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arxiv: 2604.14871 · v1 · submitted 2026-04-16 · 🌌 astro-ph.CO · hep-ph

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Microscopic primordial black holes as macroscopic dark matter from large extra dimensions

Giuseppe Filiberto Vitale , Gaetano Lambiase , Tanmay Kumar Poddar , Luca Visinelli
Authors on Pith no claims yet

Pith reviewed 2026-05-10 10:09 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-ph
keywords primordial black holesdark matterlarge extra dimensionsHawking radiationaccretioncosmological evolutionADD model
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The pith

In large extra dimensions, microscopic primordial black holes can grow rapidly into macroscopic objects and account for dark matter even with initial abundances as low as 10^{-44}.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how primordial black holes evolve in the ADD model with large extra dimensions and a TeV-scale fundamental gravity scale. When a black hole's horizon is smaller than the compactification scale, the higher-dimensional geometry produces a larger horizon at fixed mass, which suppresses the Hawking temperature. Radiation accretion then exceeds evaporation, triggering rapid mass growth. For two or more extra dimensions, black holes starting above 10^{12} grams can reach macroscopic or even solar-mass scales by matter-radiation equality. This lowers the critical initial abundance needed to match the observed dark matter density to roughly 10^{-44}, shifting the explanation from high formation rates to dynamical growth.

Core claim

For PBHs with horizon radius smaller than the compactification scale, the higher-dimensional geometry implies a larger horizon size at fixed mass and therefore a suppressed Hawking temperature. As a result, radiation accretion can overcome evaporation in the early Universe and drive a runaway phase of rapid mass growth. By numerically solving the coupled mass and energy-density evolution equations, we show that for n ≥ 2 initially microscopic PBHs with initial mass M_i ≳ 10^{12} g can grow by many orders of magnitude and potentially reach macroscopic, even solar-mass, scales by matter-radiation equality, allowing viable scenarios with β_crit ∼ 10^{-44}.

What carries the argument

Suppressed Hawking temperature arising from higher-dimensional geometry when the black hole horizon radius is smaller than the compactification scale, which lets radiation accretion exceed evaporation and produce runaway mass growth.

Load-bearing premise

The black holes must stay in the regime where their horizon radius remains smaller than the compactification scale long enough for net accretion to occur, without mergers or other effects intervening.

What would settle it

A calculation showing that the horizon radius exceeds the compactification scale before the black hole mass has grown by many orders of magnitude, halting the runaway phase.

Figures

Figures reproduced from arXiv: 2604.14871 by Gaetano Lambiase, Giuseppe Filiberto Vitale, Luca Visinelli, Tanmay Kumar Poddar.

Figure 1
Figure 1. Figure 1: FIG. 1. Phase diagram of BHs in the presence of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Hawking temperature of BHs as a function of mass [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Evolution of the energy density ratios [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Evolution of the PBH mass for [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Critical initial abundance [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Constraints on the primordial collapse fraction as a function of the formation mass [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
read the original abstract

We study the coupled cosmological evolution of primordial black holes (PBHs) and radiation in the Arkani-Hamed-Dimopoulos-Dvali (ADD) framework with $n$ large extra dimensions and a fundamental gravity scale $M_\star$ at the TeV scale. For PBHs with horizon radius smaller than the compactification scale, the higher-dimensional geometry implies a larger horizon size at fixed mass and therefore a suppressed Hawking temperature. As a result, radiation accretion can overcome evaporation in the early Universe and drive a ``runaway'' phase of rapid mass growth. By numerically solving the coupled mass and energy-density evolution equations, we show that for $n \geq 2$ initially microscopic PBHs with initial mass $M_i \gtrsim 10^{12}\,$g can grow by many orders of magnitude and potentially reach macroscopic, even solar-mass, scales by matter-radiation equality. We determine the critical initial abundance $\beta_{\rm crit}$ required for PBHs to account for the observed dark matter density and find that extra dimensions dramatically lower this threshold, allowing viable scenarios with $\beta_{\rm crit}\sim 10^{-44}$. This identifies a previously unexplored region of parameter space in which the dark matter abundance is achieved through dynamical mass growth rather than large initial collapse fractions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript studies the cosmological evolution of microscopic primordial black holes (PBHs) in the ADD framework with n large extra dimensions and TeV-scale fundamental Planck mass M_*. It claims that when the PBH horizon lies inside the compactification radius, the higher-dimensional Hawking temperature is suppressed, enabling net radiation accretion that drives runaway mass growth. Numerical integration of the coupled ODEs for PBH mass M(t) and radiation density ρ_rad(t) is reported to show that for n ≥ 2 and initial masses M_i ≳ 10^{12} g, PBHs can reach macroscopic (even solar-mass) scales by matter-radiation equality, thereby lowering the critical initial abundance to β_crit ∼ 10^{-44} so that PBHs can comprise all dark matter.

Significance. If the reported growth persists after proper treatment of the dimensional transition, the result would open a previously inaccessible region of PBH parameter space in which dark-matter abundance is achieved via dynamical mass increase rather than large initial collapse fractions. This could relax existing constraints on β and provide a concrete link between TeV-scale extra dimensions and observable PBH phenomenology.

major comments (2)
  1. [Numerical integration of the evolution equations] The manuscript states that the coupled mass and energy-density equations are solved numerically to demonstrate the growth and the low β_crit value, but provides no explicit equations, initial conditions, numerical methods, convergence checks, or error analysis. In particular, it does not specify how (or whether) the integration switches the evaporation term from the higher-dimensional suppressed T_H to the standard 4D T_H ∼ 1/M once the horizon radius r_h(M) reaches the compactification scale R. This switch is load-bearing for the central claim that runaway growth continues to solar-mass scales.
  2. [Results on mass growth and β_crit] The quoted β_crit ∼ 10^{-44} and the assertion that M_i ≳ 10^{12} g suffice for macroscopic growth by equality rest on the assumption that the higher-dimensional regime persists throughout the accretion phase. Without an explicit check that r_h remains < R up to the final mass (or a demonstration that the transition mass lies above solar mass for the quoted parameters), the reported reduction in β_crit cannot be taken as established.
minor comments (2)
  1. The abstract and main text should include at least one representative plot of M(t) and ρ_rad(t) together with the evolution of r_h(t)/R to allow the reader to verify that the higher-dimensional regime is maintained.
  2. Standard cosmological inputs (e.g., the precise form of the radiation energy density evolution and the Hubble parameter) are invoked but not written explicitly; adding them would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We have carefully considered the points raised and provide point-by-point responses below. Where appropriate, we have revised the manuscript to include additional details and clarifications.

read point-by-point responses

  1. Referee: The manuscript states that the coupled mass and energy-density equations are solved numerically to demonstrate the growth and the low β_crit value, but provides no explicit equations, initial conditions, numerical methods, convergence checks, or error analysis. In particular, it does not specify how (or whether) the integration switches the evaporation term from the higher-dimensional suppressed T_H to the standard 4D T_H ∼ 1/M once the horizon radius r_h(M) reaches the compactification scale R. This switch is load-bearing for the central claim that runaway growth continues to solar-mass scales.

    Authors: We agree that the numerical methods and equations were not presented with sufficient detail in the submitted manuscript. In the revised version, we have added a dedicated section detailing the evolution equations for the PBH mass M(t) and the radiation energy density ρ_rad(t), including the accretion and evaporation terms in the higher-dimensional regime. The initial conditions are specified as the formation time t_i corresponding to the horizon mass M_i, with the initial PBH fraction β_i. We employed a fourth-order Runge-Kutta integrator with adaptive step sizing and verified convergence by halving the tolerance and confirming that results for final masses and β_crit change by less than 1%. Regarding the dimensional transition: for the parameter space explored (n ≥ 2, M_* ~ TeV), the mass at which r_h(M) = R exceeds 10^{40} g, well above solar mass scales. Therefore, the higher-dimensional evaporation formula remains valid throughout the integration up to matter-radiation equality, and no switch is required. We have included this calculation explicitly in the revised manuscript. revision: yes

  2. Referee: The quoted β_crit ∼ 10^{-44} and the assertion that M_i ≳ 10^{12} g suffice for macroscopic growth by equality rest on the assumption that the higher-dimensional regime persists throughout the accretion phase. Without an explicit check that r_h remains < R up to the final mass (or a demonstration that the transition mass lies above solar mass for the quoted parameters), the reported reduction in β_crit cannot be taken as established.

    Authors: We have now included an explicit verification that the higher-dimensional regime persists. Specifically, we derive the horizon radius in the higher-D metric and show that r_h(M) < R for M up to at least 10^{35} g for our fiducial parameters, which covers the growth to solar-mass scales (~10^{33} g) by equality. This confirms that the suppressed Hawking temperature applies throughout, validating the reported β_crit ~ 10^{-44}. The revised manuscript contains a new figure or appendix with this check. revision: yes

Circularity Check

0 steps flagged

No significant circularity; forward numerical integration from initial conditions

full rationale

The paper derives β_crit by numerically solving the coupled ODEs for PBH mass M(t) and radiation density ρ_rad(t) forward in time from stated initial conditions (M_i, β at early epochs) using standard cosmological inputs and the higher-dimensional Hawking/accretion rates. The final β_crit is the value that produces the observed DM density at equality; it is an output of the integration, not an input or redefinition. No self-citations are load-bearing for the central claim, no parameters are fitted to the target DM abundance and then relabeled as predictions, and the higher-D regime assumptions are stated explicitly rather than smuggled via prior self-work. The derivation is self-contained against external benchmarks (Friedmann equations, ADD Schwarzschild solutions).

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on the ADD framework, modified higher-dimensional Hawking radiation, and standard early-universe cosmology; no new entities are postulated.

free parameters (3)
  • n (number of extra dimensions)
    Set to n >= 2 to enable the suppressed evaporation regime; value chosen to produce the reported growth.
  • M_star (fundamental Planck scale)
    Fixed at TeV scale per the ADD model; enters the compactification radius and temperature formula.
  • initial PBH mass M_i
    Threshold M_i ≳ 10^12 g selected so that growth reaches macroscopic scales by equality.
axioms (2)
  • domain assumption Higher-dimensional geometry implies larger horizon radius and suppressed Hawking temperature for PBHs with r_h < compactification scale
    Invoked to justify net accretion over evaporation in the early universe.
  • standard math Radiation-dominated Friedmann-Robertson-Walker background with standard energy-density evolution
    Used as the cosmological environment for the coupled PBH-radiation equations.

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Forward citations

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