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Universe
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Primordial Black Holes from Inflation
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Primordial Black Holes from Inflation

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Compact Objects".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 21723

Special Issue Editor

Prof. Dr. Cristiano Germani

E-Mail Website
Guest Editor
Institut de Ciències del Cosmos, Universitat de Barcelona, Barcelona, Spain
Interests: primordial black holes; inflation; statistics; gravitational collapse

Special Issue Information

Dear Colleagues,

Primordial black holes (PBHs) are the most economical option for explaining dark matter (DM). If generated by large fluctuations of scalar primordial perturbations, a full explanation of DM in terms of PBHs only depends on a thorough understanding of inflation. Recently, constraints on the existence of PBHs were largely updated, leaving the intriguing possibility that the DM is entirely constituted by PBHs of sub-lunar masses. In this case, their abundance is intimately related to the inflationary evolution at sub-CMB scales. Thus, the discovery of those mini PBHs would also provide important information about the initial, inflationary, stages of our Universe. The last few years were also a theatre of intense theoretical activity that provided the foundations for precise predictions of PBH abundances.  

The aim of this Special Issue is to collect the somewhat scattered literature of the last few years in a pedagogical and coherent book on the current knowledge of inflationary generated PBHs as DM.

Prof. Dr. Cristiano Germani
Guest Editor

Manuscript Submission Information

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Keywords

  • primordial black holes 
  • inflation 
  • statistics 
  • gravitational collapse

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Published Papers (8 papers)

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Research

Jump to: Review

19 pages, 1337 KiB  
Article
Two-Loop Corrections in Power Spectrum in Models of Inflation with Primordial Black Hole Formation
by Hassan Firouzjahi
Universe 2024, 10(12), 456; https://doi.org/10.3390/universe10120456 - 13 Dec 2024
Viewed by 445
Abstract
We calculated the two-loop corrections in the primordial power spectrum in models of single-field inflation incorporating an intermediate USR phase employed for PBH formation. Among the overall eleven one-particle irreducible Feynman diagrams, we calculated the corrections from the “double scoop” two-loop diagram involving [...] Read more.
We calculated the two-loop corrections in the primordial power spectrum in models of single-field inflation incorporating an intermediate USR phase employed for PBH formation. Among the overall eleven one-particle irreducible Feynman diagrams, we calculated the corrections from the “double scoop” two-loop diagram involving two vertices of quartic Hamiltonians. We demonstrate herein the fractional two-loop correction in power spectrum scales, like the square of the fractional one-loop correction. We confirm our previous findings that the loop corrections become arbitrarily large in the setup where the transition from the intermediate USR to the final slow-roll phase is very sharp. This suggests that in order for the analysis to be under perturbative control against loop corrections, one requires a mild transition with a long enough relaxation period towards the final attractor phase. Full article
(This article belongs to the Special Issue Primordial Black Holes from Inflation)
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12 pages, 621 KiB  
Article
Quantum Loop Corrections in the Modified Gravity Model of Starobinsky Inflation with Primordial Black Hole Production
by Sultan Saburov and Sergei V. Ketov
Universe 2024, 10(9), 354; https://doi.org/10.3390/universe10090354 - 4 Sep 2024
Cited by 7 | Viewed by 658
Abstract
A modified gravity model of Starobinsky inflation and primordial black hole production is proposed in good (within 1σ) agreement with current measurements of the cosmic microwave background radiation. The model is an extension of the singularity-free Appleby–Battye–Starobinsky model by the [...] Read more.
A modified gravity model of Starobinsky inflation and primordial black hole production is proposed in good (within 1σ) agreement with current measurements of the cosmic microwave background radiation. The model is an extension of the singularity-free Appleby–Battye–Starobinsky model by the R4 term with different values of the parameters whose fine-tuning leads to the efficient production of primordial black holes on smaller scales with the asteroid-size masses between 1016 g and 1020 g. Those primordial black holes may be part (or the whole) of the current dark matter, while the proposed model can be confirmed or falsified by the detection or absence of the induced gravitational waves with the frequencies in the 10−2 Hz range. The relative size of quantum (loop) corrections to the power spectrum of scalar perturbations in the model is found to be of the order of 10−3 or less, so that the model is not ruled out by the quantum corrections. Full article
(This article belongs to the Special Issue Primordial Black Holes from Inflation)
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Review

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26 pages, 996 KiB  
Review
Primordial Black Holes: Formation, Spin and Type II
by Tomohiro Harada
Universe 2024, 10(12), 444; https://doi.org/10.3390/universe10120444 - 30 Nov 2024
Viewed by 464
Abstract
Primordial black holes (PBHs) may have formed through the gravitational collapse of cosmological perturbations that were generated and stretched during the inflationary era, later entering the cosmological horizon during the decelerating phase, if their amplitudes were sufficiently large. In this review paper, we [...] Read more.
Primordial black holes (PBHs) may have formed through the gravitational collapse of cosmological perturbations that were generated and stretched during the inflationary era, later entering the cosmological horizon during the decelerating phase, if their amplitudes were sufficiently large. In this review paper, we will briefly introduce the basic concept of PBHs and review the formation dynamics through this mechanism, the estimation of the initial spins of PBHs and the time evolution of type II fluctuations, with a focus on the radiation-dominated and (early) matter-dominated phases. Full article
(This article belongs to the Special Issue Primordial Black Holes from Inflation)
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22 pages, 595 KiB  
Review
The Statistics of Primordial Black Holes in a Radiation-Dominated Universe: Recent and New Results
by Cristiano Germani and Ravi K. Sheth
Universe 2023, 9(9), 421; https://doi.org/10.3390/universe9090421 - 16 Sep 2023
Cited by 14 | Viewed by 1444
Abstract
We review the nonlinear statistics of Primordial Black Holes that form from the collapse of over-densities in a radiation-dominated Universe. We focus on the scenario in which large over-densities are generated by rare and Gaussian curvature perturbations during inflation. As new results, we [...] Read more.
We review the nonlinear statistics of Primordial Black Holes that form from the collapse of over-densities in a radiation-dominated Universe. We focus on the scenario in which large over-densities are generated by rare and Gaussian curvature perturbations during inflation. As new results, we show that the mass spectrum follows a power law determined by the critical exponent of the self-similar collapse up to a power spectrum dependent cutoff, and that the abundance related to very narrow power spectra is exponentially suppressed. Related to this, we discuss and explicitly show that both the Press–Schechter approximation and the statistics of mean profiles lead to wrong conclusions for the abundance and mass spectrum. Finally, we clarify that the transfer function in the statistics of initial conditions for Primordial Black Holes formation (the abundance) does not play a significant role. Full article
(This article belongs to the Special Issue Primordial Black Holes from Inflation)
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78 pages, 2968 KiB  
Review
Inflation and Primordial Black Holes
by Ogan Özsoy and Gianmassimo Tasinato
Universe 2023, 9(5), 203; https://doi.org/10.3390/universe9050203 - 24 Apr 2023
Cited by 105 | Viewed by 4185
Abstract
We review conceptual aspects of inflationary scenarios able to produce primordial black holes by amplifying the size of curvature fluctuations to the level required to trigger black hole formation. We identify general mechanisms to do so, both for single- and multiple-field inflation. In [...] Read more.
We review conceptual aspects of inflationary scenarios able to produce primordial black holes by amplifying the size of curvature fluctuations to the level required to trigger black hole formation. We identify general mechanisms to do so, both for single- and multiple-field inflation. In single-field inflation, the spectrum of curvature fluctuations is enhanced by pronounced gradients of background quantities controlling the cosmological dynamics, which can induce brief phases of non-slow-roll inflationary evolution. In multiple-field inflation, the amplification occurs through appropriate couplings with additional sectors characterized by tachyonic instabilities that enhance the size of their fluctuations. As representative examples, we consider axion inflation and two-field models of inflation with rapid turns in field space. We develop our discussion in a pedagogical manner by including some of the most relevant calculations and by guiding the reader through the existing theoretical literature, emphasizing general themes common to several models. Full article
(This article belongs to the Special Issue Primordial Black Holes from Inflation)
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39 pages, 523 KiB  
Review
Review on Stochastic Approach to Inflation
by Diego Cruces
Universe 2022, 8(6), 334; https://doi.org/10.3390/universe8060334 - 17 Jun 2022
Cited by 24 | Viewed by 2145
Abstract
We present a review on the state-of-the-art of the mathematical framework known as stochastic inflation, paying special attention to its derivation, and giving references for the readers interested in results coming from the application of the stochastic framework to different inflationary scenarios, especially [...] Read more.
We present a review on the state-of-the-art of the mathematical framework known as stochastic inflation, paying special attention to its derivation, and giving references for the readers interested in results coming from the application of the stochastic framework to different inflationary scenarios, especially to those of interest for primordial black hole formation. During the derivation of the stochastic formalism, we will emphasise two aspects in particular: the difference between the separate universe approach and the true long wavelength limit of scalar inhomogeneities and the generically non-Markovian nature of the noises that appear in the stochastic equations. Full article
(This article belongs to the Special Issue Primordial Black Holes from Inflation)
50 pages, 3243 KiB  
Review
PBH Formation from Spherically Symmetric Hydrodynamical Perturbations: A Review
by Albert Escrivà
Universe 2022, 8(2), 66; https://doi.org/10.3390/universe8020066 - 21 Jan 2022
Cited by 51 | Viewed by 5300
Abstract
Primordial black holes, which could have been formed in the very early Universe due to the collapse of large curvature fluctuations, are currently one of the most attractive and fascinating research areas in cosmology for their possible theoretical and observational implications. This review [...] Read more.
Primordial black holes, which could have been formed in the very early Universe due to the collapse of large curvature fluctuations, are currently one of the most attractive and fascinating research areas in cosmology for their possible theoretical and observational implications. This review article presents the current results and developments on the conditions for primordial black hole formation from the collapse of curvature fluctuations in spherical symmetry on a Friedman–Lemaître–Robertson–Walker background and its numerical simulation. We review the appropriate formalism for the conditions of primordial black hole formation, and we detail a numerical implementation. We then focus on different results regarding the threshold and the black hole mass using different sets of curvature fluctuations. Finally, we present the current state of analytical estimations for the primordial black hole formation threshold, contrasted with numerical simulations. Full article
(This article belongs to the Special Issue Primordial Black Holes from Inflation)
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80 pages, 1497 KiB  
Review
Scalar Induced Gravitational Waves Review
by Guillem Domenech
Universe 2021, 7(11), 398; https://doi.org/10.3390/universe7110398 - 21 Oct 2021
Cited by 342 | Viewed by 5504
Abstract
We provide a review on the state-of-the-art of gravitational waves induced by primordial fluctuations, so-called induced gravitational waves. We present the intuitive physics behind induced gravitational waves and we revisit and unify the general analytical formulation. We then present general formulas in a [...] Read more.
We provide a review on the state-of-the-art of gravitational waves induced by primordial fluctuations, so-called induced gravitational waves. We present the intuitive physics behind induced gravitational waves and we revisit and unify the general analytical formulation. We then present general formulas in a compact form, ready to be applied. This review places emphasis on the open possibility that the primordial universe experienced a different expansion history than the often assumed radiation dominated cosmology. We hope that anyone interested in the topic will become aware of current advances in the cosmology of induced gravitational waves, as well as becoming familiar with the calculations behind. Full article
(This article belongs to the Special Issue Primordial Black Holes from Inflation)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Primordial black holes: formation, spin and type II
Authors: Tomohiro Harada
Affiliation: Department of Physics, Rikkyo University, Toshima, Tokyo 171-8501, Japan
Abstract: Primordial black holes (PBHs) may have formed through the gravitational collapse of cosmological perturbations that were generated and stretched during the inflationary era, later entering the cosmological horizon during the decelerating phase, if their amplitudes were sufficiently large. In this article, we will briefly introduce the basic concept of PBHs and review the formation dynamics through this mechanism, the estimation of the initial spins of PBHs and the time evolution of type II fluctuations, with a focus on the radiation-dominated and (early) matter-dominated phases.

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