Halos and Voids in a Multifractal Model of Cosmic Structure

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Abstract
On the one hand, the large scale structure of matter is arguably scale invariant, and, on the other hand, halos and voids are recognized as prominent features of that structure. To unify both approaches, we propose to model the dark matter distribution as a set of fractal distributions of halos of different kinds. This model relies on the concept of multifractal as the most general scaling distribution and on a plausible notion of halo as a singular mass concentration in a multifractal. Voids arise as complementary to halos, namely, as formed by regular mass depletions. To provide halos with definite size and masses, we coarse-grain the dark matter distribution, using the length given by the lower cutoff to scaling. This allows us to relate the halo mass function to the multifractal spectrum. Hence, we find that a log-normal model of the mass distribution nicely fits in this picture and, moreover, the Press-Schechter mass function can be recovered as a bifractal limit. To support our model of fractal distributions of halos, we perform a numerical study of the distribution produced in cosmological N-body simulations. In the Virgo L-CDM GIF2 simulation, we indeed find fractal distributions of halos with various dimensions and a halo mass function of bifractal type. However, this mass function is not of Press-Schechter's type, and we interprete it instead as caused by the undersampling of the distribution at the scale of halos, due to discretization.