Kavli Affiliate: Masahiro Kawasaki

| First 5 Authors: Kentaro Kasai, Masahiro Kawasaki, Naoya Kitajima, Kai Murai, Shunsuke Neda

| Summary:

We study the clustering of primordial black holes (PBHs) and axion

miniclusters produced in the model proposed to explain the LIGO/Virgo events or

the seeds of the supermassive black holes (SMBHs) in arXiv:2006.13137. It is

found that this model predicts large isocurvature perturbations due to the

clustering of PBHs and axion miniclusters, from which we obtain stringent

constraints on the model parameters. Specifically, for the axion decay constant

$f_a=10^{16}~mathrm{GeV}$, which potentially accounts for the seeds of the

SMBHs, the PBH fraction in dark matter should be $f_mathrm{PBH}lesssim7times

10^{-10}$. Assuming that the mass of PBHs increases by more than a factor of

$mathcal{O}(10)$ due to accretion, this is consistent with the observed

abundance of SMBHs. On the other hand, for $f_a=10^{17}~mathrm{GeV}$ required

to produce PBHs of masses detected in the LIGO/Virgo, the PBH fraction should

be $f_mathrm{PBH}lesssim6times 10^{-8}$, which may be too small to explain

the LIGO/Virgo events, although there is a significant uncertainty in

calculating the merger rate in the presence of clustering.

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