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Primordial black holes (PBHs) are an important tool in cosmology to probe theprimordial spectrum of small-scale curvature perturbations that reenter thecosmological horizon during radiation domination epoch. We numerically solvethe evolution of spherically symmetric highly perturbed configurations toclarify the criteria of PBHs formation using an extremely wide class ofcurvature profiles characterized by five parameters, (in contrast to only twoparameters used in all previous papers) which specify the curvature profilesnot only at the central region but also at the outer boundary ofconfigurations. It is shown that formation or non-formation of PBHs isdetermined entirely by only two master parameters one of which can be presentedas an integral of curvature over initial configurations and the other ispresented in terms of the position of the boundary and the edge of the core.

Identifying the most crucial parameters of the initial curvature profile for primordial black hole formation