We use the results of N-body simulations on gravitational clustering in CDM models with both Gaussian and non-Gaussian initial conditions to generate projected galaxy catalogues with the same selection criteria as the Shane–Wirtanen counts of galaxies. We apply the technique for measuring 2D topology (the EP characteristic) discussed in the previous papers of this series to compare the statistical nature of the projected galaxy clustering in these simulated data sets with that of the observed galaxy catalogue. We find that all our models produce a topology dominated by a meatball shift when normalized to the known small-scale clustering properties of galaxies. This makes it rather difficult to separate the effects of non-linear gravitation clustering from phase correlations intrinsic to the primordial perturbations. It is, however, possible to discern differences in the topological behaviour of the same models at different stages of gravitational evolution using the projected catalogues.
Models characterized by a positive skewness of the distribution of primordial density perturbations are inconsistent with the Lick data, suggesting problems in reconciling models based on cosmic textures with observations. Gaussian CDM models fit the distribution of cell-counts only if they have a rather high normalization (b ≃ 1), but possess too low a coherence length compared with the Lick counts. This suggests that a CDM model with extra large-scale power would probably fit the available data. On the other hand, a CDM model with negative skewness of the primordial density field (chi-squared model) fits the cell counts well and matches both the shape and amplitude of the EP curve so that such models are also viable. These conclusions are shown to be rather insensitive to the form of the luminosity function used to construct the catalogues.