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Using cosmological N-body simulations, we study the abundance of local maxima(peaks) and minima (dips) identified in the smoothed distribution of halos anddark matter (DM) on scales of $10-100$s Mpcs. The simulations include Gaussianand local-type $f_{\rm NL}$ non-Gaussian initial conditions. The expressionderived in the literature for the abundance (irrespective of height) of peaksfor Gaussian fields is surprisingly accurate for the evolved halo and DMdensity fields for all initial conditions considered. Furthermore, the heightdistribution is very well fitted by a log-normal on quasi-linear scales. Theabundance as a function of scale depends on the cosmological parameters ($H_0$and background matter densities) through the shape of the power spectrum, butit is insensitive to the clustering amplitude. Further, the abundance in thesmoothed halo distribution is substantially different in the non-Gaussian fromthe Gaussian simulations. The interpretation of this effect is straightforwardin terms of the scale dependence of halo bias in non-Gaussian models. Theabundance of extrema extracted from three-dimensional large galaxy redshiftsurveys could be a competitive probe of the cosmological parameters and initialnon-Gaussianity. It breaks the degeneracy between $f_{\rm NL}$ and theclustering amplitude, making it complementary to counts of galaxy clusters andpeaks in weak-lensing maps.

Abundance of peaks and dips in three-dimensional mass and halo density fields: a test for cosmology