The cumulant generating function as a novel observable to cumulate weak lensing information
The cumulant generating function as a novel observable to cumulate weak lensing information
复制标题
DOI：
10.21105/astro.2212.10351
复制
发表时间：
2022-12
影响因子：
--
通讯作者：
A. Boyle;A. Barthelemy;S. Codis;C. Uhlemann;O. Friedrich
中科院分区：
文献类型：
--
作者：
A. Boyle;A. Barthelemy;S. Codis;C. Uhlemann;O. Friedrich
宇宙场的关键非高斯特性可以通过单点统计来捕获，为功率谱或相关函数的两点统计测量提供补充。大偏差理论可以根据第一原理稳健地预测轻度非线性尺度上的宇宙密度场的单点统计。它为此类场的累积生成函数 (CGF) 提供直接预测，并通过拉普拉斯逆变换提取更常用的概率密度函数 (PDF) 的预测。对于多个字段的联合单点统计，拉普拉斯逆变换很快变得更加麻烦且计算成本昂贵。在这项工作中，我们首次证明弱透镜 CGF 本身可以用作可观测值，捕获与 PDF 等量的宇宙学信息。虽然我们使用弱透镜收敛场作为一个简单且有启发性的例子，但这项工作的目的是作为在归零框架背景下基于大偏差理论的宇宙学分析的第一步，该框架排除了小尺度的贡献，以促进高度准确的理论预测。在这种情况下，该方法应该普遍适用于弱透镜和星系团的多尺度层析成像分析。
Key non-Gaussian properties of cosmological fields can be captured by their one-point statistics, providing a complement to two-point statistical measurements from power spectra or correlation functions. Large deviation theory can robustly predict the one-point statistics of cosmological density fields on mildly non-linear scales from first principles. It provides a direct prediction for the cumulant generating function (CGF) of such fields, from which a prediction for the more commonly used probability density function (PDF) is extracted through an inverse Laplace transform. For joint one-point statistics of multiple fields, the inverse Laplace transform rapidly becomes more cumbersome and computationally expensive. In this work, we demonstrate for the first time that the weak lensing CGF itself can be used as an observable that captures an equal amount of cosmological information to the PDF. While we use the weak-lensing convergence field as a simplistic and instructive example, this work is intended as a first step towards a cosmological analysis based on large deviation theory in the context of a nulling framework, which excludes contributions from small scales to facilitate highly accurate theoretical predictions. In this context, the method should be generally applicable for a multi-scale tomographic analysis of weak lensing and galaxy clustering.