We update the constraints on the fraction of the Universe that may have gone into primordial black holes (PBHs) over the mass range $10^{-5}\text{--}10^{50}$ g. Those smaller than $\sim 10^{15}$ g would have evaporated by now due to Hawking radiation, so their abundance at formation is constrained by the effects of evaporated particles on big bang nucleosynthesis, the cosmic microwave background (CMB), the Galactic and extragalactic $γ$-ray and cosmic ray backgrounds and the possible generation of stable Planck mass relics. PBHs larger than $\sim 10^{15}$ g are subject to a variety of constraints associated with gravitational lensing, dynamical effects, influence on large-scale structure, accretion and gravitational waves. We discuss the constraints on both the initial collapse fraction and the current fraction of the CDM in PBHs at each mass scale but stress that many of the constraints are associated with observational or theoretical uncertainties. We also consider indirect constraints associated with the amplitude of the primordial density fluctuations, such as second-order tensor perturbations and $μ$-distortions arising from the effect of acoustic reheating on the CMB, if PBHs are created from the high-$σ$ peaks of nearly Gaussian fluctuations. Finally we discuss how the constraints are modified if the PBHs have an extended mass function, this being relevant if PBHs provide some combination of the dark matter, the LIGO/Virgo coalescences and the seeds for cosmic structure. Even if PBHs make a small contribution to the dark matter, they could play an important cosmological role and provide a unique probe of the early Universe.
Primordial black holes, formed from rare peaks in the primordial fluctuations $ζ$, are non-rotating at zeroth order in $ζ_{\rm rms}$. We show that the spin also vanishes at first order in $ζ_{\rm rms}$, suggesting the dimensionless spin parameter $a_{\rm rms} \sim ζ_{\rm rms}^2$. We identify one quadratic contribution to the spin by calculating (and extrapolating to the formation time) the torque on a black hole due to ambient acoustic waves. For a reasonable density of primordial black holes this implies a percent level spin parameter.
We show that fragmentation of the inflaton into long-lived spatially localized oscillon configurations can lead to copious production of black holes. In a single-field inflation model primordial black holes of sublunar mass can form, and they can account for all of the dark matter. We also explore the possibility that solar-mass primordial black holes, particularly relevant for gravitational wave astronomy, are produced from the same mechanism.
We develop an analytic formalism for computing the merger rate of primordial black hole binaries with a general mass function by taking into account the torques by the surrounding primordial black holes and linear density perturbations. We find that $α=-(m_{i}+m_{j})^2\partial^{2} \ln {\mathcal R}(m_{i},m_{j})/\partial m_{i} \partial m_{j}=36/37$ is independent of the mass function. Moreover, the ratio of the merger rate density of primordial black hole binaries by taking into account the torques by the surrounding primordial black holes to by the nearest primordial black hole is independent o…
We formulate the two-point correlation function of primordial black holes (PBHs) at their formation time, based on the functional integration approach which has often been used in the context of halo clustering. We find that PBH clustering on super-Hubble scales could never be induced in the case where the initial primordial fluctuations are Gaussian, while it can be enhanced by the so-called local-type trispectrum (four-point correlation function) of the primordial curvature perturbations.
The merger rate of primordial black holes depends on their initial clustering. In the absence of primordial non-Gaussianity correlating short and large-scales, primordial black holes are distributed à la Poisson at the time of their formation. However, primordial non-Gaussianity of the local-type may correlate primordial black holes on large-scales. We show that future experiments looking for CMB $μ$-distortion would test the hypothesis of initial primordial black hole clustering induced by local non-Gaussianity, while existing limits already show that significant non-Gaussianity is necessary …
Primordial black holes are produced in a minimal UV extension to the Higgs inflation with an included $R^2$ term. We show that for parameters consistent with Standard Model measurements and Planck observation results lead to $M_{\rm PBH} \in (10^{-16}, 10^{-15}) M_\odot$ primordial black holes with significant abundance, which may consist the majority of dark matter.
Combining constraints from microlensing and Lyman-$α$ forest, we provide a simple argument to show that large spatial clustering of stellar-mass primordial black holes at the time of formation, such as the one induced by the presence of large non-Gaussianities, is ruled out. Therefore, it is not possible to evade existing constraints preventing stellar-mass primordial black holes to be a dominant constituent of the dark matter by boosting their initial clustering.
We analyze primordial non-gaussianities in presence of an ultra-slow phase during the inflationary dynamics, focusing on scenarios relevant for the production of primordial black holes. We compute the three-point correlation function of comoving curvature perturbations finding that non-gaussianities are sizable, and predominantly local. In the context of threshold statistics, we analyze their impact for the abundance of primordial black holes, and their interplay with the non-gaussianities arising from the non-linear relation between density and curvature perturbations. We find that non-gaussi…
Primordial black holes may owe their origin to the small-scale enhancement of the comoving curvature perturbation generated during inflation. Their mass fraction at formation is markedly sensitive to possible non-Gaussianities in such large, but rare fluctuations. We discuss a path-integral formulation which provides the exact mass fraction of primordial black holes at formation in the presence of non-Gaussianity. Through a couple of classes of models, one based on single-field inflation and the other on spectator fields, we show that restricting to a Gaussian statistics may lead to severe ina…
The final mass distribution of primordial black holes is sensitive to the equation of state of the Universe at the scales accessible by the power spectrum. Motivated by the presence of phase transitions in several beyond the Standard Model theories, some of which are strongly coupled, we analyze the production of primordial black holes during such phase transitions, which we model using the gauge/gravity duality. We focus in the (often regarded as physically uninteresting) case for which the phase transition is just a smooth crossover. We find an enhancement of primordial black hole production…
The properties of primordial curvature perturbations on small scales are still unknown while those on large scales have been well probed by the observations of the cosmic microwave background anisotropies and the large scale structure. In this paper, we propose the reconstruction method of primordial curvature perturbations on small scales through the merger rate of binary primordial black holes, which could form from large primordial curvature perturbation on small scales.
Models of Co-Decaying dark matter lead to an early matter dominated epoch -- prior to BBN -- which results in an enhancement of the growth of dark matter substructure. If these primordial structures collapse further they can form primordial black holes providing an additional dark matter candidate. We derive the mass fraction in these black holes (which is not monochromatic) and consider observational constraints on how much of the dark matter could be comprised in these relics. We find that in many cases they can be a significant fraction of the dark matter. Interestingly, the masses of these…
We calculate the exact formation probability of primordial black holes generated during the collapse at horizon re-entry of large fluctuations produced during inflation, such as those ascribed to a period of ultra-slow-roll. We show that it interpolates between a Gaussian at small values of the average density contrast and a Cauchy probability distribution at large values. The corresponding abundance of primordial black holes may be larger than the Gaussian one by several orders of magnitude. The mass function is also shifted towards larger masses.
We report on a novel phenomenon of the resonance effect of primordial density perturbations arisen from a sound speed parameter with an oscillatory behavior, which can generically lead to the formation of primordial black holes in the early Universe. For a general inflaton field, it can seed primordial density fluctuations and their propagation is governed by a parameter of sound speed square. Once if this parameter achieves an oscillatory feature for a while during inflation, a significant non-perturbative resonance effect on the inflaton field fluctuations takes place around a critical lengt…
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.
Primordial black holes might comprise a significant fraction of the dark matter in the Universe and be responsible for the gravitational wave signals from black hole mergers observed by the LIGO/Virgo collaboration. The spatial clustering of primordial black holes might affect their merger rates and have a significant impact on the constraints on their masses and abundances. We provide some analytical treatment of the primordial black hole spatial clustering evolution, compare our results with some of the existing N-body numerical simulations and discuss the implications for the black hole mer…
A common mechanism to form primordial black holes in the early universe is by enhancing at small-scales the scalar perturbations generated during inflation. If these fluctuations have a large enough amplitude, they may collapse into primordial black holes upon horizon re-entry. Such primordial black holes may comprise the totality of the dark matter. We offer some considerations about the formation and clustering of primordial black holes when the scalar perturbations are characterised by a broad spectrum. Using the excursion set method, as well as the supreme statistics, we show that the clou…
As a candidate bound for the Binary Black Hole (BBH) merger events detected by LIGO/Virgo, Primordial Black Holes (PBHs) provide a useful tool to investigate the primordial curvature perturbations on small scales. Using the GWTC-1 to GWTC-3 catalogs, under the scenario that PBHs originate from large primordial curvature perturbations on small scales during inflationary epoch, we for the first time reconstruct the power spectrum of primordial curvature perturbations on small scales. It is found that the value of the amplitude of the primordial power spectrum is enhanced to $\mathcal{O}(10^{-2})…
In response to a recent criticism, appeared in arXiv:2303.00341, we argue that the standard scenario to form primordial black holes in the early universe based on a phase of ultra-slow-roll in single-field inflation is not ruled out.
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 can be produced by a long range attractive fifth force stronger than gravity, mediated by a light scalar field interacting with nonrelativistic "heavy" particles. As soon as the energy fraction of heavy particles reaches a threshold, the fluctuations rapidly become nonlinear. The overdensities collapse into black holes or similar screened objects, without the need for any particular feature in the spectrum of primordial density fluctuations generated during inflation. We discuss whether such primordial black holes can constitute the total dark matter component in the Uni…
We consider the constraints on the fraction of dark matter in the universe in the form of primordial black holes taking into account the crucial role of accretion which may change both their mass and mass function. We show that accretion may drastically weaken the constraints at the present epoch for primordial black holes with masses larger than a few solar masses.
We argue that primordial black-hole formation must be described by means of extreme-value theory. This is a consequence of the large values of the energy density required to initiate the collapse of black holes in the early Universe and the finite duration of their collapse. Compared to the Gaussian description of the most extreme primordial density fluctuations, the holes' mass function is narrower and peaks towards larger masses. Secondly, thanks to the shallower fall-off of extreme-value distributions, the predicted abundance of primordial black holes is boosted by $10^{7}$ orders of magnit…
Advanced LIGO's discovery of gravitational-wave events is stimulating extensive studies on the origin of binary black holes. Assuming that the gravitational-wave events can be explained by binary primordial black hole mergers, we utilize the upper limits on the stochastic gravitational-wave background given by Advanced LIGO as a new observational window to independently constrain the abundance of primordial black holes in dark matter. We show that Advanced LIGO's first observation run gives the best constraint on the primordial black hole abundance in the mass range $1 M_\odot \lesssim M_\text…
We derive the strongest constraint on the fraction of dark matter that can be composed of low mass primordial black holes by using the observation of the Galactic Center 511 keV gamma-ray line. Primordial black holes of masses $\lesssim$ 10$^{15}$ kg will evaporate to produce $e^\pm$ pairs. The positrons will lose energy in the Galactic Center, become non-relativistic, and then annihilate with the ambient electrons. We derive robust and conservative bounds by assuming that the rate of positron injection via primordial black hole evaporation is less than what is required to explain the SPI/ INT…
Primordial black holes can have substantial spin -- a fundamental property that has a strong effect on its evaporation rate. We conduct a comprehensive study of the detectability of primordial black holes with non-negligible spin, via the searches for the neutrinos and positrons in the MeV energy range. Diffuse supernova neutrino background searches and observation of the 511 keV gamma-ray line from positrons in the Galactic center set competitive constraints. Spinning primordial black holes are probed up to a slightly higher mass range compared to non-spinning ones. Our constraint using neutr…
The next generation of gravitational-wave experiments, such as Einstein Telescope, Cosmic Explorer and LISA, will test the primordial black hole scenario. We provide a forecast for the minimum testable value of the abundance of primordial black holes as a function of their masses for both the unclustered and clustered spatial distributions at formation. In particular, we show that these instruments may test abundances, relative to the dark matter, as low as $10^{-10}$.
Primordial black holes as dark matter may be generated in single-field models of inflation thanks to the enhancement at small scales of the comoving curvature perturbation. This mechanism requires leaving the slow-roll phase to enter a non-attractor phase during which the inflaton travels across a plateau and its velocity drops down exponentially. We argue that quantum diffusion has a significant impact on the primordial black hole mass fraction making the classical standard prediction not trustable.
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 devise a novel mechanism and for the first time demonstrate that the Higgs model in particle physics can drive the inflation to satisfy the cosmic microwave background observations and simultaneously enhance the curvature perturbations at small scales to explain the abundance of dark matter in our universe in the form of primordial black holes. The production of primordial black holes is accompanied by the secondary gravitational waves induced by the first order Higgs fluctuations which is expected observable by space-based gravitational wave detectors. We propose possible cosmological prob…
We perform a hierarchical Bayesian analysis of the GWTC-2 catalog to investigate the mixed scenario in which the merger events are explained by black holes of both astrophysical and primordial origin. For the astrophysical scenario we adopt the phenomenological model used by the LIGO/Virgo collaboration and we include the correlation between different parameters inferred from data, the role of the spins in both the primordial and astrophysical scenarios, and the impact of accretion in the primordial scenario. Our best-fit mixed model has a strong statistical evidence relative to the single-pop…
We investigate a new mechanism to create large curvature perturbations on small scales due to parameter resonance in a single-field inflationary model with a small periodic structure upon the potential. After reentering the horizon, the amplified curvature perturbations can lead to observable primordial black holes as well as stochastic gravitational waves. The mass of primordial black holes and frequency of the induced gravitational waves depend on the model parameters. The resulted primordial black hole could constitute all dark matter or a fraction of dark matter in the universe, and corres…
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.
There is a growing expectation that the gravitational wave detectors will start probing the stochastic gravitational wave backgrounds in the following years. We explore the spectral shapes of gravitational waves induced to second order by scalar perturbations and presumably have been produced in the early universe. We calculate the gravitational wave spectra generated during radiation and kination eras together with the associated primordial black hole counterpart. We employ power spectra for the primordial curvature perturbation generated by $α$-attractors and nonminimal derivative coupling i…
We study the influence of lepton flavour asymmetries on the formation and the mass spectrum of primordial black holes. We estimate the detectability of their mergers with LIGO/Virgo and show that the currently published gravitational wave events may actually be described by a primordial black hole spectrum from non-zero asymmetries. We suggest to use gravitational-wave astronomy as a novel tool to probe how lepton flavour asymmetric the Universe has been before the onset of neutrino oscillations.
Primordial black holes which are produced during an epoch of matter domination are expected to spin rapidly. It is shown that this leads to an enhancement of the detectability of the stochastic gravitational-wave background from their mergers. For a specific model, we explicitly demonstrate that this yields a $50\,\%$ increase of the gravitational-wave amplitude as compared to the non-spinning case.
A standard scenario to form primordial black holes in the early universe is based on a phase of ultra-slow-roll in single-field inflation when the amplitude of the short scale modes is enhanced compared to the CMB plateau. Based on general arguments, we show that the loop corrections to the large-scale linear power spectrum from the short modes are small and conclude that the scenario is not ruled out.
The "swampland conjectures" have been recently suggested as a set of criteria to assess if effective field theories (EFTs) are consistent with a quantum gravity embedding. Such criteria, which restrict the behavior of scalar fields in the theory, have strong implications for cosmology in the early universe. As we demonstrate, they will also have direct consequences for formation of primordial black holes (PBHs) and dark matter (DM).
It was recently demonstrated that small small black holes can act as seeds for nucleating decay of the metastable Higgs vacuum, dramatically increasing the tunneling probability. Any primordial black hole lighter than $4.5 \times 10^{14}$g at formation would have evaporated by now, and in the absence of new physics beyond the standard model, would therefore have entered the mass range in which seeded decay occurs, however, such true vacuum bubbles must percolate in order to completely destroy the false vacuum; this depends on the bubble number density and the rate of expansion of the universe.…
The possibility that primordial black holes (PBHs) are the dark matter (or a fraction thereof) has attracted much attention recently. Their spatial clustering is a fundamental property which determines, among others, whether current observational constraints are evaded within a given mass range, whether merging is significant and whether primordial black holes could generate cosmological structure. We treat them as discrete objects and clarify the issue of their spatial clustering, with an emphasis on short-range exclusion and its impact on their large scale power spectrum. Even if a Poissonia…
The observational data of primordial black holes and scalar-induced gravitational waves can constrain the primordial curvature perturbation at small scales. We parameterize the primordial curvature perturbation by a broken power law form and find that it is consistent with many inflation models that can produce primordial black holes, such as nonminimal derivative coupling inflation, scalar-tensor inflation, Gauss-Bonnet inflation, and K/G inflation. The constraints from primordial black holes on the primordial curvature power spectrum with the broken power law form are obtained, where the fra…
