Halos and voids in a multifractal model of the dark matter distribution

The matter distribution is arguably scale invariant in a range of scales. On the other hand, halos and voids are recognized as prominent features of that structure. We review evidence of scale invariance in recent observations of the galaxy distribution, in particular, the Sloan Digital Sky Survey and observations of the Local Volume. This evidence shows that a simple fractal model is not sufficient. Therefore, we propose a multifractal model of the dark matter distribution realized on fractal halo populations, in which voids appear naturally. This multifractal model is supported by a numerical study of N‐body simulations of cold dark matter evolution. Interestingly, the halo mass function is of Press‐Schechter type, namely, a power‐law (with a large‐mass cutoff), but with a fixed exponent that is not related with the initial power spectrum.