Primordial non-Gaussianity and the statistics of weak lensing and other projected density fields

Estimators for weak lensing observables such as shear and convergence generally have nonlinear 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 autocorrelation 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, LP~55 Mpc/h. Furthermore, the typical scales that contribute to projected bispectra are generally smaller than those that contribute to projected power spectra. Neither of these effects is specific to lensing; thus they affect the statistics of nonlinear tracers (e.g., peaks) of any projected density field. Therefore, 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.