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Estimators for weak lensing observables such as shear and convergencegenerally have non-linear corrections, which, in principle, make weak lensingpower spectra sensitive to primordial non-Gaussianity. In this paper, wequantitatively evaluate these contributions for weak lensing auto- andcross-correlation power spectra, and show that they are strongly suppressed byprojection effects. This is a consequence of the central limit theorem, whichsuppresses departures from Gaussianity when the projection reaches over severalcorrelation lengths of the density field, L_P~55 [Mpc/h]. Furthermore, thetypical scales that contribute to projected bispectra are generally smallerthan those that contribute to projected power spectra. Both of these effectsare not specific to lensing, and thus affect the statistics of non-lineartracers (e.g., peaks) of any projected density field. Thus, the clustering ofbiased tracers of the three-dimensional density field is generically moresensitive to non-Gaussianity than observables constructed from projecteddensity fields.

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