The Space Density of Galaxy Peaks and the Linear Matter Power Spectrum

One way of recovering information about the initial conditions of the Universe is by measuring features of the cosmological density field which are preserved during gravitational evolution and galaxy formation. In this paper we study the total number density of peaks in a (galaxy) point distribution smoothed with a filter, evaluating its usefulness as a means of inferring the shape of the initial (matter) power spectrum. We find that in numerical simulations which start from Gaussian initial conditions, the peak density follows well that predicted by the theory of Gaussian density fields, even on scales where the clustering is mildly non-linear. For smaller filter scales, $r \simlt 4-6 \hmpc$, we see evidence of merging as the peak density decreases with time. On larger scales, the peak density is independent of time. One might also expect it to be fairly robust with respect to variations in biasing, i.e. the way galaxies trace mass fluctuations. We find that this is the case when we apply various biasing prescriptions to the matter distribution in simulations. If the initial conditions are Gaussian, it is possible to use the peak density measured from the evolved field to reconstruct the shape of the initial power spectrum. We describe a stable method for doing this and apply it to several biased and unbiased non-linear simulations. We are able to recover the slope of the linear matter power spectrum on scales $k \simlt 0.4 \hmpc^{-1}$. The reconstruction has the advantage of being independent of the cosmological parameters ($\Omega$, $\Lambda$, $H_0$) and of the clustering normalisation ($\sigma_8$). The peak density and reconstructed power spectrum slope therefore promise to be powerful discriminators between popular cosmological scenarios.