Constraining the initial primordial black hole clustering with CMB distortion

The merger rate of primordial black holes depends on their initial clustering. In the absence of primordial non-Gaussianity correlating short and large scales, primordial black holes are distributed à la Poisson at the time of their formation. However, primordial non-Gaussianity of the local type may correlate primordial black holes on large scales. We show that future experiments looking for cosmic microwave background μ distortion would test the hypothesis of initial primordial black hole clustering induced by local non-Gaussianity, while existing limits already show that significant non-Gaussianity is necessary to induce primordial black hole clustering.