Bayesian weak lensing tomography: Reconstructing the 3D large-scale distribution of matter with a lognormal prior

We present a Bayesian reconstruction algorithm that infers the three-dimensional large-scale matter distribution from the weak gravitational lensing effects measured in the image shapes of galaxies. The algorithm assumes that the prior probability distribution of the matter density is lognormal, in contrast to many existing methods that assume normal (Gaussian) distributed density fields. We compare the reconstruction results for both priors in a suite of increasingly realistic tests on mock data. We find that in cases of high noise levels (i.e. for low source galaxy densities and/or high shape measurement uncertainties), both normal and lognormal priors lead to reconstructions of comparable quality. In the low-noise regime, however, the lognormal model produces significantly better reconstructions than the normal model: The lognormal model 1) enforces non-negative densities, while negative densities are present when a normal prior is employed, 2) better traces the extremal values and the skewness of the true underlying distribution, and 3) yields a higher correlation between the reconstruction and the true density distribution. Hence, the lognormal model is to be preferred over the normal model, in particular since these differences become relevant for data from current and futures surveys.