The standard deviation of the initial values of the nondimensional Kerr parameter $a_{*}$ of primordial black holes (PBHs) formed in the radiation-dominated phase of the universe is estimated to the first order of perturbation for the narrow power spectrum. Evaluating the angular momentum at turn around based on linearly extrapolated transfer functions and peak theory, we obtain the expression $\sqrt{\langle a_{*}^{2} \rangle} \simeq 4.0\times 10^{-3} (M/M_{H})^{-1/3}\sqrt{1-γ^{2}}[1-0.072 \log_{10}(β_{0}(M_{H})/(1.3\times 10^{-15}))]^{-1}$, where $M_{H}$, $β_{0}(M_{H})$, and $γ$ are the mass within the Hubble horizon at the horizon entry of the overdense region, the fraction of the universe which collapsed to PBHs at the scale of $M_{H}$, and a quantity which characterizes the width of the power spectrum, respectively. This implies that for $M\simeq M_{H}$, the higher the probability of the PBH formation, the larger the standard deviation of the spins, while PBHs of $M\ll M_{H}$ formed through near-critical collapse may have larger spins than those of $M\simeq M_{H}$. In comparison to the previous estimate, the new estimate has the explicit dependence on the ratio $M/M_{\rm H}$ and no direct dependence on the current dark matter density. On the other hand, it suggests that the first-order effect can be numerically comparable to the second-order one.
We consider the role of secondary infall and accretion onto an initially overdense perturbation in matter-dominated eras, like the one which is likely to follow the end of inflation. We show that primordial black holes may form through post-collapse accretion, namely the accretion onto an initial overdensity whose collapse has not given rise to a primordial black hole. Accretion may be also responsible for the growth of the primordial black hole masses by orders of magnitude till the end of the matter-dominated era.
Primordial Black Holes in a Radiation-Dominated Universe
Bowdoin College（鲍登学院）；Queen Mary University of London（伦敦大学玛丽女王学院）；University of Pennsylvania（宾夕法尼亚大学）；Kenyon College（肯扬学院）；Case Western Reserve University（凯斯西储大学）；The Ohio State University（俄亥俄州立大学）
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 $β_{0}$ of primordial black holes. The numerical result obtained is applicable even if the density fluctuation $σ$ at horizon entry is of the order of unity. For $σ\ll 1$, we find a semi-analyti…
In the presence of the local-type primordial non-Gaussianity, it is known that the clustering of primordial black holes (PBHs) emerges even on super-horizon scales at the formation time. This effect has been investigated in the high-peak limit of the PBH formation in the radiation-dominated epoch in the literature. There is another possibility that the PBH formation takes place in the early matter-dominated epoch. In this scenario, the high-peak limit is not applicable because even initially small perturbations grow and can become a PBH. We first derive a general formula to estimate the cluste…
The accumulation of dark matter particles near the primordial black holes starts at the radiation-dominated cosmological stage and produces the central density spikes. The spikes can be the bright gamma-ray sources due to dark matter annihilation. We present the self-consistent derivation of the equation of motion of particle in the metrics of primordial black hole immersed into cosmological background. By numerical solution of this equation we find the central dark matter density profile. The density growth is suppressed in the central part of the profile compared with previous calculations.
We investigate the effect of inhomogeneity on primordial black hole formation in the matter dominated era. In the gravitational collapse of an inhomogeneous density distribution, a black hole forms if apparent horizon prevents information of the central region of the configuration from leaking. Since information cannot propagate faster than the speed of light, we identify the threshold of the black hole formation by considering the finite speed for propagation of information. We show that the production probability $β_{inhom}(σ)$ of primordial black holes, where $σ$ is density fluctuation at h…
In this paper, we have investigated the processes of evaporation and accretion of primordial black holes during the radiation-dominated era and the matter-dominated era. This subject is very important since usually these two processes are considered independent of each other. In other words, previous works consider them in such a way that they do not have a direct effect on each other, and as a result, their effects on the mass of primordial black holes are calculated separately. The calculations of this paper indicate that assuming these two processes independently of each other will lead to …
We explore the prospect of producing primordial black holes around the solar mass region during an early matter domination epoch. The early matter-dominated epoch can arise when a moduli field comes to dominate the energy density of the Universe prior to big bang nucleosynthesis. The absence of radiation pressure during a matter-dominated epoch enhances primordial black hole formation from the gravitational collapse of primordial density fluctuations. In particular, we find that primordial black holes are produced in the $0.1-10~M_{\odot}$ mass range with a favorable choice of parameters in th…
We study possibilities to explain the whole dark matter abundance by primordial black holes (PBHs) or to explain the merger rate of binary black holes estimated from the gravitational wave detections by LIGO/Virgo. We assume that the PBHs are originated in a radiation- or matter-dominated era from large primordial curvature perturbation generated by inflation. We take a simple model-independent approach considering inflation with large running spectral indices which are parametrized by $n_\text{s}, α_\text{s}$, and $β_\text{s}$ consistent with the observational bounds. The merger rate is fitte…
Primordial black holes formed in an early post-inflation matter-dominated epoch during preheating provide a novel pathway for a source of the dark matter that utilizes known physics in combination with plausible speculations about the role of quantum gravity. Two cases are considered here: survival of Planck-scale relics and an early universe accretion scenario for formation of primordial black holes of asteroid-scale masses.
In this paper, we revisit the evaporation and accretion of primordial black holes (PBHs) during cosmic history and compare them to see if both of these processes are constantly active for PBHs or not. Our calculations indicate that during the radiation-dominated era, PBHs absorb ambient radiation due to accretion, and their apparent horizon grows rapidly. This growth causes the Hawking radiation process to practically fail and all the particles that escape as radiation from PBHs to fall back into them. Nevertheless, our emphasis is that the accretion efficiency factor also plays a very importa…
We study the evolution of primordail black holes by considering present universe is no more matter dominated rather vacuum energy dominated. We also consider the accretion of radiation, matter and vacuum energy during respective dominance period. In this scenario, we found that radiation accretion efficiency should be less than 0.366 and accretion rate is much larger than previous analysis by B. Nayak et al. \cite{ns}. Thus here primordial black holes live longer than previous works \cite{ns}. Again matter accretion slightly increases the mass and lifetime of primordial black holes. However, t…
Primordial black holes (PBHs) could account for all or part of dark matter, as well as for some LIGO events. We discuss the spins of primordial black holes produced in different cosmological scenarios, with the emphasis on recently discovered possibilities. PBHs produced as a horizon-size collapse of density perturbations are known to have very small spins. In contrast, PBHs resulting from assembly of matterlike objects (particles, Q-balls, oscillons, etc.) can have large or small spins depending on their formation history and the efficiency of radiative cooling. We show that scalar radiation …
Recently, the formation of primordial black holes (PBHs) from the collapse of primordial fluctuations has received much attention. The abundance of PBHs formed during radiation domination is sensitive to the tail of the probability distribution of primordial fluctuations. We quantify the level of fine-tuning due to this sensitivity. For example, if the main source of dark matter is PBHs with mass $10^{-12}M_\odot$, then anthropic reasoning suggests that the dark matter to baryon ratio should range between 1 and 300. For this to happen, the root-mean-square amplitude of the curvature perturbati…
Certain inflationary models as well as realisations of phase transitions in the early Universe predict the formation of primordial black holes. For most mass ranges, the fraction of matter in the form of primordial black holes is limited by many different observations on various scales. Primordial black holes are assumed to be formed when overdensities that cross the horizon have Schwarzschild radii larger than the horizon. Traditionally it was therefore assumed that primordial black-hole masses were equal to the horizon mass at their time of formation. However, detailed calculations of their …
We present a scenario for fast growth of cosmological perturbations; $δ(t) \sim a(t)^s$, $a(t)$ being the scale factor, with $s > 10$ for the numerical examples reported in this article. The basic ingredients of the scenario are an early matter dominated era and the dark fermion which experiences a scalar mediated force during the epoch. Both of these arise in string/supergravity models. The fast growth occurs for sub-horizon density perturbations of the dark fermion. The fast growth has a rich set of phenomenological implications. We outline implications for the formation of primordial black …
We numerically study the primordial black hole (PBH) formation by an isocurvature perturbation of a massless scalar field on super Hubble scales in the radiation-dominated universe. As a first step we perform simulations of spherically symmetric configurations. For the initial condition, we employ the spatial gradient expansion and provide the general form of the growing mode solutions valid up through the second order in this expansion. The initial scalar field profile is assumed to be Gaussian with a characteristic comoving wavenumber $k$; $\sim\exp(-k^2R^2)$, where $R$ is the radial coordin…
We study the effects of velocity dispersion on the formation of primordial black holes~(PBHs) in a matter-dominated era. The velocity dispersion is generated through the nonlinear growth of perturbations and has the potential to impede the gravitational collapse and thereby the formation of PBHs. To make discussions clear, we consider two distinct length scales. The larger one is where gravitational collapse occurs which could lead to PBH formation, and the smaller one is where the velocity dispersion develops due to nonlinear interactions. We estimate the effect of the velocity dispersion on …
We present cosmological constraints from Planck 2015 data for a universe that is kinetically dominated at very early times. We perform a Markov chain Monte Carlo analysis to estimate parameters and use nested sampling to determine the evidence for a model comparison of the single-field quadratic and Starobinsky inflationary models with the standard $Λ$CDM cosmology. In particular we investigate how different amounts of inflation before and after horizon exit affect the primordial power spectrum and subsequently the power spectrum of the cosmic microwave background. We find that the model using…
We study production of primordial black holes (PBHs) during an early matter-dominated phase. As a source of perturbations, we consider either the inflaton field with a running spectral index or a spectator field that has a blue spectrum and thus provides a significant contribution to the PBH production at small scales. First, we identify the region of the parameter space where a significant fraction of the observed dark matter can be produced, taking into account all current PBH constraints. Then, we present constraints on the amplitude and spectral index of the spectator field as a function o…
We present precision calculations of dark radiation in the form of gravitons coming from Hawking evaporation of spinning primordial black holes (PBHs) in the early Universe. Our calculation incorporates a careful treatment of extended spin distributions of a population of PBHs, the PBH reheating temperature, and the number of relativistic degrees of freedom. We compare our precision results with those existing in the literature, and show constraints on PBHs from current bounds on dark radiation from BBN and the CMB, as well as the projected sensitivity of CMB Stage 4 experiments. As an applica…
We perform (3+1)-dimensional simulations of primordial black hole (PBH) formation starting from the spheroidal super-horizon perturbations. We investigate how the ellipticity (prolateness or oblateness) affects the threshold of PBH formation in terms of the peak amplitude of curvature perturbation. We find that, in the case of the radiation-dominated universe, the effect of ellipticity on the threshold is negligibly small for the large amplitude of perturbations expected for PBH formation.
Primordial gravitational waves (PGW) produced during inflation span a large range of frequencies, carrying information on the dynamics of the primordial universe. During an early scalar-tensor dominated epoch, the amplitude of the PGW spectrum can be enhanced over a wide range of frequencies. To study this phenomenon, we focus on a class of scalar-tensor theories, well motivated by high energy theories of dark energy and dark matter, where the scalar is conformally and disformally coupled to matter during the early cosmological evolution. For a conformally dominated epoch, the PGW spectrum has…
Two gravitational wave events, i.e. GW200105 and GW200115, were observed by the Advanced LIGO and Virgo detectors recently. In this work, we show that they can be explained by a scenario of primordial black hole binaries that are formed in the early Universe. The merger rate predicted by such a scenario could be consistent with the one estimated from LIGO and Virgo, even if primordial black holes constitute a fraction of cold dark matter. The required abundance of primordial black holes is compatible with the existing upper limits from microlensing, caustic crossing and cosmic microwave backgr…
Primordial Black Holes (PBHs) are, typically light, black holes which can form in the early Universe. There are a number of formation mechanisms, including the collapse of large density perturbations, cosmic string loops and bubble collisions. The number of PBHs formed is tightly constrained by the consequences of their evaporation and their lensing and dynamical effects. Therefore PBHs are a powerful probe of the physics of the early Universe, in particular models of inflation. They are also a potential cold dark matter candidate.
The phenomenology of primordial black hole (PBH) physics and the associated PBH abundance constraints, can be used in order to probe the physics of the early Universe. In this work, we investigate the PBH formation during the standard radiation-dominated era by studying the effect of an early F(R) modified gravity phase with a bouncing behavior which is introduced to avoid the initial spacetime singularity problem. In particular, we calculate the energy density power spectrum at horizon crossing time and then we extract the PBH abundance in the context of peak theory as a function of the param…
We elaborate on the mass function of primordial black holes in the case in which the power spectrum of the curvature perturbation is broad. For the case of a broad and flat spectrum, we argue that such a mass function is peaked at the smallest primordial black mass which can be formed and possesses a tail decaying like $M^{-3/2}$, where $M$ is the mass of the primordial black hole.
We consider cosmological evolution in Brans-Dicke theory with a population of primordial black holes. Hawking radiation from the primordial black holes impacts various astrophysical processes during the evolution of the Universe. The accretion of radiation by the black holes in the radiation dominated era may be effective in imparting them a longer lifetime. We present a detailed study of how this affects various standard astrophysical constraints coming from the evaporation of primordial black holes. We analyze constraints from the present density of the Universe, the present photon spectrum,…
We investigate the phenomenological consequences of axion-like particle (ALP) dark matter with an early matter domination triggered by primordial black holes (PBHs). We focus on light BHs with masses smaller than $\sim 10^9~$g which fully evaporate before Big Bang nucleosynthesis. We numerically solve the coupled Boltzmann equations, carefully taking the greybody factors and BH angular momentum into account. We find that the entropy injection from PBH evaporation dilutes the ALP relic abundance originally produced via the vacuum misalignment mechanism, opening the parameter space with larger s…
Assuming that inflation is followed by a phase where the energy density of the Universe is dominated by a component with a general equation of state, we evaluate the spectrum of primordial gravitational waves induced in the post-inflationary Universe. We show that if the energy density of the Universe is dominated by a component $ϕ$ before Big Bang nucleosynthesis, its equation of state could be constrained by gravitational wave experiments depending on the ratio of energy densities of $ϕ$ and radiation, and also the temperature at the end of the $ϕ$ dominated era. Also, we discuss the impact …
Within the framework that primordial black holes are formed by the direct gravitational collapse of large primordial density perturbations in the radiation dominated stage, we derive the threshold of the density contrast for the formation of rotating primordial black holes based on the simple Jeans criterion. It is found that the threshold value increases in proportion to the square of the angular momentum. We then apply the recently refined analysis on the formation threshold for non-rotating black holes to the case of rotating black holes, and contrast the derived threshold with the former. …
A possibility of pregalactic seeds of the Active Galactic Nuclei can be a nontrivial cosmological consequence of particle theory. Such seeds can appear as Primordial Black Hole (PBH) clusters, formed in the succession of phase transitions with spontaneous and then manifest breaking of the global U(1) symmetry. If the first phase transition takes place at the inflationary stage, a set of massive closed walls may be formed at the second phase transition and the collapse of these closed walls can result in formation of PBH clusters. We present the results of our studies of the evolution of such P…
Primordial Black Holes (PBHs) that form from the collapse of density perturbations are more clustered than the underlying density field. In a previous paper, we showed the constraints that this has on the prospects of PBH dark matter. In this paper we examine another consequence of this clustering: the formation of bound systems of PBHs in the early universe. These would hypothetically be the earliest gravitationally collapsed structures, forming when the universe is still radiation dominated. Depending upon the size and occupation of the clusters, PBH merging occurs before they would have oth…
There exist two kinds of stochastic gravitational-wave backgrounds associated with the primordial curvature perturbations. One is called induced gravitational wave due to the nonlinear coupling of curvature perturbations to tensor perturbations, while the other is produced by coalescences of binary primordial black holes formed when the large amplitude curvature perturbations reenter the horizon in the radiation dominant era. In this paper we find a quite useful relation for the peak frequencies of these two stochastic gravitational-wave backgrounds. This relation can not only offer a smoking-…
Angular momentum plays very important roles in the formation of PBHs in the matter-dominated phase if it lasts sufficiently long. In fact, most collapsing masses are bounced back due to centrifugal force, since angular momentum significantly grows before collapse. As a consequence, most of the formed PBHs are rapidly rotating near the extreme value $a_{*}=1$, where $a_{*}$ is the nondimensional Kerr parameter at their formation. The smaller the density fluctuation $σ_{H}$ at horizon entry is, the stronger the tendency towards the extreme rotation. Combining the effect of angular momentum with …
Primordial black hole (PBH) is a fascinating candidate for the origin of binary merger events observed by LIGO-Virgo collaboration. The spatial distribution of PBHs at formation is an important feature to estimate the merger rate. We investigate the clustering of PBHs formed by Affleck-Dine (AD) baryogenesis, where dense baryon bubbles collapse to form PBHs. We found that formed PBHs show a strong clustering due to the stochastic dynamics of the AD field. Including the clustering, we evaluate the merger rate and isocurvature perturbations of PBHs, which show significant deviations from those w…
For the first time the antineutrino spectrum formed as a result of neutron and tritium decays during the epoch of primordial nucleosynthesis is calculated. This spectrum is a non-thermal increase in addition to the standard cosmic neutrino background (C$ν$B) whose thermal spectrum was formed before the beginning of primordial nucleosynthesis. For energy larger than $10^{-2}\,$eV the calculated non-thermal antineutrino flux exceeds the C$ν$B spectrum and there are no other comparable sources of antineutrino in this range. The observations of these antineutrinos will allow us to look directly at…
