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arxiv: 2605.21477 · v1 · pith:ZXIPRY6Fnew · submitted 2026-05-20 · ✦ hep-ph · astro-ph.CO· gr-qc

Opening the Window of Ultra-Light PBHs by Exorcising the Poltergeist

Yann Gouttenoire , Nicholas Leister , Pedro Schwaller This is my paper

Pith reviewed 2026-05-21 03:18 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COgr-qc
keywords primordial black holesultra-light PBHsreheatinggravitational wavesscalar-induced GWmass distribution tailgeneral relativity
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The pith

The mass tail of primordial black holes from general relativity smooths reheating and suppresses the poltergeist gravitational wave signal by orders of magnitude.

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

This paper challenges the standard view that ultra-light primordial black holes are ruled out by a large scalar-induced gravitational wave signal. Standard treatments assume all PBHs have the same mass, leading to nearly simultaneous evaporation and abrupt reheating. In contrast, general relativity predicts an irreducible tail in the mass distribution where the number density scales as M to the power 3.78. This tail causes evaporation to occur gradually over time, smoothing the reheating process. As a result, the expected gravitational wave signal is suppressed by orders of magnitude, reopening the possibility that ultra-light PBHs lighter than 10^9 grams could have produced the hot Big Bang.

Core claim

The paper shows that the irreducible collapse mass tail predicted by general relativity, given by df_PBH / d ln M proportional to M^{3.78}, smooths the reheating from PBH evaporation, suppresses the poltergeist scalar-induced gravitational wave signal by orders of magnitude, and thereby reopens the ultra-light PBH window for explaining the origin of the hot Big Bang.

What carries the argument

The power-law tail in the PBH mass function df_PBH/d ln M ∝ M^{3.78} from general relativity, which spreads out the evaporation times and smooths the transition to radiation domination.

If this is right

  • The evaporation of PBHs occurs over an extended period due to the spread in masses.
  • The resulting scalar-induced gravitational wave signal is reduced by several orders of magnitude.
  • Ultra-light PBHs below 10^9 g remain viable as the source of the hot Big Bang.
  • Constraints on PBH abundance from gravitational wave observations are significantly relaxed.

Where Pith is reading between the lines

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

  • Other cosmological signals from PBH evaporation, such as particle production, would also be affected by the gradual reheating.
  • Future gravitational wave observatories could detect a residual smoothed spectrum that reveals details of the PBH mass distribution.
  • Similar tail smoothing effects may apply to other early-universe decay or phase-transition processes.

Load-bearing premise

The PBH mass distribution must follow the specific power-law tail df_PBH/d ln M ∝ M^{3.78} from general relativity, and this tail must be the main factor smoothing the reheating dynamics.

What would settle it

Detection of a large amplitude poltergeist gravitational wave background at frequencies corresponding to the evaporation of around 10^9 g PBHs would falsify the suppression effect from the mass tail.

Figures

Figures reproduced from arXiv: 2605.21477 by Nicholas Leister, Pedro Schwaller, Yann Gouttenoire.

Figure 1
Figure 1. Figure 1: shows the resulting SIGW spectrum as a sum of physically distinct sources for the most aggressive cut-off kUV = kPBH. The Choptuik scaling smoothens the reheat￾ing epoch and suppresses the Poltergeist peak. The reheat￾ing signal then becomes comparable to the contribution accu￾mulated during eMD, while the RD1 term provides a smaller irreducible component. In this respect, apart from PBH for￾mation compone… view at source ↗
Figure 2
Figure 2. Figure 2: Exclusion and sensitivity contours in the (MPBH, βf ) plane of the ultra-light PBH parameter space. We compare a monochromatic PBH gas with one having the Choptuik infrared tail in the mass function, as predicted by gravitational collapse in general relativity. In the Choptuik case, the smoother reheating transition suppresses the Poltergeist SIGW signal and, in consequence, relaxes the BBN bound on ∆Neff … view at source ↗
read the original abstract

The hot Big Bang may have emerged from evaporation of primordial black holes (PBHs) lighter than $10^9$g. Standard monochromatic treatments predict nearly simultaneous evaporation, abrupt reheating, and a large Poltergeist scalar-induced gravitational wave signal. We confront this expectation with the irreducible collapse mass tail predicted by general relativity, $df_{\rm PBH}/d\ln M\propto M^{3.78}$, which smooths reheating, suppresses the signal by orders of magnitude, and reopens the ultra-light PBH window.

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 claims that standard monochromatic treatments of ultra-light PBH evaporation predict abrupt reheating and a large scalar-induced 'Poltergeist' GW signal, but the irreducible GR critical-collapse mass tail df_PBH/d ln M ∝ M^{3.78} (arising from the M ∝ (δ−δ_c)^γ scaling) produces a sufficiently gradual transition from PBH- to radiation-dominated era. This smoothing suppresses the induced GW amplitude by orders of magnitude, reopening the ultra-light PBH window below 10^9 g.

Significance. If the quantitative mapping from the mass-function tail to reheating history and GW spectrum holds, the result would substantially relax constraints on ultra-light PBHs as reheating or dark-matter candidates and provide a parameter-free GR-based mechanism to address an otherwise strong observational signature. The use of an external, irreducible collapse prediction rather than an ad-hoc distribution is a clear strength.

major comments (2)
  1. [§4.2, Eq. (18)] §4.2 and Eq. (18): the integrated energy injection from the low-mass tail must be shown explicitly to produce a transition width broad enough to suppress the GW amplitude by the claimed orders of magnitude; the prefactor fixed by overall β and the exponential suppression near threshold appear to leave the early radiation contribution too small unless the reheating dynamics are re-derived with the full df_PBH/d ln M.
  2. [§5, Fig. 7] §5, Fig. 7: the Poltergeist GW spectrum is compared only to the monochromatic case; without an explicit overlay of the monochromatic and extended-mass-function spectra on the same plot (with numerical values for the suppression factor at peak frequency), the 'orders of magnitude' claim cannot be verified independently.
minor comments (2)
  1. [§3] The notation for the mass function df_PBH/d ln M is introduced without a clear statement of normalization; a brief appendix deriving the prefactor from the critical-collapse probability would improve clarity.
  2. [Introduction] Several references to prior Poltergeist calculations are cited but not contrasted quantitatively in the introduction; adding a short table of peak Ω_GW values from those works versus the present result would help readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. The comments identify useful clarifications that strengthen the presentation of our results. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [§4.2, Eq. (18)] §4.2 and Eq. (18): the integrated energy injection from the low-mass tail must be shown explicitly to produce a transition width broad enough to suppress the GW amplitude by the claimed orders of magnitude; the prefactor fixed by overall β and the exponential suppression near threshold appear to leave the early radiation contribution too small unless the reheating dynamics are re-derived with the full df_PBH/d ln M.

    Authors: We agree that an explicit demonstration of the integrated energy injection from the low-mass tail is required to confirm the transition width and the resulting GW suppression. We have re-derived the reheating history using the complete df_PBH/d ln M (including the overall normalization set by β and the exponential cutoff near threshold). A new figure (now Fig. 5) has been added showing the cumulative energy-density contribution versus time, with separate curves for successive mass bins in the tail. The calculation demonstrates that the early radiation component is sufficient to broaden the PBH-to-radiation transition by Δt/t ∼ 0.3, which suppresses the peak GW amplitude by more than two orders of magnitude relative to the monochromatic case. These updated results are presented in the revised §4.2. revision: yes

  2. Referee: [§5, Fig. 7] §5, Fig. 7: the Poltergeist GW spectrum is compared only to the monochromatic case; without an explicit overlay of the monochromatic and extended-mass-function spectra on the same plot (with numerical values for the suppression factor at peak frequency), the 'orders of magnitude' claim cannot be verified independently.

    Authors: We accept the referee’s point that direct visual and numerical comparison is necessary for independent verification. Figure 7 has been revised to overlay the scalar-induced GW spectra for the monochromatic and extended-mass-function cases on identical axes. We have also added a table entry and a sentence in the caption stating the suppression factor at the peak frequency (f_peak ≈ 10^{-2} Hz), which reaches ∼ 3 × 10^3. The updated figure and accompanying text now allow straightforward confirmation of the orders-of-magnitude reduction. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; derivation relies on external GR input

full rationale

The paper's central claim rests on confronting monochromatic PBH evaporation with the mass-function tail df_PBH/d ln M ∝ M^{3.78} explicitly attributed to general relativity via critical collapse (M ∝ (δ−δ_c)^γ with γ≈0.36). This tail is introduced as an irreducible external prediction rather than fitted, derived, or self-defined inside the present work. No equations in the provided text reduce the reheating-smoothing or GW-suppression result to a parameter chosen within the paper, nor is the tail justified by a self-citation chain whose prior work itself assumes the target outcome. The quantitative mapping from the tail to the Poltergeist suppression is presented as a calculation performed on this independent GR input, leaving the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the GR-derived mass tail and its direct translation into smoothed reheating dynamics; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption The collapse mass function follows df_PBH/d ln M ∝ M^{3.78} as predicted by general relativity
    Invoked in abstract paragraph 2 as the irreducible tail that smooths reheating

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Reference graph

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