Abundance Of Primordial Black Holes Research Articles

Scalar induced gravitational waves from primordial black hole Poisson fluctuations in f(R) gravity

The gravitational potential of a gas of initially randomly distributed primordial black holes (PBH) can induce a stochastic gravitational-wave (GW) background through second-order gravitational effects. This GW background can be abundantly generated in a cosmic era dominated by ultralight primordial black holes, with masses m PBH < 109g. In this work, we consider f(R) gravity as the underlying gravitational theory and we study its effect at the level of the gravitational potential of Poisson distributed primordial black holes. After a general analysis, we focus on the R 2 gravity model. In particular, by requiring that the scalar induced GWs (SIGWs) are not overproduced, we find an upper bound on the abundance of PBHs at formation time ΩPBH,f as a function of their mass, namely that ΩPBH,f < 5.5 × 10-5 (109g/m PBH)1/4, which is 45% tighter than the respective upper bound in general relativity. Afterwards, by considering R 2 gravity as an illustrative case study of an f(R) gravity model, we also set upper bound constraints on its mass parameter M. These mass parameter constraints, however, should not be regarded as physical given the fact that the Cosmic Microwave Background (CMB) constraints on R 2 gravity are quite tight. Finally, we conclude that the portal of SIGWs associated to PBH Poisson fluctuations can act as a novel complementary probe to constrain alternative gravity theories.

Revisiting the Affleck-Dine mechanism for primordial black hole formation

We study a primordial black hole (PBH) formation scenario based on the Affleck-Dine (AD) mechanism and investigate two PBH mass regions: M ∼ 30 M ⊙ motivated by the LIGO-Virgo observations of the binary black hole mergers and M ≳ 104 M ⊙ motivated by the observations of supermassive black holes at the center of galaxies. In the previous studies, it has been considered that the inhomogeneous AD baryogenesis generates regions with a large baryon asymmetry, some of which collapse into PBHs. In this paper, we show that this scenario is severely constrained due to the baryon asymmetry remaining outside PBHs, which would spoil the success of the big bang nucleosynthesis. Then, we propose an alternative scenario where the AD leptogenesis results in the inhomogeneous formation of Q-balls with lepton charges, which collapse into PBHs. As a result, we find that our scenario can explain the favorable PBH abundance without conflicting with the observational constraints.

Non-Gaussianity effects on the primordial black hole abundance for sharply-peaked primordial spectrum

We perturbatively study the effect of non-Gaussianities on the mass fraction of primordial black holes (PBHs) at the time of formation by systematically taking its effect into account in the one-point probability distribution function of the primordial curvature perturbation. We focus on the bispectrum and trispectrum and derive formulas that describe their effects on the skewness and kurtosis of the distribution function. Then considering the case of narrowly peaked spectra, we obtain simple formulas that concisely express the effect of the bi- and trispectra. In particular, together with the g NL and τ NL parameters of the trispectrum, we find that non-Gaussianity parameters for various types of the bispectrum are linearly combined to give an effective parameter, f NL eff, that determines the PBH mass fraction in the narrow spectral shape limit.

One-loop correction to the enhanced curvature perturbation with local-type non-Gaussianity for the formation of primordial black holes

As one of the promising candidates of cold dark matter (DM), primordial black holes (PBHs) were formed due to the collapse of over-densed regions generated by the enhanced curvature perturbations during the radiation-dominated era. The enhanced curvature perturbations are expected to be non-Gaussian in some relevant inflation models and hence the higher-order loop corrections to the curvature power spectrum might be non-negligible as well as altering the abundance of PBHs. In this paper, we calculate the one-loop correction to the curvature power spectrum with local-type non-Gaussianities characterizing by $F_{\mathrm{NL}}$ and $G_{\mathrm{NL}}$ standing for the quadratic and cubic non-Gaussian parameters, respectively. Requiring that the one-loop correction be subdominant, we find a perturbativity condition, namely $|2cAF_{\mathrm{NL}}^2+6AG_{\mathrm{NL}}|\ll 1$, where $c$ is a constant coefficient which can be explicitly calculated in the given model and $A$ denotes the variance of Gaussian part of enhanced curvature perturbation, and such a perturbativity condition can provide a stringent constraint on the relevant inflation models for the formation of PBHs.

Primordial black holes and gravitational waves in teleparallel Gravity

In this paper, we consider the possible effect of the teleparallel gravity on the production of the primordial black holes (PBH) and on the gravitational waves (GWs). We investigate the relationship between the slow roll, the e-folds number and the teleparallel parameters. We show that in the case of the teleparallel parameter delta =3, the e-folds number reaches the values 50 and 60 in consistency with the contour plot of the (r,n_{s}) plane obtained by Planck data at 1sigma and 2sigma C.L. Furthermore, we use the fraction of the energy density and the variance of the density perturbations approach to study the abundance of the production PBH. We find that the PBH overproduction can be satisfied for specific values of parameters of the non-adiabatic curvature power spectrum at some narrow parametric resonance. Moreover, to explain the GWs expected by observations, the duration of preheating should be bounded by values less or equal to 2. This bound is in agreement with values of the tensor-to-scalar ratio and the spectral index constrained by Planck data.

Rare events are nonperturbative: Primordial black holes from heavy-tailed distributions

In recent years it has been noted that the perturbative treatment of the statistics of fluctuations may fail to make correct predictions for the abundance of primordial black holes (PBHs). Moreover, it has been shown in some explicit single-field examples that the nonperturbative effects may lead to an exponential tail for the probability distribution function (PDF) of fluctuations responsible for PBH formation—in contrast to the PDF being Gaussian, as suggested by perturbation theory. In this paper, we advocate that the so-called δN formalism can be considered as a simple, yet effective, tool for the nonperturbative estimate of the tail of the PDF. We discuss the criteria a model needs to satisfy so that the results of the classical δN formalism can be trusted and most possible complications due to the quantum nature of fluctuations can be avoided. As a proof of concept, we then apply this method to a simple example and show that the tail of the PDF can be even heavier than exponential, leading to a significant enhancement of the PBH formation probability, compared with the predictions of the perturbation theory. Our results, along with other related findings, motivate the invention of new, nonperturbative methods for the problem and open up new ideas on generating PBHs with notable abundance.

Constraining primordial black holes using fast radio burst gravitational-lens interferometry with CHIME/FRB

Fast radio bursts (FRBs) represent an exciting frontier in the study of gravitational lensing, due to their brightness, extragalactic nature, and the compact, coherent characteristics of their emission. In a companion work [Kader, Leung+2022], we use a novel interferometric method to search for gravitationally lensed FRBs in the time domain using bursts detected by CHIME/FRB. There, we dechannelize and autocorrelate electric field data at a time resolution of 1.25 ns. This enables a search for FRBs whose emission is coherently deflected by gravitational lensing around a foreground compact object such as a primordial black hole (PBH). Here, we use our non-detection of lensed FRBs to place novel constraints on the PBH abundance outside the Local Group. We use a novel two-screen model to take into account decoherence from scattering screens in our constraints. Our constraints are subject to a single astrophysical model parameter -- the effective distance between an FRB source and the scattering screen, for which we adopt a fiducial distance of 1 parsec. We find that coherent FRB lensing is a sensitive probe of sub-solar mass compact objects. Having observed no lenses in $172$ bursts from $114$ independent sightlines through the cosmic web, we constrain the fraction of dark matter made of compact objects, such as PBHs, to be $f \lesssim 0.8$, if their masses are $\sim 10^{-3} M_{\odot}$.

Constraints on primordial black holes with CMB spectral distortions

In the mixed dark matter scenarios consisting of primordial black holes (PBHs) and weakly interacting massive particles (WIMPs), WIMPs can be accreted onto PBHs to form ultracompact minihalos (UCMHs) with a density spike in the early universe. Compared with the classical dark matter halo, UCMHs are formed earlier and have a higher density of center. Since the annihilation rate is proportional to the squared number density of WIMPs, it is expected that WIMPs annihilation within UCMHs is enhanced and has influences on the early universe. Between the time of recombination and matter-radiation equality, the energy released from WIMPs annihilation within UCMHs is injected into the Universe resulting in cosmic microwave background $y$-type distortion. We investigate these effects and derive the upper limits on the abundance of PBHs taking advantage of the observational results of a far infrared absolute spectrophotometer (FIRAS). We find that for the WIMPs mass range $1\ensuremath{\le}{m}_{\ensuremath{\chi}}\ensuremath{\le}1000\text{ }\text{ }\mathrm{GeV}$, the upper limits on the abundance of PBHs are $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\ensuremath{\le}{\mathrm{\ensuremath{\Omega}}}_{\mathrm{PBH}}\ensuremath{\le}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$.

Cogenesis of Baryon asymmetry and gravitational dark matter from primordial black holes

We propose a scenario where dark matter (DM) with a wide mass range from a few keV to PeV can be produced solely from evaporating primordial black holes (PBH), while being consistent with the required free streaming length for structure formation. If DM does not have any other interactions apart from gravity and the universe has a PBH dominated phase at early epoch, then PBH evaporation typically leads to overproduction of DM in this mass range. By incorporating this gravitational DM within a Type-I seesaw scenario with three right handed neutrinos (RHN), we bring the abundance of PBH generated DM within observed limits by late entropy injection due to decay of one of the RHNs, acting as the diluter. The diluter, due to its feeble coupling with the bath particles, gets produced primarily from the PBH evaporation thereby leading to the second stage of early matter domination after the end of PBH dominated era. The other two RHNs contribute to the origin of light neutrino mass and also lead to the observed baryon asymmetry via leptogenesis with contributions from both thermally and PBH generated RHNs. The criteria of DM relic and baryon asymmetry can be satisfied simultaneously if DM mass gets restricted to a ballpark in the MeV-GeV regime with the requirement of resonant leptogenesis for heavier DM mass in order to survive the large entropy dilution at late epochs.

New mechanism for primordial black hole formation during reheating

In the scalar field dark matter model virialized halos present condensed central cores called boson stars. Considering the equivalent process during reheating, we look at the formation of primordial black holes (PBHs) through the gravitational collapse of structures virialized in this era. We present the criteria necessary for collapse of either the whole structure, or that of the central core, in terms of the threshold amplitude for the primordial density contrast. This is computed for both the free and the self-interacting scalar fields. We discuss the relevance of our results for the abundance of PBHs.

Constraining High-redshift Stellar-mass Primordial Black Holes with Next-generation Ground-based Gravitational-wave Detectors

The possible existence of primordial black holes in the stellar-mass window has received considerable attention because their mergers may contribute to current and future gravitational-wave detections. Primordial black hole mergers, together with mergers of black holes originating from Population III stars, are expected to dominate at high redshifts (z ≳ 10). However, the primordial black hole merger rate density is expected to rise monotonically with redshift, while Population III mergers can only occur after the birth of the first stars. Next-generation gravitational-wave detectors such as the Cosmic Explorer (CE) and Einstein Telescope (ET) can access this distinctive feature in the merger rates as functions of redshift, allowing for direct measurement of the abundance of the two populations and hence for robust constraints on the abundance of primordial black holes. We simulate four months’ worth of data observed by a CE-ET detector network and perform hierarchical Bayesian analysis to recover the merger rate densities. We find that if the universe has no primordial black holes with masses of , the projected upper limit on their abundance f PBH as a fraction of dark matter energy density may be as low as , about two orders of magnitude lower than the current upper limits in this mass range. If instead f PBH ≳ 10−4, future gravitational-wave observations would exclude f PBH = 0 at the 95% credible interval.

Superradiant pion clouds around primordial black holes

We show that highly spinning primordial black holes of mass M ∼ 1012 kg, potentially born in a matter-dominated era after inflation, can produce clouds of pions in their vicinity via the superradiant instability, with densities up to that of nuclear matter. We discuss the electromagnetic signatures of this process, via neutral pion decay and charged pion annihilation into photons, computing in particular their contribution to the isotropic gamma-ray background. This allows us to place upper bounds on the abundance of such primordial black holes that are comparable to the ones obtained from Hawking evaporation. We also discuss the possibility of directly observing such clouds in high-redshift superclusters.

Formation and Abundance of Late-forming Primordial Black Holes as Dark Matter

We propose a novel mechanism where primordial black hole (PBH) dark matter is formed much later in the history of the universe, between the epochs of Big Bang nucleosynthesis and cosmic microwave background photon decoupling. In our setup, one does not need to modify the scale-invariant inflationary power spectra; instead, a late-phase transition in a strongly interacting fermion–scalar fluid (which occurs naturally around redshift 106 ≤ z T ≤ 108) creates an instability in the density perturbation as the sound speed turns imaginary. As a result, the dark matter perturbation grows exponentially in sub-Compton scales. This follows the immediate formation of an early dense dark matter halo, which finally evolves into PBHs due to cooling through scalar radiation. We calculate the variance of the density perturbations and the PBH fractional abundances f(M) by using a nonmonochromatic mass function. We find that the peak of our PBH mass function lies between 10−16 and 10−14 solar mass for z T ≃ 106, and thus that it can constitute the entire dark matter of the universe. In PBH formation, one would expect a temporary phase where an attractive scalar balances the Fermi pressure. We numerically confirm that such a state indeed exists, and we find the radius and density profile of the temporary static structure of the dark matter halo, which finally evolves into PBHs due to cooling through scalar radiation.

Induced gravitational waves from the cosmic coincidence

The induced gravitational wave (GW) background from enhanced primordial scalar perturbations is one of the most promising observational consequences of primordial black hole (PBH) formation from inflation. We investigate the induced GW spectrum ΩIGW from single-field inflation in the general ultra-slow-roll (USR) framework, restricting the peak frequency band to be inside 10-3-1 Hz and saturating PBH abundance to comprise all dark matter (DM) in the ultralight asteroid-mass window. By invoking successful baryogenesis driven by USR inflation, we verify the viable parameter space for the specific density ratio between baryons and PBH DM observed today, the so-called “cosmic coincidence.” We show that the cosmic coincidence requirement bounds the spectral index n UV in the high frequency limit, ΩIGW(f ≫ 1) ∝ f -2n UV , into 0 < n UV < 1, which implies that baryogenesis triggered by USR inflation for PBHs in the mass range of 10-16-10-12 M⊙ can be tested by upcoming Advanced LIGO and Virgo data and next generation experiments such as LISA, Einstein Telescope, TianQin and DECIGO.

Peaks and primordial black holes: the effect of non-Gaussianity

In light of recent developments in the field, we re-evaluate the effect of local-type non-Gaussianity on the primordial black hole (PBH) abundance (and consequently, upon constraints on the primordial power spectrum arising from PBHs). We apply peaks theory to the full, non-linear compaction, finding that, whilst the effect of non-Gaussianity is qualitatively similar to previous findings, the effect is much less significant. It is found the non-Gaussianity parameters f NL local and g NL local typically need to be approximately 1 or 2 orders of magntiude larger respectively to have a similar to that previously found. The effect will be to weaken the dependance of PBH constraints on the primordial power spectrum on the non-Gaussianity parameters, as well as to dramatically weaken constraints on the non-Gaussianity parameters (and/or PBH abundance) arising from the non-observation of dark matter isocurvature modes. We also consider the correlation between the curvature perturbation ζ and the compaction C, finding that, whilst PBHs may form at rare peaks in C these do not necessarily correspond to rare peaks in ζ — casting some doubt on many of the existing calculations of the PBH abundance.

Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation

We study the impact of stochastic noise on the generation of primordial black hole (PBH) seeds in ultra-slow-roll (USR) inflation with numerical simulations. We consider the non-linearity of the system by consistently taking into account the noise dependence on the inflaton perturbations, while evolving the perturbations on the coarse-grained background affected by the noise. We capture in this way the non-Markovian nature of the dynamics, and demonstrate that non-Markovian effects are subleading. Using the ΔN formalism, we find the probability distribution P(ℛ) of the comoving curvature perturbation ℛ. We consider inflationary potentials that fit the CMB and lead to PBH dark matter with i) asteroid, ii) solar, or iii) Planck mass, as well as iv) PBHs that form the seeds of supermassive black holes. We find that stochastic effects enhance the PBH abundance by a factor of \U0001d4aa(10)–\U0001d4aa(108), depending on the PBH mass. We also show that the usual approximation, where stochastic kicks depend only on the Hubble rate, either underestimates or overestimates the abundance by orders of magnitude, depending on the potential. We evaluate the gauge dependence of the results, discuss the quantum-to-classical transition, and highlight open issues of the application of the stochastic formalism to USR inflation.

Microlensing constraints on clustered primordial black holes

The discovery of black-hole-binary mergers through their gravitational wave (GW) emission has reopened the exciting possibility that dark matter is made, at least partly, of primordial black holes (PBHs). However, this scenario is challenged by many observational probes that set bounds on the relative PBH abundance across a broad range of viable PBH masses. Among these bounds, the ones coming from microlensing surveys lead to the strongest constraints in the mass range from $\ensuremath{\sim}{10}^{\ensuremath{-}10}$ to a few ${M}_{\ensuremath{\bigodot}}$. The upper part of this range precisely corresponds to the mass window inside which the formation of PBHs should be boosted due to the QCD phase transition in the early Universe, which makes the microlensing probes particularly important. However, it has been argued that taking into account the inevitable clustering of PBH on small scales can significantly relax or entirely remove these bounds. While the impact of PBH clustering on the GW event rate has been studied in detail, its impact on the microlensing event rate has not yet been fully assessed. In this paper, we address this issue, and show that clusters arising from isocurvature perturbations, that originating from PBHs formed from Gaussian initial curvature perturbations, do not alter the current microlensing constraints, as they are not sufficiently compact.

Mass-gap extreme mass ratio inspirals

In this work, we propose a new subclass of extreme-mass-ratio-inspirals (EMRIs): mass-gap EMRIs, consisting of a compact object in the lower mass gap $\ensuremath{\sim}(2.5\ensuremath{-}5)\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ and a massive black hole (MBH). The mass-gap object (MGO) may be a primordial black hole or produced from a delayed supernova explosion. We calculate the formation rate of mass-gap EMRIs in both the (dry) loss-cone channel and the (wet) active galactic nucleus disk channel by solving Fokker-Planck-type equations for the phase-space distribution. In the dry channel, the mass-gap EMRI rate is strongly suppressed compared to the EMRI rate of stellar-mass black holes (SBHs) as a result of mass segregation effect. In the wet channel, the suppression is roughly equal to the mass ratio of SBHs over MGOs, because the migration speed of a compact object in an active galactic nucleus disk is proportional to its mass. We find that the wet channel is much more promising to produce mass-gap EMRIs observable by spaceborne gravitation wave detectors. (Non)detection of mass-gap EMRIs may be used to distinguish different supernova explosion mechanisms and constrain the abundance of primordial black holes around MBHs.

Constraints on the abundance of supermassive primordial black holes from lensing of compact radio sources

ABSTRACT The possibility that primordial black holes (PBHs) form a part of dark matter has been considered over a wide mass range from the Planck mass ($10^{-5}~\rm g$) to the level of the supermassive black hole in the center of the galaxy. Primordial origin might be one of the most important formation channel of supermassive black holes. We use the non-detection of lensing effect of very long baseline interferometer observations of compact radio sources with extremely high angular resolution as a promising probe to constrain the abundance of intergalactic PBHs in the mass range ∼104–109 M⊙. For a sample of well-measured 543 flat-spectrum compact radio sources, no milli-lensed images are found with angular separations between 1.5 and 50 milli-arcsec. From this null search result, we derive that the fraction of dark matter made up of supermassive PBHs in the mass range ∼106–108 M⊙ is $\lesssim 1.48{{\ \rm per\, cent}}$ at $95{{\ \rm per\, cent}}$ confidence level. This constraints would be significantly improved due to the rapid increase of the number of measured compact radio sources. For instance, on the basis of none confirmed milli-lensing candidate in the latest ∼14 000 sources, we derive the abundance of supermassive PBHs and obtain that it is $\lesssim 0.06{{\ \rm per\, cent}}$ at $95{{\ \rm per\, cent}}$ confidence level.

A note on the abundance of primordial black holes: Use and misuse of the metric curvature perturbation

The formation of Primordial Black Holes (PBHs) through the collapse of large fluctuations in the early universe is a rare event. This manifests itself, for instance, through the non-Gaussian tail of the formation probability. To compute such probability and the abundance of PBHs, the curvature perturbation is frequently adopted. In this note we emphasize that its use does not provide the correct PBH formation probability. Through a path-integral approach we show that the exact calculation of the PBH abundance demands the knowledge of multivariate joint probabilities of the curvature perturbation or, equivalently, of all the corresponding connected correlators.