Florian Kuhnel, Marit Sandstad
We reinvestigate gravitational ellipsoidal collapse with special focus on its impact on primordial black-hole formation. For a generic model we demonstrate that the abundance and energy density of the produced primordial black holes will be significantly decreased when the non-sphericity of the overdensities is taken into account.
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We have studied the merger rate of primordial black holes (PBHs) in the ellipsoidal-collapse model of halo to explain the dark matter abundance by the PBH merger estimated from the gravitational waves detections via the Advanced LIGO (aLIGO) detectors. We have indicated that the PBH merger rate within each halo for the ellipsoidal models is more significant than for the spherical models. We have specified that the PBH merger rate per unit time and per unit volume for the ellipsoidal-collapse halo models is about one order of magnitude higher than the corresponding spherical models. Moreover, w…
Primordial black holes (PBHs), as a potential macroscopic candidate for dark matter, can encounter other compact objects in dark matter halos because of their random distribution. Besides, the detection of gravitational waves (GWs) related to the stellar-mass black hole-neutron star (BH-NS) mergers raises the possibility that the BHs involved in such events may have a primordial origin. In this work, we calculate the merger rate of PBH-NS binaries within the framework of ellipsoidal-collapse dark matter halo models and compare it with the corresponding results derived from spherical-collapse d…
We evaluate the effect of structure formation on the average expansion rate with a statistical treatment where density peaks and troughs are modelled as homogeneous ellipsoids. This extends earlier work that used spherical regions. We find that the shear and the presence of filamentary and planar structures have only a small impact on the results. The expansion rate times the age of the universe $Ht$ increases from 2/3 to 0.83 at late times, in order of magnitude agreement with observations, although the change is slower and takes longer than in the real universe. We discuss shortcomings that …
In the excursion set approach to structure formation initially spherical regions of the linear density field collapse to form haloes of mass $M$ at redshift $z_{\rm id}$ if their linearly extrapolated density contrast, averaged on that scale, exceeds some critical threshold, $δ_{\rm c}(z_{\rm id})$. The value of $δ_{\rm c}(z_{\rm id})$ is often calculated from the spherical or ellipsoidal collapse model, which provide well-defined predictions given auxiliary properties of the tidal field at a given location. We use two cosmological simulations of structure growth in a $Λ$ cold dark matter scen…
We use the Excursion Set formalism to compute the properties of the halo mass distribution for a stochastic barrier model which encapsulates the main features of the ellipsoidal collapse of dark matter halos. Non-markovian corrections due to the sharp filtering of the linear density field in real space are computed with the path-integral technique introduced by Maggiore & Riotto (2010). Here, we provide a detailed derivation of the results presented in Corasaniti & Achitouv (2011) and extend the mass function analysis to higher redshift. We also derive an analytical expression for the linear h…
We describe an algorithm for identifying ellipsoidal haloes in numerical simulations, and quantify how the resulting estimates of halo mass and shape differ with respect to spherical halo finders. Haloes become more prolate when fit with ellipsoids, the difference being most pronounced for the more aspherical objects. Although the ellipsoidal mass is systematically larger, this is less than 10% for most of the haloes. However, even this small difference in mass corresponds to a significant difference in shape. We quantify these effects also on the initial mass and deformation tensors, on which…
Simulations of Ellipsoidal Primordial Black Hole Formation
通过相对论数值模拟，研究了非球形扰动坍缩形成原初黑洞的阈值，发现临界参数遵循超椭圆曲线，且微小非球形性在临界振幅下可避免黑洞形成。
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.
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 …
The smallest dark matter haloes are the first objects to form in the hierarchical structure formation of cold dark matter (CDM) cosmology and are expected to be the densest and most fundamental building blocks of CDM structures in our universe. Nevertheless, the physical characteristics of these haloes have stayed illusive, as they remain well beyond the current resolution of N-body simulations (at redshift zero). However, they dominate the predictions (and uncertainty) in expected dark matter annihilation signal, amongst other astrophysical observables. Using the conservation of total energy …
"The self-induced collapse hypothesis" was introduced by D. Sudarsky and collaborators to explain the origin of cosmic structure from a perfect isotropic and homogeneous universe during the inflationary regime. In this paper, we calculate the power spectrum for the tensor modes, within the semiclassical gravity approximation, with the additional hypothesis of a generic self-induced collapse of the inflaton's wave function; we also compute an estimate for the tensor-to-scalar ratio. Based on this calculation, we show that the considered proposal exhibits a strong suppression of the tensor modes…
Compact Binary Merger Rate in Dark-Matter Spikes
本文计算球形与椭球形坍缩暗物质晕模型下暗物质尖峰中的致密双星并合率，发现椭球坍缩可增强并合率，且原初黑洞双星结果符合 LIGO-Virgo 观测。
Primordial black holes (PBHs) are a useful tool in cosmology to probe primordial inhomogeneities on small scales that reenter the Hubble radius during the radiation dominated epoch. In this paper, a phenomenon we call the double formation of PBHs, described below, is explored. Suppose there exists a highly perturbed region which will collapse to form a PBH after the horizon crossing of this region, and farther that this region is superposed on much larger region, which also collapses upon reentry. One then expects the collapse of the central smaller region at the time of the crossing of this r…
Primordial Black Holes in a Radiation-Dominated Universe
通过3+1广义相对论模拟，研究辐射主导时期超密区域直接坍缩形成原初黑洞的阈值，发现临界密度扰动在0.77到0.83之间。
We use two cosmological simulations of structure formation in the LambdaCDM scenario to study the evolutionary histories of dark-matter haloes and to characterize the Lagrangian regions from which they form. We focus on haloes identified at redshift z_id=0 and show that the classic ellipsoidal collapse model systematically overestimates their collapse times. If one imposes that halo collapse takes place at z_id, this model requires starting from a significantly lower linear density contrast than what is measured in the simulations at the locations of halo formation. We attempt to explain this …
Large-amplitude density perturbations may have collapsed during the radiation dominated epoch of the Universe to form primordial black holes (PBHs). There are several constraints to the abundance of PBHs that stem from evaporation or gravitational effects. Due to the connection between primordial perturbations and the formation of PBHs, constraints on the present-day abundance of PBHs can be translated into limits on the primordial curvature power spectrum. We introduce several new observational and forecasted constraints to the amplitude of the primordial power spectrum and incorporate in our…
The Reheating process at the end of inflation is often modeled by an oscillating scalar field which shows a background dust-like behaviour, prompting the analysis of gravitational collapse and black hole formation in this era to be approached by the spherical collapse of standard structure formation. In the scalar field dark matter structure formation process virialized halos halt the direct collapse, resulting in halos with condensed central cores at the de Broglie scale of the dominant scalar field. We show that a similar process can take place during reheating, leading to the formation of p…
Primordial Black Hole Formation in Rastall Gravity: Shifted Collapse Threshold and Exponential Abundance Sensitivity
研究Rastall引力中原始黑洞的形成，发现该参数改变了坍缩动力学，影响密度波动增长、黑洞形成临界阈值和视界交叉时的波动幅度，表明原始黑洞形成对Rastall引力扰动层面的修改具有敏感性和独立探测能力。
Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
研究随机效应如何影响原始黑洞的丰度和质量，通过压缩函数分析不同质量种子黑洞的坍缩过程，发现随机冲击可使丰度增加36个数量级，但存在收敛性问题。
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…
Primordial naked singularities
本文提出早期宇宙引力坍缩不仅形成原初黑洞，还会产生原初裸奇点，并探讨其对暗物质等宇宙可观测特征的影响。
We estimate the spin distribution of primordial black holes based on the recent study of the critical phenomena in the gravitational collapse of a rotating radiation fluid. We find that primordial black holes are mostly slowly rotating.
The statistical properties of the primordial density perturbations has been considered in the past decade as a powerful probe of the physical processes taking place in the early universe. Within the inflationary paradigm, the properties of the bispectrum are one of the keys that serves to discriminate among competing scenarios concerning the details of the origin of cosmological perturbations. However, all of the scenarios, based on the conventional approach to the so-called "quantum-to-classical transition" during inflation, lack the ability to point out the precise physical mechanism respons…
We want to study the perturbation growth of an initial seed of an ellipsoidal shape in Top-Hat collapse model of structure formation in the Modified Chaplygin gas cosmology. Considering reasonable values of the constants and the parameters of the model under study, it is shown that a very small deviation from spherical symmetry (ellipsoidal geometry) in the initial seed leads to a final highly non-spherical structure which can be considered as a candidate for justifying already known cosmological structures as cosmic walls and filaments.
Nearly Monochromatic Primordial Black Holes as total Dark Matter from Bubble Collapse
该研究提出一个双场模型，通过非最小耦合实现原初黑洞作为总暗物质的形成机制，无需增强原始曲率扰动。
Primordial Black Holes from Primordial Voids
研究通过原初空洞的非线性反弹机制，揭示了原初黑洞形成的新途径，并探讨其对暗物质丰度和宇宙学信号的影响。
Primordial black hole formation processes with full numerical relativity
本论文利用全数值相对论模拟物质主导早期宇宙中的原初黑洞形成，区分直接坍缩与吸积坍缩机制，并分析黑洞快速增长及旋转形成时的质量、角动量转移效率。
We reconsider the ellipsoidal-collapse model and extend it in two ways: We modify the treatment of the external gravitational shear field, introducing a hybrid model in between linear and non-linear evolution, and we introduce a virialisation criterion derived from the tensor virial theorem to replace the ad-hoc criterion employed so far. We compute the collapse parameters delta_c and Delta_v and find that they increase with ellipticity e and decrease with prolaticity p. We marginalise them over the appropriate distribution of e and p and show the marginalised results as functions of halo mass…
Gravitational-wave signatures of primordial black hole clusters and the imprint of an early dense-core collapse
针对原初黑洞团自旋产生与宇宙学存续的矛盾，本研究提出致密核心+延展暗晕的结构模型，通过N体模拟揭示其引力波特征，为引力波观测解读提供新框架。
Why the Universal Threshold for Primordial Black Hole Formation is Universal
本研究利用临界引力坍缩的自相似性，证明了以体积平均压实函数表示的原初黑洞形成阈值与扰动形状无关，从而解释其普适性。
Primordial black holes (PBHs) are of fundamental interest in cosmology and astrophysics, and have received much attention as a dark matter candidate and as a potential source of gravitational waves. One possible PBH formation mechanism is the gravitational collapse of cosmic strings. Thus far, the entirety of the literature on PBH production from cosmic strings has focused on the collapse of (quasi)circular cosmic string loops, which make up only a tiny fraction of the cosmic loop population. We demonstrate here a novel PBH formation mechanism: the collapse of a small segment of cosmic string …
From Cosmic Bounces to Primordial Black Holes: The Role of Primordial Magnetic Fields
研究非奇异ekpyrotic反弹产生的原初磁场对原初黑洞形成的作用，通过保留有限波数截断计算曲率谱等，确定原初黑洞丰度，明确有限波数截断和坍缩假设在关联反弹磁生成与原初黑洞丰度中的关键作用。
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.
Gravitational Lensing in More Realistic Dark Matter Halo Models
本研究采用更现实的暗物质晕模型（含椭球塌缩等条件）分析引力透镜，结合 NFW 和 Einasto 轮廓及点质量与 SIS 模型计算爱因斯坦半径等观测量，发现现实模型能显著增强透镜效应并更准确反映暗物质复杂结构。
We examine the shape of the primordial black hole mass distribution arising from a peak in the primordial power spectrum. In light of improvements to the modelling, we revisit the claim that the effects of critical collapse produce a distribution that is not described by the commonly assumed lognormal, showing that this conclusion remains valid, particularly for narrow peaks where the shape of the mass distribution is insensitive to the peak properties and critical collapse determines a minimum width. We propose some alternative models that may better describe the shape, both for the narrow pe…
The first billion years in the evolution of the Universe mark the formation of the first stars, black holes and galaxies. The radiation from the first galaxies plays an important role in determining the final state of primordial gas collapsing in a neighboring halo. This is due to the fact that the primary coolant for primordial gas is molecular hydrogen, which can be dissociated into atomic hydrogen by Lyman-Werner photons in the energy range $11.2 - 13.6$~eV. While cooling by molecular hydrogen leads to Pop. III star formation, cooling by atomic hydrogen can lead to the formation of a superm…
Relic gravitational waves from primordial gravitational collapses
本文通过混合数值分析研究早期宇宙声壳碰撞产生的随机引力波背景，其峰值频率和振幅取决于哈勃视界与声壳丰度，可为未来探测器及已蒸发原初黑洞提供观测约束。
Primordial Black Hole Formation in a Scalar Field Dominated Universe: Investigation of the Critical nature of the Collapse
本文通过相对论数值模拟研究了标量场主导宇宙中原初黑洞形成的临界坍缩，发现其与辐射主导情形均表现出II型临界行为且临界指数相近，证实了临界指数的近普适性。
Primordial power spectrum from an objective collapse mechanism: The simplest case
本文基于半经典引力和CSL客观坍缩模型，从最简单选择出发构建坍缩机制，打破暴胀期Bunch-Davies真空的对称性，得到与标准谱一致且符合宇宙微波背景观测的原初功率谱。
In excursion set theory the computation of the halo mass function is mapped into a first-passage time process in the presence of a barrier, which in the spherical collapse model is a constant and in the ellipsoidal collapse model is a fixed function of the variance of the smoothed density field. However, N-body simulations show that dark matter halos grow through a mixture of smooth accretion, violent encounters and fragmentations, and modeling halo collapse as spherical, or even as ellipsoidal, is a significant oversimplification. We propose that some of the physical complications inherent to…
On Formation of Primordial Naked Singularities
本文研究由带非平凡势的最小耦合标量场引发的原初引力坍缩，给出视界面不形成并产生可被外部观测者看到的原初裸奇点的参数范围。
We show that primordial black holes can be produced from the collapse of large isocurvature perturbations of the cold dark matter. We develop a novel procedure to compute the resulting black hole abundance by studying matched perturbations of matter-only universes, and we use our procedure to translate observational constraints on black hole abundances into model-independent constraints on cold dark matter isocurvature perturbations over a wide range of scales. The constraint on the typical amplitude of the primordial perturbations weakens slightly slower than linearly on small scales.
Evidences for the primordial black holes (PBH) presence in the early Universe renew permanently. New limits on their mass spectrum challenge existing models of PBH formation. One of the known model is based on the closed walls collapse after the inflationary epoch. Its intrinsic feature is multiple production of small mass PBH which might contradict observations in the nearest future. We show that the mechanism of walls collapse can be applied to produce substantially different PBH mass spectra if one takes into account the classical motion of scalar fields together with their quantum fluctuat…
Gravitational collapse, primordial black hole, and gravitational wave in Einstein--Gauss-Bonnet theory with two scalar fields
本文在含两个标量场的爱因斯坦-高斯-博内理论中，通过重构方法研究加速膨胀宇宙中的引力坍缩与原初黑洞形成，并揭示黑洞形成期间高频引力波传播速度因高斯-博内耦合而发生方向性改变。
Primordial Black Hole Formation via Inverted Bubble Collapse
提出反转气泡坍缩新机制形成原初黑洞，自然实现球对称坍缩，可产生质量高达10^-7至10^-5太阳质量的单色黑洞，解释OGLE和Subaru HSC微引力透镜事件。
In this paper, we explore the possibility of accreting primordial black holes as the source of heating for the collapsing gas in the context of the direct collapse black hole scenario for the formation of super-massive black holes (SMBHs) at high redshifts, $z\sim 6-7$. One of the essential requirements for the direct collapse model to work is to maintain the temperature of the in falling gas at $\approx 10^4$ K. We show that even under the existing abundance limits, the primordial black holes of masses $\gtrsim 10^{-2} \ {\rm M}_\odot$, can heat the collapsing gas to an extent that the ${\rm …
A small fraction, $f$, of cosmic string loops can collapse to form Primordial Black Holes (PBHs). Constraints on the abundance of PBHs can therefore be used to constrain $f$. We update these calculations, taking into account the PBH extended mass function, and find $f < 10^{-31} (G μ/ c^2)^{-3/2}$. This is roughly two orders of magnitude tighter than previous constraints. The improvement from the tighter constraints on the abundance of PBHs is partly off-set by refinements to the theoretical calculation of the cosmic string loop formation rate.
The existence (and abundance) of primordial black holes (PBHs) is governed by the power spectrum of primordial perturbations generated during inflation. So far no PBHs have been observed, and instead, increasingly stringent bounds on their existence at different scales have been obtained. Up until recently, this has been exploited in attempts to constrain parts of the inflationary power spectrum that are unconstrained by cosmological observations. We first point out that the simple translation of the PBH non-observation bounds into constraints on the primordial power spectrum is inaccurate as …
Towards supermassive primordial black holes from inflationary bubbles
本研究探讨暴胀气泡演化成超大质量原初黑洞（SMPBHs）的机制，分析亚临界气泡通过隧穿贡献SMPBHs的可能，提出SMPBHs初始成团机制以提升双体并合率，解释NANOGrav信号。
We propose a novel primordial black hole (PBH) formation mechanism based on a first-order phase transition (FOPT). If a fermion species gains a huge mass in the true vacuum, the corresponding particles get trapped in the false vacuum as they do not have sufficient energy to penetrate the bubble wall. After the FOPT, the fermions are compressed into the false vacuum remnants to form non-topological solitons called Fermi-balls, and then collapse to PBHs due to the Yukawa attractive force. We derive the PBH mass and abundance, showing that for a $\mathcal{O}({\rm GeV})$ FOPT the PBHs could be $\s…
Beyond isolated curvature peaks: collective collapse and multiple Primordial Black Hole formation
本研究通过数值模拟发现原初曲率扰动并非一对一形成原初黑洞，引入新诊断量并补充线性表面强度，表明坍缩结果还与曲率环境的空间范围等因素相关。
In this work, we study the effect of a high-precision semianalytical mass function on the merger rate of primordial black holes (PBHs) in dark matter halos. For this purpose, we first explain a theoretical framework for dark matter halo models and introduce relevant quantities such as halo density profile, concentration parameter, and a high-precision semianalytical function namely Del Popolo (DP) mass function. In the following, we calculate the merger rate of PBHs in the framework of ellipsoidal-collapse dark matter halo models while considering the DP mass function, and compare it with our …
It is generally believed that angular momentum is distributed during the gravitational collapse of the primordial star forming cloud. However, so far there has been little understanding of the exact details of the distribution. We use the modified version of the Gadget-2 code, a three-dimensional smoothed-particle hydrodynamics simulation, to follow the evolution of the collapsing gas in both idealized as well as more realistic minihalos. We find that, despite the lack of any initial turbulence and magnetic fields in the clouds the angular momentum profile follows the same characteristic power…
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 radiation emitted by horizonless exotic compact objects (ECOs), such as wormholes, 2-2-holes, fuzzballs, gravastars, boson stars, collapsed polymers, superspinars etc., is expected to be strongly suppressed when compared to the radiation of black holes. If large primordial curvature fluctuations collapse into such objects instead of black holes, they do not evaporate or evaporate much slower than black holes and could thus constitute all of the dark matter with masses below $M < 10^{-16}M_\odot.$ We reevaluate the relevant experimental constraints for light ECOs in this mass range and show…
Primordial black hole formation in k-inflation models
该研究探讨了k-本质膨胀模型中原始黑洞的形成机制及当前丰度计算方法。
Despite the ever growing observational evidence for the existence of the large scale magnetic fields, their origin and the evolution are not fully understood. If the magnetic fields are of primordial origin, they result in the generation of the secondary matter density perturbations and the previous studies show that such density perturbations enhance the number of dark matter halos. We extend the conventional spherical collapse model by including the Lorentz force which has not been implemented in the previous analysis to study the evolution of density perturbations produced by primordial mag…
The mass distribution of dark matter halos is a sensitive probe of primordial non-Gaussianity (NG). We derive an analytical formula of the halo mass function by perturbatively computing excursion set path-integrals for a non-Gaussian density field with non-vanishing skewness, fnl. We assume a stochastic barrier model which captures the main features of the ellipsoidal collapse of halos. Contrary to previous results based on extensions of the Press-Schechter formalism to NG initial conditions, we find that the non-spherical collapse of halos directly alter the signature of primordial NG. This p…
Using the concept of apparent horizon for dynamical black holes, we revisit the formation of primordial black holes (PBH) in the early universe for both linear and non-linear regimes. First, we develop the perturbation theory for spherically symmetric spacetimes to study the formation of spherical PBHs in linear regime and we fix two gauges. We also introduce a well defined gauge invariant quantity for the expansion. Using this quantity, we argue that PBHs do not form in the linear regime. Finally, we study the non-linear regime. We adopt the spherical collapse picture by taking a closed FRW m…
Primordial black holes, which could have been formed in the very early Universe due to the collapse of large curvature fluctuations, are nowadays 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-Lemaitre-Robertson-Walker background and its numerical simulation. We review the appropriate formalism for the condition…
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