Optimal filtering of three-dimensional, weak-lensing data

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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.