The double formation of primordial black holes

Primordial black holes (PBHs) are a useful tool in cosmology to probe primordial inhomogeneities on small scales that reenter the Hubble radius during the radiation dominated epoch. In this paper, a phenomenon we call the double formation of PBHs, described below, is explored. Suppose there exists a highly perturbed region which will collapse to form a PBH after the horizon crossing of this region, and farther that this region is superposed on much larger region, which also collapses upon reentry. One then expects the collapse of the central smaller region at the time of the crossing of this region, followed by another collapse of the larger perturbation at the time of its respective crossing. The smaller PBH, formed earlier, should be swallowed in the second collapse leading to a single larger PBH as the final state. This paper reports the first direct numerical confirmation of such double PBH formation. Related to this, we also discuss the effects of high-frequency modes on the formation of PBHs.