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 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.
