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 \`a 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 $\mu$-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.
