Effects of Weak Lensing on the Topology of Cosmic Microwave Background Maps

We investigate the non-Gaussian signatures in cosmic microwave background maps induced by the intervening large-scale structure through weak lensing. In order to measure the deviation from the Gaussian behavior of the intrinsic temperature anisotropies, we use a family of three morphological descriptors, the so-called Minkowski functionals. We show analytically how these quantities depend on the temperature threshold and compare the results to numerical experiments including the instrumental effects of Planck. Minkowski functionals can directly measure the statistical properties of the displacement field and hence provide useful constraints on large-scale structure formation in the past.