Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2502.05194 |
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Inhaltsangabe:
- 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.