Which Formation Mechanism Show Strong Clustering of Primordial Black Holes? (Cosmology)

Masahiro Kawasaki and colleagues investigated the clustering of primordial black holes (PBHs) formed by Affleck-Dine (AD) baryogenesis. They found that formed PBHs showed strong clustering due to stochastic dynamics of the AD field. Their study recently appeared in Arxiv.

In recent years, the LIGO-Virgo collaboration has detected gravitational waves emitted by merging binary black holes, which revealed the existence of black holes with masses ∼ 10−100 M. Interestingly, many of observed black holes have heavy masses around 30M. The origin of these massive black holes is still unknown. One fascinating candidate is the primordial origin.

We have already discussed number of possible mechanisms which give rise to primordial black holes such as, by solo-multi bumps, by first-order phase transition, by fall of inflation, by fifth force etc. One of the PBHs formation scenario we haven’t discussed yet is Affleck-Dine (AD) baryogenesis. In this scenario, the IR mode of the AD field diffuses by quantum fluctuations during inflation and has multiple vacua just after inflation. Then, while the origin of the AD field becomes the true vacuum, the false vacuum has a non-zero field value. The inhomogeneity of the field value results in the inhomogeneous baryogenesis, which forms baryon-rich bubbles. At the QCD phase transition, baryons in the bubbles form massive nucleons and generate density fluctuations. If the bubbles are large enough, the density fluctuations grow sufficiently and then collapse into PBHs at the horizon reentry. PBHs generated in this scenario can have masses larger than 10 M and are expected to explain the origin of LIGO-Virgo events.

Kawasaki and colleagues investigated the clustering of PBH’s formed by this scenario. They have studied the stochastic dynamics of the AD field during inflation and derived the PBH formation rate. They have also estimated the two-point correlation function of PBHs, which characterized the clustering of PBH’s.

They found that, formed PBHs show strong clustering due to stochastic dynamics of the AD field. They have also obtained a reduced PBH correlation function given below:

They used this reduced PBH correlation function to investigate the effect of the clustering on two phenomena related to PBHs; isocurvature fluctuations and the merger rate distribution.

First, PBHs induce isocurvature fluctuations due to their Poisson fluctuations, and the clustering also sources isocurvature fluctuations. They have estimated the power spectrum of density fluctuation of PBHs (as shown in fig. 2 below) and have put the upper bound on the PBH abundance and the significance of clustering by using the current isocurvature constraints from the Planck satellite as shown in Fig. 3 below.

Second, the clustering of PBHs can drastically change the binary formation rate of PBHs, and the resultant merger rate density. They have found that the merger rate increases with the clustering for a small PBH abundance due to the enhanced binary formation rate, while it decreases for a large PBH abundance since the three-body problem occurs more frequently for the clustered PBHs. As a result, it was found that it is difficult for their model to explain the LIGO-Virgo event rate of binary mergers when they conservatively neglect the binary merger in three-body systems.

“In future work, we will see whether our model can explain the merger rate observed by LIGO-VIRGO collaboration by correctly including PBH mergers in three-body systems.”

— concluded authors of the study

All images credit except featured: Masahiro Kawasaki et al.

Reference: Masahiro Kawasaki, Kai Murai, Hiromasa Nakatsuka, “Strong clustering of primordial black holes from Affleck-Dine mechanism”, Arxiv, pp. 1-18, 2021. e-Print: ArXiv: 2107.03580

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