Primordial black holes as biased tracers

Primordial black holes (PBHs) are theoretical black holes which can be formed during the radiation dominant era through the gravitational collapse of radiational overdensities. It has been well known that in the context of the structure formation in our Universe such collapsed objects, e.g., halos/galaxies, could be considered as bias tracers of underlying matter fluctuations and the halo/galaxy bias has been studied well. Applying such a biased tracer picture to PBHs, we investigate the large scale clustering of PBHs and obtain an almost mass-independent constraint to the scenario that the dark matter (DM) consists of PBHs. We focus on the case where the statistics of the primordial curvature perturbations is almost Gaussian, but with small local-type non-Gaussianity. If PBHs account for the DM abundance, such a large scale clustering of PBHs behaves as nothing but the matter isocurvature perturbation which is strictly constrained by the observations of cosmic microwave backgrounds (CMBs). From this constraint, we show that, in the case where a certain single field causes both CMB temperature perturbations and PBH formation, the PBH-DM scenario is excluded even with quite small local-type non-Gaussianity, vertical bar f(NL)vertical bar similar to O(0.01).