Primordial Black Holes

• Primordial black holes are gravitationally collapsed objects formed from early-Universe density fluctuations, offering insights into dark matter and cosmic structure.
• They arise from diverse mechanisms—including inflationary fluctuations, phase transitions, and defect collapse—that produce a broad, non-monochromatic mass spectrum.
• Observational constraints from gamma-ray emissions, microlensing, and gravitational waves tightly limit PBH abundance and inform future probes of early-universe physics.

Primordial black holes (PBHs) are gravitationally collapsed objects formed in the early Universe—well before the onset of star formation or the assembly of galaxies. Their existence, first postulated in the 1960s and 1970s, links microphysics, large-scale cosmological structure, dark matter, high energy theory, and quantum gravity. Theoretical models predict a rich range of formation mechanisms and mass spectra, while a broad spectrum of astrophysical, cosmological, and particle physics observations provide strong constraints on their possible abundance and properties.

1. Historical Development and Conceptual Foundations

The PBH paradigm emerged from the realization that large-amplitude density fluctuations in the early Universe could collapse directly to black holes if the overdensity at horizon entry exceeds a critical value. Zel’dovich and Novikov first articulated that, in a hot big-bang cosmology, sufficiently large perturbations could be gravitationally unstable and collapse on timescales shorter than the cosmological expansion time. Hawking expanded the picture, introducing the criterion that collapse is possible when a mass $M$ is contained within its Schwarzschild radius ($R_S = 2GM/c^2$). The subsequent realization that black holes radiate thermally (Hawking radiation) introduced a quantum channel for constraining PBH abundance and lifespan (Carr et al., 21 Feb 2025).

2. Mechanisms of Formation

Standard Collapse from Inflationary or Early-Universe Fluctuations

PBHs can form from horizon-scale overdense regions during radiation or matter domination if the local density contrast $\delta = (\rho - \bar{\rho})/\bar{\rho}$ exceeds a critical value $\delta_c$, typically $\delta_c \sim w$ where $w$ is the equation-of-state parameter ($w=1/3$ for radiation) (Green, 2014, Carr et al., 21 Feb 2025, Green, 23 Feb 2024). The probability of collapse is exponentially sensitive to the amplitude of density fluctuations,

$$\beta(M) \simeq \mathrm{erfc} \left( \frac{\delta_c}{\sqrt{2\sigma(M)}} \right),$$

where $\sigma(M)$ is the r.m.s. amplitude of fluctuations smoothed on the relevant scale. Inflationary models generating an enhanced small-scale power spectrum—via ultra-slow-roll or step features in the inflaton potential—can increase $\sigma$ to the required values, exponentially boosting PBH formation (Inomata et al., 2021, Biagetti et al., 2018). In the case of critical collapse, the PBH mass scales as $M = \kappa M_H (\delta - \delta_c)^{\gamma}$ (typically, $\gamma \approx 0.36$ for radiation) with $M_H$ the horizon mass at collapse (Green, 2014).

Collapse During Early Dust-like Stages or via Phase Transitions

If the Universe experienced an early matter (dust) dominated phase (e.g., from superheavy metastable particle domination), density perturbations could grow $\propto t^{2/3}$, accentuating PBH formation. In such cases, the collapse probability $W_{PBH} \sim \delta^{13/2}(t_i)$ for perturbations entering the horizon at $t_i$ (0801.0116).

First-order phase transitions produce PBHs via the nucleation and collision of true-vacuum bubbles. A false vacuum bag (FVB) can form between two colliding bubbles; if the bag’s size becomes smaller than its gravitational radius, it contracts to form a PBH. The condition for black hole formation is

$\Delta < r_g = 2GM,$

with $\Delta$ the wall thickness (0801.0116). Under typical conditions, the probability of PBH formation per bubble collision can approach unity.

Collapse of Topological Defects and Domain Walls

In models with pseudo-Nambu-Goldstone fields and explicit symmetry breaking (e.g., axion-like theories), closed domain walls generated by fluctuations during inflation can collapse into massive PBHs when their energy is concentrated within the gravitational radius. The minimal and maximal PBH masses from this channel are $M_{min} \sim f (m_{pl}/\Lambda)^2$ and $M_{max} \sim m_{pl}^3/(f\Lambda^2),$ where $f$ is the symmetry-breaking scale and $\Lambda$ the explicit breaking parameter (0801.0116, Escrivà et al., 2022).

Other Channels

Additional mechanisms include PBH formation from cosmic string loop collapse (Green, 2014), the energy stored in confining flux tubes (such as color QCD strings or analogous string theory objects) (Dvali et al., 2021), or from the collapse of bound states of supermassive particles in the early Universe (Meissner et al., 2021).

3. PBH Mass Spectrum and Statistical Properties

PBH masses are typically set by the horizon mass at the formation epoch: $$M_{PBH} \sim M_H \sim 10^{15} \, \text{g} \left( \frac{t}{10^{-23} \ \text{s}} \right),$$ allowing masses spanning from sub-Planckian up to supermassive scales, depending on formation time and channel (Carr, 2014, Carr et al., 21 Feb 2025, Escrivà et al., 2022). Critical collapse and extended formation scenarios generally produce a broad, non-monochromatic mass spectrum. Some models, notably variations of the Affleck-Dine scenario for baryogenesis, predict a log-normal PBH mass spectrum: $$\frac{dN}{dM} = \mu^2 \exp\left[ -\gamma \ln^2 (M/M_0) \right],$$ where $\mu,\gamma,M_0$ are parameters fixed by the microphysics and cosmological evolution (Dolgov, 2017). Extended spectra require careful “bin-by-bin” comparison with observational bounds (Carr et al., 2016).

The statistical properties of the initial fluctuations—especially non-Gaussianity and deviations from sphericity—influence both the collapse threshold and resultant mass function. Enhanced clustering at formation can affect subsequent merger rates and dynamical evolution (Green, 23 Feb 2024).

4. Astrophysical and Cosmological Constraints

Evaporation and High-Energy Particle Emission

PBHs lighter than $\sim 10^{15}$ g evaporate via Hawking radiation over cosmic timescales,

$T = \frac{1}{8\pi G M},$

$\tau_{BH} \sim \frac{M^3}{m_{pl}^4}.$

The evaporation injects gamma-rays, leptons, baryons, and possibly exotic particles. The absence of excess gamma-ray backgrounds, distortion of light element abundances in BBN, and exotic particle fluxes (e.g., gravitinos) imposes stringent upper bounds on the allowed abundance of low-mass PBHs (Carr, 2014, MacGibbon et al., 2015).

Gravitational Lensing

Searches for the lensing of background stars (microlensing) constrain PBHs in the range $\sim 10^{20} - 10^{34}$ g. Femtolensing of gamma-ray bursts and other lensing signatures probe even lower masses. The lack of detected lensing events through numerous surveys (e.g., EROS, OGLE, MACHO, Kepler) imposes tight limits on the PBH fraction in multiple mass intervals (Green, 2014, Carr et al., 2021).

Dynamical and Large-Scale Structure Effects

PBHs of $\gtrsim 10\,M_\odot$ affect the survival and dynamics of wide binaries, globular clusters, galactic disks, and can induce Poisson fluctuations which modify large-scale structure growth. Tidal disruption, dynamical friction, and accretion (with attendant electromagnetic signatures and CMB spectral distortions) further constrain the PBH population (Carr et al., 2016, Carr, 2019).

Constraints Table (Selected)

Mass Range	Principal Constraints	Tightest Bounds
$M < 10^{15}$ g	Hawking evaporation, $\gamma$-rays, BBN	$f_{PBH} \ll 1$
$10^{17}$–$10^{23}$ g	Microlensing, femtolensing, CMB	$f_{PBH}$ limited by lensing
$10$–$10^3\,M_\odot$	Microlensing, mergers (LIGO), wide binaries, CMB accretion	$f_{PBH} \lesssim 1$ in some windows

5. Signatures, Cosmological Roles, and Impact

PBHs as Dark Matter and Structure Seeds

PBHs are non-baryonic, behave as cold dark matter ($\rho_{PBH} \propto a^{-3}$), and are a natural candidate for the dark matter, especially in mass windows not excluded by current constraints (notably $10^{17}$–$10^{23}$ g and $10$–$10^2\,M_\odot$) (Carr et al., 2021, Carr, 2019). If their mass distribution is extended, PBHs can simultaneously provide dark matter, seeds for supermassive black holes (SMBHs) in galactic nuclei, and potentially explain intermediate-mass black holes in globular clusters or dwarf galaxies (Dolgov, 2017, Carr et al., 21 Feb 2025).

Massive PBHs (e.g., $M_{\rm PBH} \gtrsim 10^2\,M_\odot$) can act as early “seeds” for galaxy and cluster formation, producing a “seed effect” (single PBHs enhancing collapse locally) or a “Poisson effect” (fluctuations in number density augmenting structure power on small scales) (Carr, 2019).

Gravitational Wave Astronomy

LIGO/Virgo’s detection of black hole mergers with component masses in the tens of $M_\odot$ invigorated PBH models, as mergers could result from primordial binaries formed from early-universe spatial clustering. The predicted merger rates, mass, and spin distributions differ from stellar formation channels and offer powerful diagnostics (Escrivà et al., 2022, Arbey et al., 2020). Additionally, PBHs produce “induced” second-order gravitational waves during collapse, with energy density and spectrum closely tied to the primordial curvature spectrum. Upcoming missions (e.g., LISA, SKA) targeting stochastic GW backgrounds may further constrain PBH scenarios.

PBH-Induced Modifications to Early Star Formation

High-resolution simulations of structure formation in cosmologies with a significant PBH component show nuanced, mass-dependent effects. Massive PBHs ($M_{\rm PBH} \gtrsim 10^2\,M_\odot$) can accelerate the formation of Population III (Pop III) stars by deepening gravitational potentials, shifting cosmic dawn to higher redshifts. Lower-mass PBHs, if sufficiently abundant, can suppress star formation or delay the collapse of gas minihalos via tidal disruption and heating. These effects yield constraints on PBH mass function and abundance, testable with upcoming 21-cm cosmology and galaxy surveys (e.g., JWST) (Koulen et al., 6 Jun 2025).

PBHs and Quantum Gravity

Since PBH evaporation is a quantum effect, PBHs provide a unique setting to test semiclassical gravity and explore quantum gravity corrections. Unresolved theoretical issues include the possible existence of stable Planck-mass evaporation remnants, modifications induced by quantum gravity effects (e.g., in Loop Quantum Gravity), memory effects, and potential departures from the no-hair conjecture (Arbey et al., 2020, Arbey, 14 May 2024). Observationally, signatures from modified evaporation or remnant accumulation remain speculative but are actively explored in the context of dark matter and early-universe physics.

6. Theoretical Challenges and Open Problems

Despite the development of sophisticated frameworks—such as the compaction function, peak theory for the collapse threshold, and fully nonlinear numerical simulations—significant uncertainties remain. The PBH formation rate is exponentially sensitive to the exact value of $\delta_c$, the nature (Gaussian vs. non-Gaussian) of primordial fluctuations, their spatial clustering at formation, and the role of extended or multi-modal mass functions (Escrivà et al., 2022, Green, 23 Feb 2024, Carr et al., 2016).

A central theoretical challenge is robustly mapping inflationary model parameters (e.g., features in the inflaton potential) onto observable PBH mass spectra while faithfully capturing all stochastic and critical phenomena. Observationally, differentiating between primordial and astrophysical black holes—especially at the level of spins, merger rates, and clustering—remains a nontrivial task.

7. Prospects and Future Directions

The PBH research landscape is rapidly evolving. While most historical attention centered on constraint-setting, emphasis is increasingly shifting toward leveraging multi-messenger signals (GW, EM, and astroparticle channels) to distinguish PBHs from other compact object populations and to seek positive evidence for primordial origins (Carr et al., 21 Feb 2025). 21-cm cosmology and very-high-redshift galaxy surveys will probe the effects of PBHs on early star formation (Koulen et al., 6 Jun 2025). Detailed spin and mass measurements of merging black holes, the detection of sub-Chandrasekhar-mass black holes (potentially via induced collapse in low-mass stars (Oncins et al., 2022)), and the search for unique signatures in gravitational-wave and electromagnetic backgrounds define key avenues for progress.

The PBH framework thus remains central to many frontiers in cosmology, astrophysics, and high-energy theory: a unique intersection of quantum gravity, dark matter, and structure formation. The confluence of next-generation observations and advanced simulations promises to clarify the role of primordial black holes in the cosmic narrative.