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arxiv: 2605.05232 · v1 · submitted 2026-04-28 · 🌀 gr-qc · astro-ph.CO

Recognition: unknown

Inflation driven by repulsive-like primordial black holes

Konstantinos Dialektopoulos, Theodoros Papanikolaou, Vasilios Zarikas

Authors on Pith no claims yet

Pith reviewed 2026-05-09 20:47 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.CO
keywords primordial black holesinflationSwiss-cheese modelrepulsive metricearly dark energyHubble tensionquasi-de Sitter expansiongraceful exit
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The pith

A universe filled with primordial black holes whose metrics show repulsive-like behaviour undergoes an early quasi-de Sitter expansion that can serve as inflation.

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

The paper establishes that a universe filled with primordial black holes whose local spacetime metrics exhibit repulsive-like behaviour, when embedded in the Swiss-cheese cosmological framework, produces an early phase of quasi-de Sitter expansion. For light black holes with masses below 5 times 10 to the 8 grams that evaporate before Big Bang Nucleosynthesis, this expansion becomes an exponential inflationary phase that ends naturally as the black holes evaporate, with reheating supplied by the evaporation process. Black holes around 10 to the 12 grams in mass with abundances between 0.107 and 0.5 near matter-radiation equality can instead function as an early dark energy component, which naturally helps ease the Hubble tension. The approach requires no extra scalar fields or parameter fine-tuning.

Core claim

We review a new natural inflationary mechanism operated by repulsive-like primordial black holes. In particular, working within the Swiss-cheese cosmological framework, we find that a Universe filled with PBHs, whose spacetime metric presents a repulsive-like behaviour, is characterised by an early quasi-de-Sitter cosmic expansion phase. Notably, for light PBHs with m < 5 × 10^8 g, evaporating before Big Bang Nucleosynthesis (BBN), one is met with an exponential inflationary phase with graceful exit and reheating proceeding through PBH evaporation. Furthermore, one finds as well that PBHs with m ∼ 10^12 g and abundances 0.107 < Ω^eq_PBH < 0.5 near matter-radiation equality can act as anearly

What carries the argument

The repulsive-like behaviour of the spacetime metric of primordial black holes in the Swiss-cheese cosmological framework, which induces the global quasi-de Sitter expansion.

If this is right

  • Light PBHs below 5×10^8 g produce an exponential inflationary phase with graceful exit.
  • Reheating of the universe occurs through the evaporation of these light PBHs.
  • PBHs of mass ∼10^12 g with abundances 0.107 to 0.5 near equality act as early dark energy.
  • The mechanism generates inflation and early dark energy effects without additional fields or fine-tuning.

Where Pith is reading between the lines

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

  • This PBH-driven mechanism could leave observable signatures in the stochastic gravitational wave background or in the spectrum of evaporated particles.
  • Abundance constraints from microlensing or gamma-ray observations would directly test whether the required masses and densities exist.
  • The model suggests that inhomogeneous cosmologies with modified local metrics might replace the need for homogeneous inflaton fields in some scenarios.
  • If the repulsive metric holds, it offers a potential link between early-universe acceleration and late-time dark energy hints through a single population of objects.

Load-bearing premise

The spacetime metric of the primordial black holes must exhibit repulsive-like behaviour within the Swiss-cheese model so that their collective presence produces the required quasi-de Sitter expansion without extra fields.

What would settle it

A measurement of the very early expansion rate that shows no quasi-de Sitter phase, or observational bounds that place PBH masses and abundances outside the ranges needed for the predicted inflation or early dark energy effects, would disprove the central claim.

Figures

Figures reproduced from arXiv: 2605.05232 by Konstantinos Dialektopoulos, Theodoros Papanikolaou, Vasilios Zarikas.

Figure 1
Figure 1. Figure 1: Left Panel: We depict 𝜌c as a function of the regularising fundamental length scale 𝐿. Right Panel: We display 𝜌evap (color-bar axis) as a function of the PBH mass 𝑚 (𝑥-axis) and the scale 𝐿 (𝑦-axis). The grey region 𝐿 > 4𝐺N𝑚 3 √ 3 , where horizonless objects are realized, is not of theoretical interest, while the magenta one, where 𝜌evap < 𝜌BBN is observationally excluded. 4.2 Early dark energy contributi… view at source ↗
Figure 2
Figure 2. Figure 2: The dynamics of the cosmological horizon 𝐻 −1 for a Universe dominated by repulsive primordial black holes of Hayward type. The new inflationary mechanism introduced in [52] opens new perspectives to study, in partic￾ular to find specific quantum gravity frameworks where such PBHs can be produced and study the associated cosmological phenomenology. Indicatively, we need to mention that such PBH-driven earl… view at source ↗
read the original abstract

We review a new natural inflationary mechanism operated by repulsive-like primordial black holes (PBHs). In particular, working within the ``Swiss - Cheese" cosmological framework, we find that a Universe filled with PBHs, whose spacetime metric presents a repulsive-like behaviour, is characterised by an early quasi-de-Sitter cosmic expansion phase. Notably, for light PBHs with $m < 5 \times 10^8 \mathrm{g}$, evaporating before Big Bang Nucleosynthesis (BBN), one is met with an exponential inflationary phase with graceful exit and reheating proceeding through PBH evaporation. Furthermore, one finds as well that PBHs with $m \sim 10^{12}\mathrm{g}$ and abundances $0.107 < \Omega^\mathrm{eq}_\mathrm{PBH} < 0.5$ near matter-radiation equality can act as an early dark energy component, easing in this way naturally the Hubble tension.

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 paper claims that in the Swiss-cheese cosmological framework, a universe filled with primordial black holes (PBHs) whose interior metrics exhibit repulsive-like behavior undergoes an early quasi-de Sitter expansion phase. For light PBHs with m < 5 × 10^8 g evaporating before BBN, this produces exponential inflation with graceful exit and reheating via PBH evaporation. PBHs with m ∼ 10^12 g and abundances 0.107 < Ω^eq_PBH < 0.5 near matter-radiation equality act as an early dark energy component that naturally eases the Hubble tension.

Significance. If rigorously derived and shown to hold, the result would be significant as a field-free, PBH-based mechanism for inflation and a natural resolution to the Hubble tension, with implications for early-universe cosmology and PBH abundance constraints.

major comments (2)
  1. [Swiss-cheese construction and effective dynamics] The central claim that repulsive-like PBH interiors in the Swiss-cheese construction drive a global quasi-de Sitter phase is load-bearing but unsupported. In the Einstein-Straus matching, the global scale-factor evolution remains fixed by the FLRW cheese Friedmann equation; junction conditions affect only the surface stress tensor and local geometry. The manuscript provides no explicit derivation or volume-averaged effective stress-energy tensor demonstrating w ≈ −1 domination (see the construction in the model section and the results for the inflationary phase).
  2. [Parameter choices and results] The specific ranges m < 5 × 10^8 g (for inflation) and 0.107 < Ω^eq_PBH < 0.5 (for early dark energy) are presented as yielding the desired quasi-de Sitter and Hubble-tension effects. No independent derivation from the junction conditions or dynamics is shown; the windows appear selected to match targets rather than predicted, undermining the 'natural' and 'parameter-free' aspects of the proposal.
minor comments (2)
  1. [Introduction and model setup] Define 'repulsive-like' behavior explicitly by reference to the interior metric (e.g., negative-mass Schwarzschild or SdS with negative Λ) at first use.
  2. [References] Add references to the original Einstein-Straus Swiss-cheese paper and standard PBH evaporation calculations to contextualize the junction conditions and reheating.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address the major comments point by point below, providing clarifications on the effective dynamics and the origin of the quoted parameter ranges. We have revised the manuscript to include the requested explicit derivations.

read point-by-point responses

  1. Referee: The central claim that repulsive-like PBH interiors in the Swiss-cheese construction drive a global quasi-de Sitter phase is load-bearing but unsupported. In the Einstein-Straus matching, the global scale-factor evolution remains fixed by the FLRW cheese Friedmann equation; junction conditions affect only the surface stress tensor and local geometry. The manuscript provides no explicit derivation or volume-averaged effective stress-energy tensor demonstrating w ≈ −1 domination (see the construction in the model section and the results for the inflationary phase).

    Authors: We appreciate the referee highlighting the need for a rigorous derivation. While the cheese follows the standard FLRW Friedmann equation, the Israel junction conditions at the boundaries of the repulsive-like interiors generate a surface stress-energy tensor. When volume-averaged over the Swiss-cheese lattice (accounting for the PBH volume fraction), this contributes an effective negative-pressure term. In the revised model section we now explicitly compute this volume-averaged effective stress-energy tensor from the junction conditions, showing that w_eff ≈ −1 during the epoch when the holes occupy a non-negligible fraction of the volume, thereby driving the quasi-de Sitter phase. This derivation supports the central claim without altering the underlying cheese evolution. revision: yes

  2. Referee: The specific ranges m < 5 × 10^8 g (for inflation) and 0.107 < Ω^eq_PBH < 0.5 (for early dark energy) are presented as yielding the desired quasi-de Sitter and Hubble-tension effects. No independent derivation from the junction conditions or dynamics is shown; the windows appear selected to match targets rather than predicted, undermining the 'natural' and 'parameter-free' aspects of the proposal.

    Authors: The ranges follow directly from the model dynamics. The upper mass bound m < 5 × 10^8 g is obtained from the Hawking evaporation timescale τ_evap ∝ m^3, requiring evaporation before BBN (t ≲ 1 s) so that reheating occurs via PBH decay; this is independent of the junctions but is a necessary condition for the inflationary scenario to be viable. The abundance interval 0.107 < Ω^eq_PBH < 0.5 is found by solving the modified expansion history that incorporates the effective w derived from the junction conditions, selecting the values that produce the required early dark-energy-like contribution to reduce the sound horizon while remaining consistent with BBN and CMB bounds. The revised results section now presents these steps explicitly, demonstrating that the windows are predicted by the repulsive-like dynamics rather than chosen ad hoc. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation remains independent of its target outputs

full rationale

The paper constructs an effective quasi-de Sitter phase from the Swiss-cheese matching of repulsive-like PBH interiors to an FLRW cheese. The quoted mass and abundance windows appear as derived consequences of the junction conditions and evaporation dynamics rather than parameters fitted to force the desired expansion or Hubble-tension relief. No self-definitional loop, fitted-input-renamed-as-prediction, or load-bearing self-citation is exhibited in the given text; the central claim is therefore not equivalent to its inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claim rests on the Swiss-cheese framework and the postulate of repulsive-like PBH metrics, with mass and abundance ranges chosen to produce inflation and early dark energy effects. No independent evidence or derivations for these choices are visible in the abstract.

free parameters (2)
  • PBH mass threshold for inflation
    m < 5 × 10^8 g chosen so evaporation occurs before BBN to enable graceful exit
  • PBH abundance window for early dark energy
    0.107 < Ω^eq_PBH < 0.5 selected near matter-radiation equality to ease Hubble tension
axioms (1)
  • domain assumption Swiss-cheese cosmological framework applies to a universe filled with PBHs
    Invoked to model the global expansion driven by local repulsive-like metrics
invented entities (1)
  • repulsive-like primordial black holes no independent evidence
    purpose: To generate quasi-de Sitter expansion and early dark energy
    Postulated metric behavior not standard for PBHs; no independent falsifiable prediction supplied

pith-pipeline@v0.9.0 · 5464 in / 1692 out tokens · 38202 ms · 2026-05-09T20:47:27.832628+00:00 · methodology

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Reference graph

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