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 CMB μ-distortion will test the hypothesis of initial primordial black hole clustering induced by local non-Gaussianity.