Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function

Abstract We study stochastic effects in viable ultra-slow-roll inflation models that produce primordial black holes. We consider asteroid, solar, and supermassive black hole seed masses. In each case, we simulate 10 8 patches of the universe that may collapse into PBHs. In every patch, we follow 4 × 10 4 momentum shells to construct its spherically symmetric profile from first principles, without introducing a window function. We include the effects of critical collapse and the radiation era transfer function. The resulting compaction function profiles are very spiky due to stochastic kicks. This can enhance the PBH abundance by up to 36 orders of magnitude, depending on the mass range and collapse criterion. The PBH mass function shifts to higher masses and widens significantly. These changes may have a large effect on observational constraints of PBHs and make it possible to generate PBHs with a smaller amplitude of the power spectrum. However, convergence issues for the mass function remain. The results call for redoing collapse simulations to determine the collapse criterion for spiky profiles.