Post-Born corrections to the one-point statistics of (CMB) lensing convergence obtained via large deviation theory

Abstract

Weak lensing of galaxies and 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 onepoint probability distribution (PDF), and we quantify using perturbation theory the corrections coming from post-Born effects, meaning beyond the straight-line and independent lenses 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 percents) 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 into 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 percent for apertures above ∼ 10 arcminutes and typically in the three sigmas region around the mean.

Nuw CDM cosmology from the weak lensing convergence PDF

“…An obvious place to start would be with introducing multiple source redshifts to examine the constraining power of a tomographic analysis, which Liu et al (2018) found produced significant improvements in forecasted constraints on Mν . In Barthelemy et al (2020c), the model for the PDF outlined in this work was applied to the CMB lensing PDF, and the cosmological constraints achievable with such a formalism would be another interesting avenue for exploration, although the non-Gaussian information content is smaller so the PDF might be a relatively weaker measurement in this case. This can easily be re-written in terms of φ cyl (y), which is the form that is implemented in our code.…”

Weak lensing "post-Born" effects are equivalent to pure lens-lens couplings

“…As we have mentioned in section II, while these terms are often called "post-Born" in the literature (e.g. [51,52]), the Weyl potentials Ψ W in the integrands are evaluated along the unperturbed path x, and hence morally speaking we are still applying the Born Approximation.…”

Probability distribution function of the aperture mass field with large deviation theory

“…Although they could affect the higher-order (joint) cumulants we are computing and the convergence PDF, it was showed analytically in Bernardeau et al (1997) and numerically in Petri et al (2017) that the effect on the convergence skewness for the sources and scales of interest is negligible. A prescription to include those effects, mostly relevant in the context of CMB lensing, in the depicted formalism i.e large deviation theory was given in Barthelemy et al (2020b).…”

“…The mental image one could form is that of clustered chunks of matter blurred by these lensing terms. Those corrections were shown to be of little importance in the case of the PDF of the convergence field at scales relevant for perturbation theory (θ ∼ 10 arcmin) and relatively small redshifts relevant for upcoming cosmic shear surveys such as Euclid/LSST (z ∼ 1 − 2) (Barthelemy et al 2020b).…”

“…Extending this result to the aperture mass PDF boils down to computing the post-Born corrections on the dominant non-Gaussian term that makes the PDF, namely its reduced skewness. Using equation ( 41) of Barthelemy et al (2020b) the post-Born correction to the third moment of a filtered convergence field is given by…”