Probing the dark side of gravitational clustering: weak lensing statistics at large smoothing angle

The weak lensing surveys have the potential to probe directly the clustering statistics of dark matter in the universe. Recent studies have shown that it is possible to predict analytically the whole probability distribution function (pdf) and the bias associated with the collapsed objects in the highly non-linear regime using the hierarchical ansatz. We extend such studies to the quasi-linear regime where the hierarchical ansatz is replaced by the tree-level perturbative calculations to an arbitrary order. It is shown how the generating function techniques can be coupled with the perturbative calculations to compute the complete pdf and the bias in the quasi-linear regime for the weak-lensing convergence field. We study how these quantities depend on the smoothing angle and the source red-shift in different realistic cosmological scenarios. We show that it is possible to define a reduced convergence whose statistics is similar to underlying 3D mass distribution for small smoothing angle but it resembles projected mass distribution for large smoothing angles. We have also compared our perturbative results with log-normal model for pdf and bias and found a good agreement between the two analytical results.