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arxiv: 2604.26005 · v1 · submitted 2026-04-28 · ✦ hep-ph · astro-ph.CO

Recognition: unknown

Asteroid-mass Primordial Black Holes as Dark Matter from Supersymmetry

Andrea Boccia, Marco Chianese

Pith reviewed 2026-05-07 15:46 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords primordial black holesdark mattersupersymmetryMSSMequation of stateearly universecurvature perturbations
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0 comments X

The pith

Supersymmetry lets asteroid-mass primordial black holes explain all dark matter by softening the early universe.

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

The paper shows that heavy supersymmetric particles in the MSSM cause a temporary softening of the universe's equation of state when they turn non-relativistic. This boosts the formation of primordial black holes in the asteroid-mass range from a broad primordial curvature spectrum. For supersymmetric masses above about 10^5 GeV the resulting PBH abundance can match the full dark matter density while staying inside observational limits. In the Standard Model the same setup produces either too few or too heavy PBHs that are ruled out by microlensing and other bounds. Lighter supersymmetric spectra shift the PBH masses upward into strongly constrained regimes.

Core claim

In supersymmetric extensions of the Standard Model the presence of heavy particles leads to a transient softening of the equation of state during their non-relativistic transition. This effect enhances the formation of asteroid-mass primordial black holes, enabling them to account for the total dark matter abundance when supersymmetric masses exceed approximately 10^5 GeV while remaining consistent with current bounds. For lighter spectra production shifts toward masses above 10^22 g that are excluded by microlensing searches.

What carries the argument

The transient softening of the equation of state during the non-relativistic transition of heavy supersymmetric particles, which increases the efficiency of PBH formation from curvature perturbations.

If this is right

  • For supersymmetric masses above 10^5 GeV the PBH mass function rises enough in the asteroid window to supply the entire dark matter density.
  • The same initial conditions in the Standard Model produce PBH abundances excluded by existing constraints.
  • Lighter supersymmetric mass spectra move PBH production above 10^22 g and thereby reduce the allowed dark matter fraction.
  • The shape of the PBH mass function varies with the three characteristic mass scales of the MSSM spectrum.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Asteroid-mass PBH searches could indirectly constrain the scale of supersymmetry.
  • Similar softening effects might appear in other models containing heavy non-relativistic species.
  • The mechanism ties the amplitude of the primordial spectrum directly to the supersymmetry-breaking scale.
  • Gravitational-wave backgrounds from PBH binaries could carry a distinct signature of the enhanced low-mass population.

Load-bearing premise

The primordial curvature power spectrum is assumed to be broad and approximately scale-invariant.

What would settle it

A null result from microlensing or gravitational-wave searches that rules out an enhanced asteroid-mass PBH population at the predicted level for supersymmetric masses above 10^5 GeV would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.26005 by Andrea Boccia, Marco Chianese.

Figure 1
Figure 1. Figure 1: FIG. 1. Equation of state parameter as a function of tem view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Primordial black hole mass fraction view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Maximum enhancement of the PBH mass fraction in view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Maximum allowed DM fraction in PBHs, view at source ↗
read the original abstract

We study the formation of asteroid-mass Primordial Black Holes (PBHs) as a dark matter candidate in supersymmetric extensions of the Standard Model. We show that the presence of heavy particles predicted in the Minimal Supersymmetric Standard Model (MSSM) can lead to a transient softening of the equation of state of the Universe during their non-relativistic transition, enhancing PBH formation. We compute the effective equation of state for different realizations of the MSSM mass spectrum, parametrized by three characteristic mass scales. Assuming a broad and approximately scale-invariant primordial curvature power spectrum, we evaluate the resulting PBH mass functions and compare them with current observational constraints. We find that, for supersymmetric masses above $\sim 10^5\,\mathrm{GeV}$, the PBH mass function is significantly enhanced in the asteroid-mass window, allowing PBHs to account for the total dark matter abundance without violating existing bounds. In contrast, within the Standard Model the same configurations lead to PBH mass functions that are observationally excluded. For lighter supersymmetric mass spectra, PBH production is shifted toward masses above $\sim 10^{22}\,\mathrm{g}$, which are strongly constrained by microlensing searches, thereby reducing their allowed contribution to the dark matter density.

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 formation of asteroid-mass primordial black holes (PBHs) as dark matter in supersymmetric extensions of the Standard Model. It argues that heavy MSSM particles induce a transient softening of the cosmic equation of state during their non-relativistic transition, enhancing PBH production. Parametrizing the MSSM spectrum by three characteristic mass scales and assuming a broad, approximately scale-invariant primordial curvature power spectrum, the authors compute effective equations of state, derive PBH mass functions, and conclude that supersymmetric masses above ~10^5 GeV allow PBHs to comprise all dark matter in the asteroid-mass window without violating bounds, while the Standard Model case is excluded and lighter spectra are constrained by microlensing.

Significance. If the quantitative results hold, the work establishes a concrete link between supersymmetry and viable PBH dark matter by exploiting beyond-Standard-Model particle thresholds to evade Standard Model constraints on early-universe PBH formation. This could motivate targeted searches for asteroid-mass PBHs and high-scale supersymmetry, while highlighting the sensitivity of PBH abundance to the timing of non-relativistic transitions in extended particle spectra.

major comments (2)
  1. [Abstract and results on PBH mass functions] The central quantitative claim (PBH mass function enhancement allowing all dark matter for supersymmetric masses ≳10^5 GeV) is presented without visible error propagation, full numerical details of the effective EoS integration, or explicit uncertainty bands on the power spectrum amplitude; this renders the precise mass threshold and abundance normalization only partially substantiated.
  2. [Section on primordial power spectrum and PBH formation] The derivation of the PBH mass function relies on the assumption of a broad and approximately scale-invariant primordial curvature power spectrum; no sensitivity analysis to deviations from exact scale invariance or to the amplitude normalization is provided, yet this assumption directly controls the overall normalization and the localization of the enhancement to the asteroid-mass window.
minor comments (2)
  1. [Abstract] The abstract would benefit from a brief statement of the asteroid-mass range (e.g., 10^17–10^22 g) and the precise observational bounds used for comparison.
  2. [MSSM spectrum parametrization] Notation for the three characteristic mass scales should be introduced with explicit symbols and ranges in the main text to improve readability of the EoS parametrization.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the positive assessment of its potential significance. We address each major comment below and describe the revisions we will implement to improve the substantiation and robustness of our results.

read point-by-point responses

  1. Referee: [Abstract and results on PBH mass functions] The central quantitative claim (PBH mass function enhancement allowing all dark matter for supersymmetric masses ≳10^5 GeV) is presented without visible error propagation, full numerical details of the effective EoS integration, or explicit uncertainty bands on the power spectrum amplitude; this renders the precise mass threshold and abundance normalization only partially substantiated.

    Authors: We agree that greater transparency in the numerical procedures and uncertainties would strengthen the presentation. In the revised manuscript we will expand the relevant sections to provide explicit details of the effective equation-of-state integration, including the numerical method, time-stepping scheme, and convergence tests. We will also add uncertainty bands to the PBH mass-function figures that reflect the range of primordial power-spectrum amplitudes consistent with our broad, approximately scale-invariant assumption. A full Bayesian error-propagation analysis over all model parameters lies beyond the scope of the present study, but the added documentation and bands will make the reported threshold of ~10^5 GeV and the associated abundance more clearly substantiated. revision: partial

  2. Referee: [Section on primordial power spectrum and PBH formation] The derivation of the PBH mass function relies on the assumption of a broad and approximately scale-invariant primordial curvature power spectrum; no sensitivity analysis to deviations from exact scale invariance or to the amplitude normalization is provided, yet this assumption directly controls the overall normalization and the localization of the enhancement to the asteroid-mass window.

    Authors: We acknowledge that the robustness of the results with respect to the primordial spectrum assumptions merits explicit demonstration. In the revised manuscript we will add a dedicated subsection (and accompanying figures) that explores the sensitivity of the PBH mass function to (i) small deviations from exact scale invariance, parameterized by a spectral index n_s = 1 + δ with |δ| ≲ 0.05, and (ii) variations in the overall amplitude within the window that still permits appreciable PBH formation. These tests will show that the enhancement in the asteroid-mass range for supersymmetric masses ≳ 10^5 GeV persists across the explored variations, while clarifying how the normalization and localization depend on the assumed spectrum. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation uses standard inputs to compute output

full rationale

The paper takes as given a broad approximately scale-invariant primordial curvature power spectrum and parametrizes the MSSM by three mass scales. It computes the effective equation of state from the non-relativistic transitions of those particles, then applies standard PBH formation formulas to obtain the mass function. The enhancement in the asteroid-mass window for m ≳ 10^5 GeV (and the contrast with the SM) follows directly as a calculated consequence; it is not equivalent to any input by construction, nor is any result renamed from a fit. No load-bearing self-citation or ansatz smuggling is present in the stated chain.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim depends on standard cosmological evolution plus an assumed primordial power spectrum shape and amplitude, with the MSSM spectrum parametrized by three free mass scales whose specific values are chosen to illustrate the enhancement.

free parameters (2)
  • three characteristic mass scales
    MSSM spectrum parametrized by three characteristic mass scales whose values control the timing and strength of the EoS softening.
  • amplitude of primordial curvature power spectrum
    Broad approximately scale-invariant spectrum whose overall amplitude is used to normalize the PBH abundance to the dark matter density.
axioms (2)
  • standard math Standard FLRW cosmology with radiation-to-matter transitions governed by particle content
    Invoked to compute the effective equation of state during non-relativistic transitions of heavy particles.
  • domain assumption MSSM particle spectrum and their decoupling behavior
    Presence and mass ordering of heavy supersymmetric particles assumed to produce the transient softening.

pith-pipeline@v0.9.0 · 5517 in / 1394 out tokens · 47375 ms · 2026-05-07T15:46:03.576747+00:00 · methodology

discussion (0)

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