Abundance of peaks and dips in 3D mass and halo density fields: a test for cosmology

Using cosmological N-body simulations, we study the abundance of local maxima (peaks) and minima (dips) identified in the smoothed distribution of haloes and dark matter (DM) on scales of 10-100 s Mpcs. The simulations include Gaussian and local-type f_NL non-Gaussian initial conditions. The expression derived in the literature for the abundance (irrespective of height) of peaks for Gaussian fields is surprisingly accurate for the evolved halo and DM density fields for all initial conditions considered. Furthermore, the height distribution is very well fitted by a lognormal on quasi-linear scales. The abundance as a function of scale depends on the cosmological parameters (H₀ and background matter densities) through the shape of the power spectrum, but it is insensitive to the clustering amplitude. Further, the abundance in the smoothed halo distribution is substantially different in the non-Gaussian from the Gaussian simulations. The interpretation of this effect is straightforward in terms of the scale dependence of halo bias in non-Gaussian models. The abundance of extrema extracted from 3D large galaxy redshift surveys could be a competitive probe of the cosmological parameters and initial non-Gaussianity. It breaks the degeneracy between f_NL and the clustering amplitude, making it complementary to counts of galaxy clusters and peaks in weak-lensing maps.