Primordial Non-Gaussianity and the Statistics of Weak Lensing and other Projected Density Fields

TL;DR

This paper demonstrates that projection effects significantly suppress the sensitivity of weak lensing power spectra to primordial non-Gaussianity, highlighting the limited impact of non-Gaussianity on projected density field statistics.

Contribution

The study quantitatively evaluates the influence of primordial non-Gaussianity on weak lensing observables and shows projection effects strongly diminish this sensitivity, a result applicable to all projected density fields.

Findings

Projection effects suppress non-Gaussianity signals in weak lensing spectra.

Projected bispectra are influenced by smaller scales than power spectra.

Clustering of biased tracers is more sensitive to non-Gaussianity than projected observables.

Abstract

Estimators for weak lensing observables such as shear and convergence generally have non-linear corrections, which, in principle, make weak lensing power spectra sensitive to primordial non-Gaussianity. In this paper, we quantitatively evaluate these contributions for weak lensing auto- and cross-correlation power spectra, and show that they are strongly suppressed by projection effects. This is a consequence of the central limit theorem, which suppresses departures from Gaussianity when the projection reaches over several correlation lengths of the density field, L_P~55 [Mpc/h]. Furthermore, the typical scales that contribute to projected bispectra are generally smaller than those that contribute to projected power spectra. Both of these effects are not specific to lensing, and thus affect the statistics of non-linear tracers (e.g., peaks) of any projected density field. Thus, the clustering of biased tracers of the three-dimensional density field is generically more sensitive to non-Gaussianity than observables constructed from projected density fields.