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Title: Primordial black holes in linear and non-linear regimes

Abstract

We revisit the formation of primordial black holes (PBHs) in the radiation-dominated era for both linear and non-linear regimes, elaborating on the concept of an apparent horizon. Contrary to the expectation from vacuum models, we argue that in a cosmological setting a density fluctuation with a high density does not always collapse to a black hole. To this end, we first elaborate on the perturbation theory for spherically symmetric space times in the linear regime. Thereby, we introduce two gauges. This allows to introduce a well defined gauge-invariant quantity for the expansion of null geodesics. Using this quantity, we argue that PBHs do not form in the linear regime irrespective of the density of the background. Finally, we consider the formation of PBHs in non-linear regimes, adopting the spherical collapse picture. In this picture, over-densities are modeled by closed FRW models in the radiation-dominated era. The difference of our approach is that we start by finding an exact solution for a closed radiation-dominated universe. This yields exact results for turn-around time and radius. It is important that we take the initial conditions from the linear perturbation theory. Additionally, instead of using uniform Hubble gauge condition, both density and velocity perturbationsmore » are admitted in this approach. Thereby, the matching condition will impose an important constraint on the initial velocity perturbations δ {sup h} {sub 0} = −δ{sub 0}/2. This can be extended to higher orders. Using this constraint, we find that the apparent horizon of a PBH forms when δ > 3 at turn-around time. The corrections also appear from the third order. Moreover, a PBH forms when its apparent horizon is outside the sound horizon at the re-entry time. Applying this condition, we infer that the threshold value of the density perturbations at horizon re-entry should be larger than δ {sub th} > 0.7.« less

Authors:
;  [1];  [2]
  1. Department of Physics, Sharif University of Technology, Tehran (Iran, Islamic Republic of)
  2. School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)
Publication Date:
OSTI Identifier:
22676147
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 06; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; BLACK HOLES; DENSITY; DISTURBANCES; EXACT SOLUTIONS; EXPANSION; FLUCTUATIONS; GAUGE INVARIANCE; NONLINEAR PROBLEMS; PERTURBATION THEORY; SOUND WAVES; SPACE-TIME; SYMMETRY; UNIVERSE; VELOCITY

Citation Formats

Allahyari, Alireza, Abolhasani, Ali Akbar, and Firouzjaee, Javad T., E-mail: allahyari@physics.sharif.edu, E-mail: j.taghizadeh.f@ipm.ir. Primordial black holes in linear and non-linear regimes. United States: N. p., 2017. Web. doi:10.1088/1475-7516/2017/06/041.
Allahyari, Alireza, Abolhasani, Ali Akbar, & Firouzjaee, Javad T., E-mail: allahyari@physics.sharif.edu, E-mail: j.taghizadeh.f@ipm.ir. Primordial black holes in linear and non-linear regimes. United States. doi:10.1088/1475-7516/2017/06/041.
Allahyari, Alireza, Abolhasani, Ali Akbar, and Firouzjaee, Javad T., E-mail: allahyari@physics.sharif.edu, E-mail: j.taghizadeh.f@ipm.ir. Thu . "Primordial black holes in linear and non-linear regimes". United States. doi:10.1088/1475-7516/2017/06/041.
@article{osti_22676147,
title = {Primordial black holes in linear and non-linear regimes},
author = {Allahyari, Alireza and Abolhasani, Ali Akbar and Firouzjaee, Javad T., E-mail: allahyari@physics.sharif.edu, E-mail: j.taghizadeh.f@ipm.ir},
abstractNote = {We revisit the formation of primordial black holes (PBHs) in the radiation-dominated era for both linear and non-linear regimes, elaborating on the concept of an apparent horizon. Contrary to the expectation from vacuum models, we argue that in a cosmological setting a density fluctuation with a high density does not always collapse to a black hole. To this end, we first elaborate on the perturbation theory for spherically symmetric space times in the linear regime. Thereby, we introduce two gauges. This allows to introduce a well defined gauge-invariant quantity for the expansion of null geodesics. Using this quantity, we argue that PBHs do not form in the linear regime irrespective of the density of the background. Finally, we consider the formation of PBHs in non-linear regimes, adopting the spherical collapse picture. In this picture, over-densities are modeled by closed FRW models in the radiation-dominated era. The difference of our approach is that we start by finding an exact solution for a closed radiation-dominated universe. This yields exact results for turn-around time and radius. It is important that we take the initial conditions from the linear perturbation theory. Additionally, instead of using uniform Hubble gauge condition, both density and velocity perturbations are admitted in this approach. Thereby, the matching condition will impose an important constraint on the initial velocity perturbations δ {sup h} {sub 0} = −δ{sub 0}/2. This can be extended to higher orders. Using this constraint, we find that the apparent horizon of a PBH forms when δ > 3 at turn-around time. The corrections also appear from the third order. Moreover, a PBH forms when its apparent horizon is outside the sound horizon at the re-entry time. Applying this condition, we infer that the threshold value of the density perturbations at horizon re-entry should be larger than δ {sub th} > 0.7.},
doi = {10.1088/1475-7516/2017/06/041},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 06,
volume = 2017,
place = {United States},
year = {Thu Jun 01 00:00:00 EDT 2017},
month = {Thu Jun 01 00:00:00 EDT 2017}
}
  • Primordial black holes (PBHs) can form in the early Universe from the collapse of rare, large density fluctuations. They have never been observed, but this fact is enough to constrain the amplitude of fluctuations on very small scales which cannot be otherwise probed. Because PBHs form only in very rare large fluctuations, the number of PBHs formed is extremely sensitive to changes in the shape of the tail of the fluctuation distribution — which depends on the amount of non-Gaussianity present. We first study how local non-Gaussianity of arbitrary size up to fifth order affects the abundance and constraints frommore » PBHs, finding that they depend strongly on even small amounts of non-Gaussianity and the upper bound on the allowed amplitude of the power spectrum can vary by several orders of magnitude. The sign of the non-linearity parameters (f{sub NL}, g{sub NL}, etc.) are particularly important. We also study the abundance and constraints from PBHs in the curvaton scenario, in which case the complete non-linear probability distribution is known, and find that truncating to any given order (i.e. to order f{sub NL} or g{sub NL}, etc.) does not give accurate results.« less
  • We explore the role of non-Gaussian fluctuations in primordial black hole (PBH) formation and show that the standard Gaussian assumption, used in all PBH formation papers to date, is not justified. Since large spikes in power are usually associated with flat regions of the inflaton potential, quantum fluctuations become more important in the field dynamics, leading to mode-mode coupling and non-Gaussian statistics. Moreover, PBH production requires several {sigma} (rare) fluctuations in order to prevent premature matter dominance of the universe, so we are necessarily concerned with distribution tails, where any intrinsic skewness will be especially important. We quantify this argumentmore » by using the stochastic slow-roll equation and a relatively simple analytic method to obtain the final distribution of fluctuations. We work out several examples with toy models that produce PBH{close_quote}s, and test the results with numerical simulations. Our examples show that the naive Gaussian assumption can result in errors of many orders of magnitude. For models with spikes in power, our calculations give sharp cutoffs in the probability of large positive fluctuations, meaning that Gaussian distributions would vastly overproduce PBH{close_quote}s. The standard results that link inflation-produced power spectra and PBH number densities must then be reconsidered, since they rely quite heavily on the Gaussian assumption. We point out that since the probability distributions depend strongly on the nature of the potential, it is impossible to obtain results for general models. However, calculating the distribution of fluctuations for any specific model seems to be relatively straightforward, at least in the single inflaton case. {copyright} {ital 1997} {ital The American Physical Society}« less
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