Population Of Primordial Black Holes Research Articles

One-loop power spectrum in ultra slow-roll inflation and implications for primordial black hole dark matter

We apply the in-in formalism to address the question of whether the size of the one-loop spectrum of curvature fluctuations in ultra-slow-roll inflation models designed for producing a large population of primordial black holes implies a breakdown of perturbation theory. We consider a simplified piece-wise description of inflation, in which the ultra-slow-roll phase is preceded and followed by slow-roll phases linked by transitional periods. We work in the δϕ-gauge, including all relevant cubic and quartic interactions and the necessary counterterms to renormalize the ultraviolet divergences, regularized by a cutoff. The ratio of the one-loop to the tree-level contributions to the spectrum of curvature perturbations is controlled by the duration of the ultra-slow-roll phase and of the transitions. Our results indicate that perturbation theory does not necessarily break in well-known models proposed to account for all the dark matter in the form of primordial black holes.

Revisiting primordial black hole capture by neutron stars

A sub-solar mass primordial black hole (PBH) passing through a neutron star, can lose enough energy through interactions with the dense stellar medium to become gravitationally bound to the star. Once captured, the PBH would sink to the core of the neutron star, and completely consume it from the inside. In this paper, we improve previous energy-loss calculations by considering a realistic solution for the neutron star interior, and refine the treatment of the interaction dynamics and collapse likelihood. We then consider the effect of a sub-solar PBH population on neutron stars near the Galactic center. We find that it is not possible to explain the lack of observed pulsars near the galactic center through dynamical capture of PBHs, as the velocity dispersion is too high. We then show that future observations of old neutron stars close to Sgr A* could set stringent constraints on the PBHs abundance. These cannot however be extended in the currently unconstrained asteroid-mass range, since PBHs of smaller mass would lose less energy in their interaction with the neutron star and end up in orbits that are too loosely bound and likely to be disrupted by other stars in the Galactic center.

Disentangling the Black Hole Mass Spectrum with Photometric Microlensing Surveys

From the formation mechanisms of stars and compact objects to nuclear physics, modern astronomy frequently leverages surveys to understand populations of objects to answer fundamental questions. The population of dark and isolated compact objects in the Galaxy contains critical information related to many of these topics, but is only practically accessible via gravitational microlensing. However, photometric microlensing observables are degenerate for different types of lenses, and one can seldom classify an event as involving either a compact object or stellar lens on its own. To address this difficulty, we apply a Bayesian framework that treats lens type probabilistically and jointly with a lens population model. This method allows lens population characteristics to be inferred despite intrinsic uncertainty in the lens class of any single event. We investigate this method’s effectiveness on a simulated ground-based photometric survey in the context of characterizing a hypothetical population of primordial black holes (PBHs) with an average mass of 30M ⊙. On simulated data, our method outperforms current black hole (BH) lens identification pipelines and characterizes different subpopulations of lenses while jointly constraining the PBH contribution to dark matter to ≈25%. Key to robust inference, our method can marginalize over population model uncertainty. We find the lower mass cutoff for stellar origin BHs, a key observable in understanding the BH mass gap, particularly difficult to infer in our simulations. This work lays the foundation for cutting-edge PBH abundance constraints to be extracted from current photometric microlensing surveys.

Primordial black holes as a dark matter candidate in theories with supersymmetry and inflation

We show that supersymmetry and inflation, in a broad class of models, generically lead to formation of primordial black holes (PBHs) that can account for dark matter. Supersymmetry predicts a number of scalar fields that develop a coherent condensate along the flat directions of the potential at the end of inflation. The subsequent evolution of the condensate involves perturbative decay, as well as fragmentation into Q-balls, which can interact by some long-range forces mediated by the scalar fields. The attractive scalar long-range interactions between Q-balls facilitates the growth of Q-balls until their ultimate collapse to black holes. For a flat direction lifted by supersymmetry breaking at the scale Λ ∼ 100 TeV, the black hole masses are of the order of (M 3 Planck/Λ2) ∼ 1022 g, in the allowed range for dark matter. Similar potentials with a lower scale Λ (not necessarily associated with supersymmetry) can result in a population of primordial black holes with larger masses, which can explain some recently reported microlensing events.

Primordial black holes and gravitational waves from dissipation during inflation

We study the generation of a localized peak in the primordial spectrum of curvature perturbations from a transient dissipative phase during inflation, leading to a large population of primordial black holes. The enhancement of the power spectrum occurs due to stochastic thermal noise sourcing curvature fluctuations. We solve the stochastic system of Einstein equations for many realizations of the noise and obtain the distribution for the curvature power spectrum. We then propose a method to find its expectation value using a deterministic system of differential equations. In addition, we find a single stochastic equation whose analytic solution helps to understand the main features of the spectrum. Finally, we derive a complete expression and a numerical estimate for the energy density of the stochastic background of gravitational waves induced at second order in perturbation theory. This includes the gravitational waves induced during inflation, during the subsequent radiation epoch and their mixing. Our scenario provides a novel way of generating primordial black hole dark matter with a peaked mass distribution and a detectable stochastic background of gravitational waves from inflation.

Revisiting constraints on WIMPs around primordial black holes

While primordial black holes (PBHs) with masses ${M}_{\mathrm{PBH}}\ensuremath{\gtrsim}{10}^{\ensuremath{-}11}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ cannot comprise the entirety of dark matter, the existence of even a small population of these objects can have profound astrophysical consequences. A subdominant population of PBHs will efficiently accrete dark matter particles before matter-radiation equality, giving rise to high-density dark matter spikes. We consider here the scenario in which dark matter is comprised primarily of weakly interacting massive particles (WIMPs) with a small subdominant contribution coming from PBHs, and revisit the constraints on the annihilation of WIMPs in these spikes using observations of the isotropic gamma-ray background (IGRB) and the cosmic microwave background (CMB), for a range of WIMP masses, annihilation channels, cross sections, and PBH mass functions. We find that the constraints derived using the IGRB have been significantly overestimated (in some cases by many orders of magnitude), and that limits obtained using observations of the CMB are typically stronger than, or comparable to, those coming from the IGRB. Importantly, we show that $\ensuremath{\sim}\mathcal{O}({M}_{\ensuremath{\bigodot}})$ PBHs can still contribute significantly to the dark matter density for sufficiently low WIMP masses and p-wave annihilation cross sections.

Detectability of gravitational waves from primordial black holes orbiting Sgr A*

In this work we characterize the expected gravitational wave signal detectable by the planned space-borne interferometer LISA and the proposed next generation space-borne interferometer $\mu$Ares arising from a population of primordial black holes orbiting Sgr A*, the super-massive black hole at the Galactic center. Assuming that such objects indeed form the entire diffuse mass allowed by the observed orbit of S2 in the Galactic center, under the simplified assumption of circular orbits and monochromatic mass function, we assess the expected signal in gravitational waves, either from resolved and non-resolved sources. We estimate a small but non negligible chance of $\simeq$ 10% of detecting one single 1 M$_{\odot}$ primordial black hole with LISA in a 10-year-long data stream, while the background signal due to unresolved sources would essentially elude any reasonable chance of detection. On the contrary, $\mu$Ares, with a $\simeq$ 3 orders-of-magnitude better sensitivity at $\simeq$ 10$^{-5}$ Hz, would be able to resolve $\simeq$ 140 solar mass primordial black holes in the same amount of time, while the unresolved background should be observable with an integrated signal-to-noise ratio $\gtrsim$ 100. Allowing the typical PBH mass to be in the range 0.01-10 M$_{\odot}$ would increase LISA chance of detection to $\simeq$ 40% towards the lower limit of the mass spectrum. In the case of $\mu$Ares, instead, we find a "sweet spot" just about 1 M$_{\odot}$, a mass for which the number of resolvable events is indeed maximized.

Broad search for gravitational waves from subsolar-mass binaries through LIGO and Virgo’s third observing run

We present a search for gravitational waves from the coalescence of binaries which contain at least one subsolar-mass component using data from the LIGO and Virgo observatories through the completion of their third observing run. The observation of a merger with a component below $1\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ would be a clear sign of either new physics or the existence of a primordial black hole population; these black holes could also contribute to the dark matter distribution. Our search targets binaries where the primary has mass ${M}_{1}$ between 0.1 and $100\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ and the secondary has mass ${M}_{2}$ from 0.1 to $1\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ for ${M}_{1}<20\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ and 0.01 to $1\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ for ${M}_{1}\ensuremath{\ge}20\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. Sources with ${M}_{1}<7\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, ${M}_{2}>0.5\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ are also allowed to have orbital eccentricity up to ${e}_{10}\ensuremath{\sim}0.3$. This search region covers from comparable to extreme mass ratio sources up to ${10}^{4}:1$. We find no statistically convincing candidates and so place new upper limits on the rate of mergers; our analysis sets the first limits for most subsolar sources with $7{M}_{\ensuremath{\bigodot}}<{M}_{1}<20\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ and tightens limits by $\ensuremath{\sim}8\ifmmode\times\else\texttimes\fi{}(1.6\ifmmode\times\else\texttimes\fi{})$ where ${M}_{1}>20\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ (${M}_{1}<7\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$). Using these limits, we constrain the dark matter fraction to below $0.3(0.7)%$ for 1 $(0.5)\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ black holes assuming a monochromatic mass function. Due to the high merger rate of primordial black holes beyond the individual source horizon distance, we also use the lack of an observed stochastic background as a complementary probe to limit the dark matter fraction. We find that although the limits are, in general, weaker than those from the direct search, they become comparable at $0.1\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$.

Searching for a subpopulation of primordial black holes in LIGO-Virgo gravitational-wave data

With several dozen binary black hole events detected by LIGO/Virgo to date and many more expected in the next few years, gravitational-wave astronomy is shifting from individual-event analyses to population studies. Using the GWTC-2 catalog, we perform a hierarchical Bayesian analysis that for the first time combines several state-of-the-art astrophysical formation models with a population of primordial black holes (PBHs) and constrains the fraction of a putative subpopulation of PBHs in the data. We find that this fraction depends significantly on the set of assumed astrophysical models. While a primordial population is statistically favored against certain competitive astrophysical channels, such as globular clusters and nuclear stellar clusters, a dominant contribution from the stable-mass-transfer isolated formation channel drastically reduces the need for PBHs, except for explaining the rate of mass-gap events like GW190521. The tantalizing possibility that black holes formed after inflation are contributing to LIGO/Virgo observations could only be verified by further reducing uncertainties in astrophysical and primordial formation models, and it may ultimately be confirmed by third-generation interferometers.

How to assess the primordial origin of single gravitational-wave events with mass, spin, eccentricity, and deformability measurements

A population of primordial black holes formed in the early Universe could contribute to at least a fraction of the black-hole merger events detectable by current and future gravitational-wave interferometers. With the ever-increasing number of detections, an important open problem is how to discriminate whether a given event is of primordial or astrophysical origin. We systematically present a comprehensive and interconnected list of discriminators that would allow us to rule out, or potentially claim, the primordial origin of a binary by measuring different parameters, including redshift, masses, spins, eccentricity, and tidal deformability. We estimate how accurately future detectors (such as the Einstein Telescope and LISA) could measure these quantities, and we quantify the constraining power of each discriminator for current interferometers. We apply this strategy to the GWTC-3 catalog of compact binary mergers. We show that current measurement uncertainties do not allow us to draw solid conclusions on the primordial origin of individual events, but this may become possible with next-generation ground-based detectors.

Search for black hole hyperbolic encounters with gravitational wave detectors

In recent years, the proposal that there is a large population of primordial black holes living in dense clusters has been gaining popularity. One natural consequence of these dense clusters will be that the black holes inside will gravitationally scatter off each other in hyperbolic encounters, emitting gravitational waves that can be observed by current detectors. In this paper we will derive how to compute the gravitational waves emitted by black holes in hyperbolic orbits, taking into account up to leading order spin effects. We will then study the signal these waves leave in the network of gravitational wave detectors currently on Earth. Using the properties of the signal, we will detail the data processing techniques that can be used to make it stand above the detector noise. Finally, we will look for these signals from hyperbolic encounters in the publicly available LIGO-Virgo data. For this purpose we will develop a two step trigger. The first step of the trigger will be based on looking for correlations between detectors in the time–frequency domain. The second step of the trigger will make use of a residual convolutional neural network, trained with the theoretical predictions for the signal, to look for hyperbolic encounters. With this trigger we find 8 hyperbolic encounter candidates in the 15.3 days of public data analyzed. Some of these candidates are promising, but the total number of candidates found is consistent with the number of false alarms expected from our trigger.

Asymmetric reheating by primordial black holes

We investigate Hawking evaporation of a population of primordial black holes (PBHs) prior to Big Bang Nucleosynthesis (BBN) as a mechanism to achieve asymmetric reheating of two sectors coupled solely by gravity. While the visible sector is reheated by the inflaton or a modulus, the dark sector is reheated by PBHs. Compared to inflationary or modular reheating of both sectors, there are two advantages: $(i)$ inflaton or moduli mediated operators that can subsequently thermalize the dark sector with the visible sector are not relevant to the asymmetric reheating process; $(ii)$ the mass and abundance of the PBHs provide parametric control of the thermal history of the dark sector, and in particular the ratio of the temperatures of the two sectors. Asymmetric reheating with PBHs turns out to have a particularly rich dark sector phenomenology, which we explore using a single self-interacting real scalar field in the dark sector as a template. Four thermal histories, involving non-relativistic and relativistic dark matter (DM) at chemical equilibrium, followed by the presence or absence of cannibalism, are explored. These histories are then constrained by the observed relic abundance in the current Universe and the Bullet Cluster. The case where PBHs dominate the energy density of the Universe, and reheat both the visible as well as the dark sectors, is also treated in detail.

Axion-like particles from primordial black holes shining through the Universe

We consider a cosmological scenario in which the very early Universe experienced a transient epoch of matter domination due to the formation of a large population of primordial black holes (PBHs) with masses M ≲ 109 g, that evaporate before Big Bang nucleosynthesis. In this context, Hawking radiation would be a non-thermal mechanism to produce a cosmic background of axion-like particles (ALPs). We assume the minimal scenario in which these ALPs couple only with photons. In the case of ultralight ALPs (m a ≲ 10-9 eV) the cosmic magnetic fields might trigger ALP-photon conversions, while for masses m a ≳ 10 eV spontaneous ALP decay in photon pairs would be effective. We investigate the impact of these mechanisms on the cosmic X-ray background, on the excess in X-ray luminosity in Galaxy Clusters, and on the process of cosmic reionization.

Earth-mass primordial black hole mergers as sources for nonrepeating fast radio bursts

Fast radio bursts (FRBs) are mysterious astronomical radio transients with extremely short intrinsic duration. Until now, the physical origins of them still remain elusive especially for the non-repeating FRBs. Strongly inspired by recent progress on possible evidence of Earth-mass primordial black holes, we revisit the model of Earth-mass primordial black holes mergers as sources for non-repeating FRBs. Under the null hypothesis that the observed non-repeating FRBs are originated from the mergers of Earth-mass primordial black holes, we analyzed four independent samples of non-repeating FRBs to study the model parameters i.e. the typical charge value $q_{\rm{c}}$ and the power index $\alpha$ of the charge distribution function of the primordial black hole population $\phi(q) \propto (q/q_{\rm{c}})^{-\alpha}$ which describe how the charge was distributed in the population. $q$ is the charge of the hole in the unit of $\sqrt{G} M$, where $M$ is the mass of the hole. It turns out that this model can explain the observed data well. {Assuming the monochromatic mass spectrum for primordial black holes}, we get the average value of typical charge $\bar{q}_{\rm{c}}/10^{-5}=1.59^{+0.08}_{-0.18}$ and the power index $\bar{\alpha}=4.53^{+0.21}_{-0.14}$ by combining the fitting results given by four non-repeating FRB samples. The event rate of the non-repeating FRBs can be explained in the context of this model, if the abundance of the primordial black hole populations with charge $q \gtrsim 10^{-6}$ is larger than $10^{-5}$ which is far below the upper limit given by current observations for the abundance of Earth-mass primordial black holes. In the future, simultaneous detection of FRBs and high frequency gravitational waves produced by mergers of Earth-mass primordial black holes may directly confirm or deny this model.

Precision calculation of dark radiation from spinning primordial black holes and early matter-dominated eras

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 application, we consider the case of PBHs formed during an early matter-dominated era (EMDE). We calculate graviton production from various PBH spin distributions pertinent to EMDEs, and find that PBHs in the entire mass range up to $10^9\,$g will be constrained by measurements from CMB Stage 4 experiments, assuming PBHs come to dominate the Universe prior to Hawking evaporation. We also find that for PBHs with monochromatic spins $a^*>0.81$, all PBH masses in the range $10^{-1}\,{\rm g} < M_{\rm BH} <10^9\,$g will be probed by CMB Stage 4 experiments.

Two populations of LIGO-Virgo black holes

We analyse the LIGO-Virgo data, including the recently released GWTC-2dataset, to test a hypothesis that the data contains more than one population of black holes. We perform a maximum likelihood analysis including a population of astrophysical black holes with a truncated power-law mass function whose merger rate follows from star formation rate, and a population of primordial black holes for which we consider log-normal and critical collapse mass functions. We find that primordial black holes alone are strongly disfavoured by the data, while the best fit is obtained for the template combining astrophysical and primordial merger rates. Alternatively, the data may hint towards two different astrophysical black hole populations. We also update the constraints on primordial black hole abundance from LIGO-Virgo observations finding that in the 2–400 mass range they must comprise less than 0.2% of dark matter.

Consistency of Primordial Black Hole Dark Matter with LIGO/Virgo Merger Rates.

The LIGO/Virgo Collaboration has by now observed or constrained the gravitational merger rates of different classes of compact objects. We consider the possibility that the bulk of these mergers are primordial black hole (PBH) mergers of PBHs formed during the QCD epoch making up the entirety of the dark matter. Having shown in a companion paper that mergers due to the initial binary population formed in the early Universe are likely negligible, we compute current merger rates in PBH clusters in which the typical PBH resides. We consider two scenarios: (i)the PBH mass function dictated by the QCD equation of state and (ii)the PBH mass function dictated by the existence of a peak in the inflationary perturbation spectrum. In the first scenario, which is essentially parameter-free, we reproduce very well the merger rates for heavy BHs, the merger rate of mass-asymmetric BHs such as GW190814, a recently discovered merger of a 23 M_{⊙} black hole with a 2.6 M_{⊙} object, and can naturally explain why LIGO/Virgo has not yet observed mergers of two light PBHs from the dominant ∼1 M_{⊙} PBH population. In the second scenario, which has some parameter freedom, we match well the observed rate of heavy PBHs but can currently not explain the rate for mass-asymmetric events. In either case, it is tantalizing that in both scenarios PBH merger rates made with a minimum of assumptions match most LIGO/Virgo observed rates very well.

Primordial black holes as dark matter and gravitational waves from bumpy axion inflation

We consider a mechanism for producing a significant population of primordial black holes (PBHs) and an observable stochastic gravitational wave background (SGWB) within string theory inspired models of inflation. In this framework where inflaton is identified as a non-compact axion-like field, sub-leading non-perturbative effects can superimpose steep cliffs connected by smooth plateaus onto the underlying axion potential. In the presence of coupling to Abelian gauge fields, the motion of axion on the cliff-like region(s) of its potential triggers a localized production of one helicity state of gauge fields due to the temporary fast-roll of axion around such a feature. In this setup, primordial fluctuations sourced by vector fields exhibit a localized peak in momentum space corresponding to modes that exit the horizon when the axion velocity is maximal. As an application of this general mechanism, we present an example of axion inflation which both matches Planck observations at CMB scales and generates a population of light PBHs (MPBH ≃ 10−13 M⊙) that can account for all dark matter. In this scenario, the enhanced scalar fluctuations that leads to PBHs also generate an observable SGWB of induced origin at LISA scales. The amplitude and shape of the resulting GW signal inherits specific properties (such as non-Gaussianity and its shape) of its scalar sources that may allow us to distinguish this mechanism from other inflationary scenarios and astrophysical backgrounds. This GW signal together with an observation of PBH distribution at the corresponding scales can thus provide a window to the inflationary dynamics on scales much smaller than those probed by Cosmic Microwave Background (CMB) and Large Scale Structure (LSS) Measurements.

The Impact of the Mass Spectrum of Lenses in Quasar Microlensing Studies. Constraints on a Mixed Population of Primordial Black Holes and Stars

Abstract We show that quasar microlensing magnification statistics induced by a population of point microlenses distributed according to a mass spectrum can be very well approximated by that of a single-mass, monochromatic, population. When the spatial resolution (physically defined by the source size) is small compared with the Einstein radius, the mass of the monochromatic population matches the geometric mean (GM) of the mass spectrum. Otherwise, the best-fit mass can be larger. Taking into account the degeneracy with the GM, the interpretation of quasar microlensing observations under the hypothesis of a mixed population of primordial black holes and stars makes the existence of a significant population of intermediate mass black holes (∼100M ⊙) unlikely but allows, within a 2σ confidence interval, the presence of a large population (≳40% of the total mass) of substellar black holes (∼0.01M ⊙).

Exploring Primordial Black Holes from the Multiverse with Optical Telescopes.

Primordial black holes (PBHs) are a viable candidate for dark matter if the PBH masses are in the currently unconstrained "sublunar" mass range. We revisit the possibility that PBHs were produced by nucleation of false vacuum bubbles during inflation. We show that this scenario can produce a population of PBHs that simultaneously accounts for all dark matter, explains the candidate event in the Subaru Hyper Suprime-Cam (HSC) data, and contains both heavy black holes as observed by LIGO and very heavy seeds of supermassive black holes. We demonstrate with numerical studies that future observations of HSC, as well as other optical surveys, such as LSST, will be able to provide a definitive test for this generic PBH formation mechanism if it is the dominant source of dark matter.