Optimal filtering of three-dimensional, weak-lensing data

大尺度结构的弱引力透镜效应已经成为约束宇宙学信息的一种很有前途和潜在的强大工具，特别是物质密度参数、暗物质涨落的幅度、描述暗能量密度的参数和暗物质结构的功率谱。传统上，角相关函数等两点统计量是从调查数据中得出的，然后与理论预测进行比较。目前还不清楚这种方法是否最大化了可以从引力透镜数据中提取的信息。我们建议研究三维引力透镜的宇宙学信息量。我们打算遵循的方法是通过宇宙学参数的信噪比相对于滤光片形状的泛函导数来搜索应用于透镜可观测的球谐、径向傅立叶模的线性滤光片。此外，我们还希望通过拉格朗日乘子研究施加在滤波器上的各种边界条件的影响，并量化模型偏差。

Weak gravitational lensing by large-scale structures has turned into a promising and potentially powerful tool to constrain cosmological information, in particular the matter-density parameter, the amplitude of dark-matter fluctuations, parameters describing the dark energy density and the power spectrum of the dark-matter structures. Conventionally, two-point statistics such as angular correlation functions are derived from survey data which are then compared to theoretical predictions. It is by no means clear that this approach maximises the information that can be extracted from gravitational-lensing data. We propose here to study the cosmological information content of three-dimensional gravitational lensing. The approach we intend to follow searches for a linear filter to be applied to spherical-harmonic, radial Fourier modes of lensing observables by means of a functional derivative of the signal-to-noise ratio of cosmological parameters with respect to the filter shape. In addition, we want to study effects of various boundary conditions imposed on the filter by means of Lagrange multipliers and to quantify model biases.