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arxiv: 2605.28953 · v1 · pith:P33XBN5Onew · submitted 2026-05-27 · 🌀 gr-qc · astro-ph.CO

Signatures of loop quantum gravity in primordial black hole cosmologies

Antoine Dierckx , S\'ebastien Clesse , Francesca Vidotto This is my paper

Pith reviewed 2026-06-29 10:19 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.CO
keywords primordial black holesloop quantum gravitydark matterHawking evaporationPlanckian remnantsgravitational wavesearly universe cosmology
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The pith

Primordial black holes near 10^3 kg mass let their remnants form all dark matter after natural reheating.

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

The paper examines whether dark matter could be made of stable Planckian remnants left by evaporating primordial black holes, a possibility raised by loop quantum gravity. It maps out mass-dependent regimes and shows that PBHs below 10^3 kg overproduce relics while those between 10^3 kg and 10^12 kg leave relics as only a minor dark-matter fraction. A narrow window around 10^3 kg permits Hawking evaporation to reheat the universe so that the remnants account for all present dark matter, with the initial PBH abundance free to range from 10^{-10} to order one without fine-tuning. The resulting early matter-dominated phase amplifies fluctuations and sources observable scalar-induced gravitational waves.

Core claim

A PBH mass around 10^3 kg allows Hawking evaporation to reheat the Universe while the remnants entirely constitute the present-day DM. This scenario does not require fine-tuning the initial abundance of PBHs of this mass, which could range from 10^{-10} to order one. These early-Universe cosmologies produce distinct observational signatures through scalar-induced gravitational waves sourced by primordial or Poisson fluctuations amplified by the early PBH-dominated era, and through constraints on the effective number of relativistic degrees of freedom.

What carries the argument

Mass-dependent Hawking evaporation of primordial black holes that leaves stable Planckian remnants, whose abundance is limited by overproduction or underproduction constraints and whose early dominance creates an amplified gravitational-wave background.

If this is right

  • Any observational evidence for PBHs lighter than 10^3 kg would overproduce Planckian relics and thereby challenge models with quasi-stable remnants.
  • Hawking radiation from PBHs between 10^3 kg and 10^12 kg restricts Planckian relics to a highly subdominant dark-matter component.
  • The early PBH-dominated era amplifies scalar-induced gravitational waves that current and future detectors (LIGO/Virgo/KAGRA, Einstein Telescope, LISA) can observe.
  • Measurements of the effective number of relativistic degrees of freedom together with gravitational-wave data can jointly bound both the initial PBH abundance and the present-day relic abundance.

Where Pith is reading between the lines

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

  • The narrow viable mass window implies that any confirmation would tie loop-quantum-gravity remnants to dark matter in a way that is robust against variations in initial conditions.
  • The amplified gravitational-wave spectrum may carry a distinct shape set by the duration of the PBH-dominated phase, offering a potential discriminator from other early-matter-domination models.
  • Non-detection of the predicted waves in the relevant frequency bands could exclude this remnant-dark-matter channel even before direct relic searches become feasible.

Load-bearing premise

Loop quantum gravity yields stable Planckian remnants from primordial black hole evaporation that persist unchanged to the present day and can serve as dark matter.

What would settle it

Detection of primordial black holes with masses well below or above the 10^3 kg window together with a relic density inconsistent with the predicted range, or the absence of the expected gravitational-wave background from an early PBH-dominated era, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.28953 by Antoine Dierckx, Francesca Vidotto, S\'ebastien Clesse.

Figure 1
Figure 1. Figure 1: FIG. 1. The history of the Universe is divided into four dis [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Upper bounds on the initial PBH abundance [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Time evolution of the relative densities of DM excluding remnants Ω [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Scalar-induced GW spectrum today for a PBH mass [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Zoom of the parameter space ( [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Temperature of the thermal bath at [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Reheating temperature [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Variation of the effective number of relativistic degrees of freedom ∆ [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Simulation results for the maximum initial PBH abundance [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
read the original abstract

The possibility that Dark Matter (DM) is partially or totally constituted by stable Planckian remnants of light Primordial Black Holes (PBHs), suggested for instance by Loop Quantum Gravity (LQG), is investigated. Distinct phenomenological regimes are identified, including scenarios that trigger an early matter-dominated epoch. New constraints are derived on the initial PBH and final remnant abundances. We show that a significant initial abundance of PBHs lighter than $10^3$ kg would overproduce Planckian relics, implying that any observational evidence for such PBHs would challenge models with quasi-stable remnants. Conversely, the products of Hawking radiation from PBHs with masses between $10^3$ and $10^{12}$ kg impose that Planckian relics could only be a highly subdominant DM component. We identify a PBH mass around $10^3$ kg for which Hawking evaporation naturally reheats the Universe while the remnants entirely constitute the present-day DM. Such a scenario does not require fine-tuning the initial abundance of PBH of this mass, which could range from $10^{-10}$ to order one. These early-Universe cosmologies yield distinct observational signatures: scalar-induced gravitational waves sourced by primordial or Poisson fluctuations that are amplified by the early PBH-dominated era. Current and future observations of LIGO/Virgo/KAGRA, the Einstein Telescope and LISA, as well as probes of the effective number of relativistic degrees of freedom, can be used to probe and constrain the initial PBH abundance and the present-day abundance of Planckian relics.

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 investigates the possibility that dark matter consists of stable Planckian remnants from evaporating light primordial black holes (PBHs), as suggested by loop quantum gravity. It identifies distinct phenomenological regimes (including early matter-dominated epochs), derives constraints on initial PBH and final remnant abundances, and highlights a specific PBH mass window around 10^3 kg where Hawking evaporation reheats the universe while the remnants account for all present-day dark matter without fine-tuning the initial abundance (allowed range 10^{-10} to O(1)). The work also predicts observable signatures in scalar-induced gravitational waves (amplified by the PBH-dominated era) and the effective number of relativistic degrees of freedom, testable with LIGO/Virgo/KAGRA, Einstein Telescope, LISA, and cosmological probes.

Significance. If the remnant-stability assumption holds, the paper supplies a concrete, falsifiable link between LQG-motivated remnants and early-universe cosmology. The identification of a natural reheating + DM-matching window at ~10^3 kg, together with the broad allowed initial-abundance range and the explicit GW and N_eff signatures, constitutes a strength. The work is grounded in standard Hawking evaporation and cosmology applied to the remnant hypothesis and offers clear observational targets.

major comments (2)
  1. [Abstract and Introduction] Abstract (opening sentence) and §1: The entire scenario, including the reheating calculation and the DM abundance matching at the ~10^3 kg mass, rests on the assumption that LQG produces stable, non-evaporating Planckian remnants. No derivation from LQG area quantization, effective dynamics, or specific model is supplied to justify why the remnant does not continue to radiate or decay after reaching the Planck scale. This is load-bearing for the central claim.
  2. [Abstract] Abstract (paragraph on the 10^3 kg window): The statement that the initial PBH abundance 'could range from 10^{-10} to order one' without fine-tuning is asserted but not demonstrated via explicit evolution equations for the abundance; the supporting calculation that maps the evaporation endpoint to the observed DM density is not shown in the provided text and is required to substantiate the 'no fine-tuning' claim.
minor comments (2)
  1. [Abstract] The abstract refers to 'distinct phenomenological regimes' but does not enumerate them; adding a short list or table in the introduction would improve readability.
  2. [Abstract] Notation for the initial PBH fraction and remnant fraction should be defined consistently when first introduced; the transition between the two is not always clear from the abstract alone.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment of the manuscript's significance, and constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and Introduction] Abstract (opening sentence) and §1: The entire scenario, including the reheating calculation and the DM abundance matching at the ~10^3 kg mass, rests on the assumption that LQG produces stable, non-evaporating Planckian remnants. No derivation from LQG area quantization, effective dynamics, or specific model is supplied to justify why the remnant does not continue to radiate or decay after reaching the Planck scale. This is load-bearing for the central claim.

    Authors: We agree that remnant stability is a foundational assumption of the scenario. The manuscript explicitly frames the work as an investigation of the phenomenological consequences of stable Planckian remnants 'suggested for instance by Loop Quantum Gravity (LQG)', rather than a derivation of that stability from first principles. A full derivation from LQG area quantization or effective dynamics lies outside the scope of this cosmology-focused paper and would require a separate quantum-gravity analysis. revision: no

  2. Referee: [Abstract] Abstract (paragraph on the 10^3 kg window): The statement that the initial PBH abundance 'could range from 10^{-10} to order one' without fine-tuning is asserted but not demonstrated via explicit evolution equations for the abundance; the supporting calculation that maps the evaporation endpoint to the observed DM density is not shown in the provided text and is required to substantiate the 'no fine-tuning' claim.

    Authors: The referee is correct that the explicit evolution equations and the mapping from evaporation endpoint to present-day DM density should be shown more transparently to support the no-fine-tuning statement. In the revised manuscript we will insert the relevant Boltzmann equations for the PBH and remnant energy densities together with the analytic mapping that yields the quoted abundance window for a PBH mass of ~10^3 kg. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard cosmology applied to external LQG hypothesis

full rationale

The paper takes the stability of Planckian remnants as a motivating hypothesis suggested by LQG without deriving it internally or via self-citation chains. All constraints on PBH abundances, reheating, and DM matching follow from standard Hawking evaporation rates and cosmological evolution equations applied to this assumption. No predictions reduce to fitted parameters by the paper's own equations, and no load-bearing steps invoke self-citations or ansatze smuggled from prior work. The derivation chain is independent and self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

Abstract provides limited detail; relies on standard cosmological evolution and Hawking radiation, with the key assumption of stable LQG remnants introduced without independent evidence here.

axioms (2)
  • domain assumption Loop quantum gravity produces stable Planckian remnants that do not evaporate further
    Invoked in the first sentence as the motivating scenario for the entire investigation
  • standard math Standard Hawking radiation and cosmological evolution apply to PBHs
    Used to derive abundance constraints and reheating
invented entities (1)
  • Planckian relics as dark matter component no independent evidence
    purpose: Constitute present-day dark matter
    Postulated as stable end-products of PBH evaporation in LQG; no independent falsifiable handle provided in the abstract

pith-pipeline@v0.9.1-grok · 5818 in / 1492 out tokens · 32425 ms · 2026-06-29T10:19:55.515689+00:00 · methodology

discussion (0)

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Reference graph

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