin 的尺度上。我们发现，在我们的设置中，所考虑的非高斯统计提供了比角功率谱更严格的约束。峰值计数显示出最大的潜力，将 $\Omega_{\mathrm{m}} - \sigma_8$ 平面中的品质因数 (FoM) 增加了大约 4 倍。使用所有非高斯的组合分析除了功率谱之外的统计数据使 FoM 增加了 5 倍，并将 $S_8$ 上的误差减少了 $\approx$ 25\%。我们发现将非高斯统计与角功率谱相结合时，断层扫描的重要性降低了。非高斯统计确实从断层扫描中获益较少，并且最小计数和 Minkowski 泛函在非断层扫描设置中增加了对星系内在对齐的一些鲁棒性。我们进一步发现，角功率谱和非高斯统计的结合使我们能够在分析中应用保守的尺度削减，从而有助于最大限度地减少重子和相对论效应的影响，同时保持宇宙学的约束力。我们公开了用于进行此分析的代码。