The shape of non-Gaussianities

We study the dependence on the configuration in momentum space of the primordial three-point function of density perturbations in several different scenarios: standard slow-roll inflation, curvaton and variable decay models, ghost inflation, models with higher derivative operators and the DBI model of inflation. We define a cosine between the distributions using a measure based on the ability of experiments to distinguish between them. We find that models fall into two broad categories with fairly orthogonal distributions: models where non-Gaussianity is created on crossing the horizon during inflation and models in which the evolution beyond the horizon dominates. In the first case the three-point function is largest for equilateral triangles, while in the second the dominant contribution to the signal comes from the influence of long wavelength modes on small wavelength ones. We show that, because the distributions in these two cases are so different, translating constraints on parameters of one model to those of the other on the basis of the normalization of the three-point function for equilateral triangles can be very misleading.