Post-Born corrections to the one-point statistics of (CMB) lensing convergence obtained via large deviation theory. Issue 3 (9th April 2020) - Barthelemy, Alexandre; Codis, Sandrine; Bernardeau, Francis
ABSTRACT: Weak lensing of galaxies and cosmic microwave background (CMB) photons through the large-scale structure of the Universe is one of the most promising cosmological probes with upcoming experiments dedicated to its measurements such as Euclid /LSST and CMB Stage 4 experiments. With increasingly precise measurements, there is a dire need for accurate theoretical predictions. In this work, we focus on higher order statistics of the weak-lensing convergence field, namely its cumulants such as skewness and kurtosis and its one-point probability distribution function (PDF), and we quantify using perturbation theory the corrections coming from post-Born effects, meaning beyond the straight-line and independent lens approximations. At first order, two such corrections arise: lens–lens couplings and geodesic deviation. Though the corrections are small for low source redshifts (below a few per cent) and therefore for galaxy lensing, they become important at higher redshifts, notably in the context of CMB lensing, where the non-Gaussianities computed from tree-order perturbation theory are found to be of the same order as the signal itself. We include these post-Born corrections on the skewness in a prediction for the one-point convergence PDF obtained with large deviation theory and successfully test these results against numerical simulations. The modelled PDF is indeed shown to perform better than the per cent for apertures above ∼10 arcmin and typically in the 3σ region around the mean.