Evolution of the cluster abundance in non-Gaussian models

We carry out N -body simulations of several non-Gaussian structure formation models, including Peebles' isocurvature cold dark matter model, cosmic string models, and a model with primordial voids. We compare the evolution of the cluster mass function in these simulations with that predicted by a modified version of the Press–Schechter formalism. We find that the Press–Schechter formula can accurately fit the cluster evolution over a wide range of redshifts for all of the models considered, with typical errors in the mass function of less than 25 per cent, considerably smaller than the amount by which predictions for different models may differ. This work demonstrates that the Press–Schechter formalism can be used to place strong model-independent constraints on non-Gaussianity in the Universe.