Threshold for PBH formation in the type-II region and its analytical estimation
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866915625003122688 |
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| author | Escrivà, Albert |
| author_facet | Escrivà, Albert |
| contents | We numerically simulate the formation of Primordial Black Holes (PBHs) in a radiation-dominated Universe under the assumption of spherical symmetry, driven by the collapse of adiabatic fluctuations, for different curvature profiles $ζ$. Our results show that the threshold for PBH formation, defined as the peak value of the critical compaction function $\mathcal{C}_{c}(r_m)$ (where $r_m$ is the scale at which the peak occurs), does not necessarily asymptotically saturate to its maximum possible value in the type-I region for sufficiently sharp profiles. Instead, the threshold is found in the type-II region with $\mathcal{C}_{c}(r_m)$ being a minimum. We find, for the cases tested, that this is a general trend associated with profiles that exhibit extremely large curvatures in the linear component of the compaction function $\mathcal{C}_{l}(r) \equiv -4r ζ'(r)/3$ shape around its peak $r_m$ (spiky shapes). To measure this curvature at $r_m$, we define a dimensionless parameter, $κ\equiv -r^{2}_m \mathcal{C}_l''(r_m)$, and we find that the thresholds observed in the type-II region occur for sufficiently large $κ$ for the profiles we have used, contrary to expectations. By defining the threshold in terms of $\mathcal{C}_{l,c}(r_m)$, we extend previous analytical estimations to the type-II region, which is shown to be accurate within a few percent when compared to the numerical simulations for the tested profiles. Our results suggest that current PBH abundance calculations for models where the threshold lies in the type-II region may have been overestimated due to the general assumption that it should saturate at the boundary between the type-I and type-II regions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05814 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Threshold for PBH formation in the type-II region and its analytical estimation Escrivà, Albert Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Theory We numerically simulate the formation of Primordial Black Holes (PBHs) in a radiation-dominated Universe under the assumption of spherical symmetry, driven by the collapse of adiabatic fluctuations, for different curvature profiles $ζ$. Our results show that the threshold for PBH formation, defined as the peak value of the critical compaction function $\mathcal{C}_{c}(r_m)$ (where $r_m$ is the scale at which the peak occurs), does not necessarily asymptotically saturate to its maximum possible value in the type-I region for sufficiently sharp profiles. Instead, the threshold is found in the type-II region with $\mathcal{C}_{c}(r_m)$ being a minimum. We find, for the cases tested, that this is a general trend associated with profiles that exhibit extremely large curvatures in the linear component of the compaction function $\mathcal{C}_{l}(r) \equiv -4r ζ'(r)/3$ shape around its peak $r_m$ (spiky shapes). To measure this curvature at $r_m$, we define a dimensionless parameter, $κ\equiv -r^{2}_m \mathcal{C}_l''(r_m)$, and we find that the thresholds observed in the type-II region occur for sufficiently large $κ$ for the profiles we have used, contrary to expectations. By defining the threshold in terms of $\mathcal{C}_{l,c}(r_m)$, we extend previous analytical estimations to the type-II region, which is shown to be accurate within a few percent when compared to the numerical simulations for the tested profiles. Our results suggest that current PBH abundance calculations for models where the threshold lies in the type-II region may have been overestimated due to the general assumption that it should saturate at the boundary between the type-I and type-II regions. |
| title | Threshold for PBH formation in the type-II region and its analytical estimation |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.05814 |