Evaporation of primordial black holes in the early Universe: Mass and spin distributions

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Evaporation of primordial black holes in the early Universe: Mass and spin distributions

Andrew Cheek, Lucien Heurtier, Yuber F. Perez-Gonzalez, and Jessica Turner

Phys. Rev. D 108, 015005 – Published 6 July 2023

Abstract

Many cosmological phenomena lead to the production of primordial black holes in the early Universe. These phenomena often create a population of black holes with extended mass and spin distributions. As these black holes evaporate via Hawking radiation, they can modify various cosmological observables, lead to the production of dark matter, modify the number of effective relativistic degrees of freedom, $N_{eff}$ , source a stochastic gravitational wave background and alter the dynamics of baryogenesis. We consider the Hawking evaporation of primordial black holes that feature nontrivial mass and spin distributions in the early Universe. We demonstrate that the shape of such a distribution can strongly affect most of the aforementioned cosmological observables. We outline the numerical machinery we use to undertake this task. We also release a new version of FRISBHEE that handles the evaporation of primordial black holes with an arbitrary mass and spin distribution throughout cosmic history.

Received 4 January 2023
Accepted 11 June 2023

DOI:https://doi.org/10.1103/PhysRevD.108.015005

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Evolution of the Universe

Particles & Fields

Authors & Affiliations

Andrew Cheek^1,*, Lucien Heurtier ^2,†, Yuber F. Perez-Gonzalez^2,‡, and Jessica Turner ^2,§

¹Astrocent, Nicolaus Copernicus Astronomical Center of the Polish Academy of Sciences, ul.Rektorska 4, 00-614 Warsaw, Poland
²Institute for Particle Physics Phenomenology, Durham University, South Road DH1 3LE, Durham, United Kingdom

^*acheek@camk.edu.pl
^†lucien.heurtier@durham.ac.uk
^‡yuber.f.perez-gonzalez@durham.ac.uk
^§jessica.turner@durham.ac.uk

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Issue

Vol. 108, Iss. 1 — 1 July 2023

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Images

Figure 1
The left plot shows the log normal mass distribution with $M_{c} = 10^{6} g$ for $σ = 0.5$ , 1.0, 2.0 shown in violet, teal and yellow, respectively. The central plot shows the power law mass distribution with $M_{c} = 10 g$ and $M_{c} 1 0^{σ} = 10^{6} g$ for $α = 1$ , 2, 3 shown in violet, teal and yellow, respectively. The right plot shows the mass distributions generated through metric preheating [81] (taken from Appendix C, Fig. 8) and critical collapse [82, 83, 84], using $M_{c} = 10^{5.6} g$ to align the two distributions.
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Figure 2
Top panels: Time evolution of the comoving mass distribution $f \equiv a^{3} (t) f_{PBH}$ for a log-normal (left panel), power-law (central panel), and critical collapse (right panel) distributions. The log-normal distribution is taken to have a width $σ = 1$ and the central mass considered is $M_{c} = 10^{2} g$ . $τ_{M_{c}}$ indicates the lifetime of a PBH with a mass equal to $M_{c}$ . Bottom panels: Evolution of a mass and spin distribution $f_{PBH} (M, a_{⋆}, t)$ as a function of time, starting with a log-normal distribution in mass, and the universal spin distribution obtained in Ref. [94]. The left (right) most plot shows the initial (final) distribution at time an initial (final) time. The colored lines are iso-contours of the distribution, whereas the lifetime $τ$ denotes the lifetime of the PBH with initial mass and spin at the peak of the distribution. The shaded region represents the region where PBHs would have a lifetime shorter than the corresponding time $t - t_{in}$ , and can therefore not be present in the Universe at time $t$ .
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Figure 3
The right plot shows the evolution of the PBH relative abundance $Ω_{PBH}$ as a function of the number of $e$ -folds $N$ for log-normal distributions of PBHs with varying widths $σ$ . The central plot shows the same but for power-law distributions of PBHs with varying exponents $α$ , and minimum mass $M_{c} = 10 g$ . Plain, dotted, and dashed lines stand for the evaporation of distributions with, respectively, $M_{c} 1 0^{σ} = 10, 10^{2.5}$ , and $10^{5} g$ . The right plot shows the PBH evolution as a function of the number of $e$ -folds $N$ for the distributions from critical collapse and metric preheating (see Sec. 2a).
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Figure 4
Lines showing the $β^{'}$ and $M_{c}$ values required to produce the correct relic abundance from PBH evaporation only. The DM particle we consider is a fermion with a mass of 1 GeV. We show a range of PBH distributions; on the left, we show log-normal distributions with a range of widths, $σ = 0.1$ , 0.5, 1.0, 2.0 in orange, green, red and purple, respectively. On the right, we have a power law distribution with $α = 2.5$ and $σ = 3$ in orange, the critical collapse (CC) distribution in green and the metric preheating (MP) distribution in red. In both panels, the monochromatic PBH distribution is depicted with a blue dotted line for reference. The black dashed lines that overlay the solid lines show where warm DM constraints are in conflict with the PBH-produced DM.
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Figure 5
Contribution to $Δ N_{eff}$ for gravitons (left) and new light scalar degrees of freedom (right) from the evaporation of PBHs. In the left panel, the mass distribution is log-normal, with a constant width $σ = 0.005$ and central mass $M_{c}$ , and the colorbar represents the width of the spin distribution, taken to be Gaussian, centered at $⟨ a_{⋆} ⟩ = 0.7$ , and with width $σ_{a_{⋆}}$ . The red dot-dashed line indicates the result for the merger spin distribution from Ref. [94]. On the right panel, we consider Schwarzschild PBHs with different examples of mass distributions, log-normal (red), power-law (yellow), critical collapse (emerald), and metric preheating (purple). The black dashed lines indicate the values that are excluded from BBN limits.
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Figure 6
Gravitational wave spectrum obtained from the evaporation of gravitons. We consider a variety of mass distributions (left), $M_{c} = 10^{4} g$ , and an initial PBH energy fraction of $β^{'} = 10^{- 7}$ . We also exhibit the effect of spin for BH distributions (right), where the $M_{c}$ and $β^{'}$ is the same but $⟨ a_{⋆} ⟩ = 0.9999$ . The power-law distribution in mass has parameters $σ = 3$ and $α = 2.5$ and the Gaussian in $a_{⋆}$ has the width $σ = 0.1$ .
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Physical Review D

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