Clustering of primordial black holes formed in a matter-dominated epoch
  In the presence of the local-type primordial non-Gaussianity, it is known
that the clustering of primordial black holes (PBHs) emerges even on
super-horizon scales at the formation time. This effect has been investigated
in the high-peak limit of the PBH formation in the radiation-dominated epoch in
the literature. There is another possibility that the PBH formation takes place
in the early matter-dominated epoch. In this scenario, the high-peak limit is
not applicable because even initially small perturbations grow and can become a
PBH. We first derive a general formula to estimate the clustering of PBHs with
primordial non-Gaussianity without assuming the high-peak limit, and then apply
this formula to a model of PBH formation in a matter-dominated epoch.
Clustering is less significant in the case of the PBH formation in the
matter-dominated epoch than that in the radiation-dominated epoch.
Nevertheless, it is much larger than the Poisson shot noise in many cases.
Relations to the constraints of the isocurvature perturbations by the cosmic
microwave background radiation are quantitatively discussed.
