Description
We have investigated primordial black holes formation within a model of the early Universe dominated by a massless scalar field, developing a numerical spherically symmetric code dedicated to this problem. Imposing initial conditions on super horizon scales using the gradient expansion approach, we show that a massless scalar filed is equivalent to a perfect fluid, where the pressure is equal to the total energy density, only in the regime of cosmological expansion, while during the gravitational collapse space-like gradients arises and the comoving slicing is failing. For this reason, moving to a constant mean curvature slicing, we follow entirely the numerical evolution of cosmological perturbations, also during the gravitational collapse, computing the threshold for primordial black hole formation, and the corresponding mass distribution described by critical collapse.
