Simulations of PBH formation at the QCD epoch and comparison with the GWTC-3 catalog (2209.06196v2)

Abstract: The probability of primordial black hole (PBH) formation is known to be boosted during the Quantum Chromodynamics (QCD) crossover due to a slight reduction of the equation of state. This induces a high peak and other features in the PBH mass distribution. But the impact of this variation during the PBH formation has been so far neglected. In this work we simulate for the first time the formation of PBHs by taking into account the varying equation of state at the QCD epoch, compute the over-density threshold using different curvature profiles and find that the resulting PBH mass distributions are significantly impacted. The expected merger rate distributions of early and late PBH binaries is comparable to the ones inferred from the GWTC-3 catalog for dark matter fractions in PBHs within $0.1 < f_{\rm PBH} <1 $. The distribution of gravitational-wave events estimated from the volume sensitivity could explain mergers around $30-50 M_\odot$, with asymmetric masses like GW190814, or in the pair-instability mass gap like GW190521. However, none of the considered cases leads to a multi-modal distribution with a secondary peak around $8-15 M_\odot$, as suggested by the GWTC-3 catalog, possibly pointing to a mixed population of astrophysical and primordial black holes.

• The paper demonstrates that incorporating a dynamic equation of state lowers the PBH formation threshold during the QCD epoch.
• Nonlinear simulations accurately predict a solar-mass peak in the PBH mass distribution from cosmological fluctuations.
• The study bridges theoretical models with GWTC-3 data, refining our understanding of dark matter origins and gravitational wave sources.

An Analysis of Primordial Black Hole Formation at the QCD Epoch

This paper explores the formation of primordial black holes (PBHs) during the QCD epoch, focusing on the impact of a dynamic equation of state on the mass distribution of PBHs. The research involves simulating the nonlinear collapse of cosmological fluctuations, and these simulations are pivotal in deriving the threshold conditions for PBH formation under varying cosmological parameters.

The authors detail how the probability of PBH formation is contingent on the equation of state transitioning during the QCD epoch. This transition is characterized by a reduction in the equation of state parameter, $w$, which temporarily decreases to $w \approx 0.23$ at this epoch, in contrast to the $w = \frac{1}{3}$ value during a radiation-dominated Universe. They meticulously compute the over-density threshold for black hole formation using various curvature profiles.

Key results indicate that employing a constant equation of state, as has been standard practice in previous studies, underestimates the threshold for PBH formation and consequently overestimates their abundance. By accounting for the QCD effect, the threshold value is lowered, leading to a peak in the PBH mass distribution around solar mass scales, with implications suggesting that this could explain some features observed in the gravitational-wave events catalog (GWTC-3).

The implications of these findings span both theoretical and observational realms. Theoretically, this approach offers a refined model that adequately captures the thermodynamics of the early Universe's equation of state. From an observational perspective, this model can provide constrained scenarios where observed gravitational waves might originate from earlier PBH mergers, indicating PBH populations that may constitute a significant fraction of dark matter. However, none of the cases considered lead to a multimodal distribution with a secondary peak around $8-15 M_\odot$, as suggested by existing gravitational wave data, potentially pointing to a mixed population of astrophysical and primordial black holes.

On the mode of simulation, the intricate techniques of semi-analytical and numerical approaches employed illuminate the gravitational collapse dynamics in detail, offering more accurate predictions in contrast to previous assumptions. These models illustrate the gravitational forces at small scales and the implications of varying curvature profiles on primordial perturbation, thus enabling a deeper understanding of early Universe conditions conducive to PBH formation.

In conclusion, the paper makes significant contributions to our understanding of PBH formation within the context of evolving cosmological conditions during the QCD epoch. The nuanced approach exemplifies a crucial step forward in improving convergence between theoretical models and empirical data. Future research could extend these simulations to other cosmic epochs with different thermal histories, offering broader insights into the conditions necessary for PBH formation and their role in cosmic structure formation and dark matter composition.

This work positions itself as a critical tool for evaluating primordial cosmological models and could serve as a stepping stone for furthering our understanding of gravitational wave sources beyond the current frameworks.