Maximally hard universe and mass spectrum of primordial black holes

The mass spectrum of primordial black holes formed in a universe with maximally hard equation of state of matter is calculated with allowance for the influence of small-scale inhomogeneities on the dynamical development of large scale perturbations. The basic object of investigation is the field of initial deviations of the density, which are characterized by a normal distribution and standard deviation approximated by a power function of the reciprocal of the mass. It is shown that for a flat spectrum of initial perturbations of the metric the mass distribution function of the primordial black holes has a clear maximum. The influence of accreting matter on the mass spectrum of the resulting objects is estimated. It is noted that dissipation of the small-scale perturbations does not change the qualitative or quantitative conclusions of the paper