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Primordial black hole formation in the matter-dominated phase of the Universe

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abstract

We investigate primordial black hole formation in the matter-dominated phase of the Universe, where nonspherical effects in gravitational collapse play a crucial role. This is in contrast to the black hole formation in a radiation-dominated era. We apply the Zel'dovich approximation, Thorne's hoop conjecture, and Doroshkevich's probability distribution and subsequently derive the production probability $\beta_{0}$ of primordial black holes. The numerical result obtained is applicable even if the density fluctuation $\sigma$ at horizon entry is of the order of unity. For $\sigma\ll 1$, we find a semi-analytic formula $\beta_{0}\simeq 0.05556 \sigma^{5}$, which is comparable with the Khlopov-Polnarev formula. We find that the production probability in the matter-dominated era is much larger than that in the radiation-dominated era for $\sigma\lesssim 0.05$, while they are comparable with each other for $\sigma\gtrsim 0.05$. We also discuss how $\sigma$ can be written in terms of primordial curvature perturbations.

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2026 5 2020 2

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representative citing papers

Constraints on Primordial Black Holes

astro-ph.CO · 2020-02-27 · accept · novelty 4.0

Updated compilation shows PBHs are tightly constrained across 55 orders of magnitude in mass, ruling out dominant dark matter contributions except in narrow windows, with many limits carrying observational uncertainties.

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