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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2502.05194 |
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| _version_ | 1866915760098508800 |
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| author | Farooq, Owais Zahoor, Romana Francis, Balungi |
| author_facet | Farooq, Owais Zahoor, Romana Francis, Balungi |
| contents | Primordial black holes (PBHs) can form during radiation domination from rare primordial perturbations that re-enter the Hubble radius and undergo gravitational collapse. We derive PBH mass distributions using Press--Schechter theory completed by the excursion-set first-crossing construction. We define the smoothed density contrast $δ_R$ and its variance $S(R)=σ^2(R)$, and connect $S$ to the primordial curvature spectrum $\mathcal{P}_{\mathcal R}(k)$ through the radiation-era transfer. For Gaussian statistics and a constant collapse threshold $δ_c$, the formation fraction is an $\operatorname{erfc}$ tail with a controlled rare-event asymptotic. For a sharp-$k$ filter, $δ(S)$ is Markovian; solving the diffusion equation with an absorbing barrier yields the first-crossing density $f(S)=\frac{δ_c}{\sqrt{2π}}S^{-3/2}\exp\!\big(-δ_c^2/(2S)\big)$. This gives a differential formation fraction $\mathrm{d}β/\mathrm{d}\ln M=f(S)\,\big|\mathrm{d}S/\mathrm{d}\ln M\big|$ and a mass-conserving formation-era mass function $\mathrm{d}n_{\mathrm{PBH}}/\mathrm{d}M$. We then map to the present-day PBH dark-matter fraction per logarithmic mass, $f_{\mathrm{PBH}}(M)$, using horizon-entry scaling $M\propto k^{-2}$ and radiation-era redshifting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Press-Schechter Formalism and The PBH Mass Distributions Farooq, Owais Zahoor, Romana Francis, Balungi Cosmology and Nongalactic Astrophysics Primordial black holes (PBHs) can form during radiation domination from rare primordial perturbations that re-enter the Hubble radius and undergo gravitational collapse. We derive PBH mass distributions using Press--Schechter theory completed by the excursion-set first-crossing construction. We define the smoothed density contrast $δ_R$ and its variance $S(R)=σ^2(R)$, and connect $S$ to the primordial curvature spectrum $\mathcal{P}_{\mathcal R}(k)$ through the radiation-era transfer. For Gaussian statistics and a constant collapse threshold $δ_c$, the formation fraction is an $\operatorname{erfc}$ tail with a controlled rare-event asymptotic. For a sharp-$k$ filter, $δ(S)$ is Markovian; solving the diffusion equation with an absorbing barrier yields the first-crossing density $f(S)=\frac{δ_c}{\sqrt{2π}}S^{-3/2}\exp\!\big(-δ_c^2/(2S)\big)$. This gives a differential formation fraction $\mathrm{d}β/\mathrm{d}\ln M=f(S)\,\big|\mathrm{d}S/\mathrm{d}\ln M\big|$ and a mass-conserving formation-era mass function $\mathrm{d}n_{\mathrm{PBH}}/\mathrm{d}M$. We then map to the present-day PBH dark-matter fraction per logarithmic mass, $f_{\mathrm{PBH}}(M)$, using horizon-entry scaling $M\propto k^{-2}$ and radiation-era redshifting. |
| title | Press-Schechter Formalism and The PBH Mass Distributions |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2502.05194 |