Abstract
We study the formation of primordial black holes (PBHs) in strongly super-cooled first-order phase transitions. The mechanism is based on the presence of remnants dominated by the false vacuum that scale slower with the expansion of the Universe than their surroundings where this energy was already converted into radiation. We compute the PBH formation from these remnants including the contribution from the false vacuum and the bubble walls, by estimating the collapse using the hoop conjecture and by considering both regions collapsing immediately when entering the horizon and sub-horizon regions that collapse as their compactness grows. We show that for exponential bubble nucleation rate, Γ ∝ eβt, the primordial black hole formation implies β/H ≳ 3.8, where H denotes the Hubble rate, if the potential energy of the false vacuum is ∆V ≲ (1012 GeV)4, as otherwise a too large abundance of long-lived PBHs forms. The observed dark matter abundance can be formed in asteroid mass PBHs if β/H ≃ 3.8 and 105 GeV ≲ ∆V1/4 ≲ 108 GeV. Finally, we consider also the effect of the second order correction to the exponential nucleation rate showing that the PBH abundance is mainly determined by the average radius of the true vacuum bubbles.
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Acknowledgments
This work was supported by the Polish National Agency for Academic Exchange within Polish Returns Programme under agreement PPN/PPO/2020/1/00013/U/00001 and the Polish National Science Center grant 2018/31/D/ST2/02048. The work of V.V. was supported by the European Union’s Horizon Europe research and innovation program under the Marie Skłodowska-Curie grant agreement No. 101065736, by the European Regional Development Fund through the CoE program grant TK133 and by the Estonian Research Council grant PRG803.
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Lewicki, M., Toczek, P. & Vaskonen, V. Primordial black holes from strong first-order phase transitions. J. High Energ. Phys. 2023, 92 (2023). https://doi.org/10.1007/JHEP09(2023)092
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DOI: https://doi.org/10.1007/JHEP09(2023)092