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arxiv: 2605.14044 · v1 · submitted 2026-05-13 · 🌌 astro-ph.CO · hep-ph

Recognition: no theorem link

The Magnetic Origin of Primordial Black Holes: Ultralight PBHs and Secondary GWs

Subhasis Maiti , Debaprasad Maity
Authors on Pith no claims yet

Pith reviewed 2026-05-15 02:05 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-ph
keywords primordial black holesmagnetogenesisgravitational wavesinflationcurvature perturbationsreheatingultralight PBHs
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The pith

Inflationary magnetic fields induce ultralight primordial black holes across a wide mass range.

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

This work develops a magnetogenesis scenario during inflation that creates large curvature perturbations at small scales. These perturbations trigger the formation of ultralight PBHs over a broad mass spectrum without requiring ultra-slow-roll dynamics. The setup also generates a stochastic gravitational wave background from the magnetic fields and from PBH evaporation, carrying signatures of the model parameters. Readers should care as it connects magnetic field generation in the early universe to observable black holes and waves, offering a new probe of inflation and reheating.

Core claim

We propose a magnetogenesis model in which large curvature perturbations are induced at small scales, leading to the efficient production of ultralight PBHs across a broad mass spectrum. We analyze the phenomenological implications of these ultralight PBHs for early-Universe cosmology, particularly during reheating, and compute the resulting stochastic gravitational wave background generated by both the electromagnetic spectrum and evaporating PBHs, which exhibits distinctive features tied to the underlying magnetogenesis model parameters.

What carries the argument

Magnetogenesis model that sources large small-scale curvature perturbations from primordial inflationary magnetic fields to enable PBH production.

If this is right

  • Efficient production of ultralight PBHs without ultra-slow-roll inflation
  • Stochastic GW background with model-specific features from EM fields and PBH evaporation
  • Phenomenological implications during the reheating era
  • Inflationary magnetic fields as a testable source for ultralight PBHs

Where Pith is reading between the lines

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

  • Detection of matching GW signals could confirm the magnetogenesis scenario
  • PBH searches in ultralight regime may constrain early magnetic field strengths
  • The model suggests potential links between magnetic fields and other cosmological observables like CMB distortions

Load-bearing premise

The magnetogenesis model produces sufficiently strong small-scale curvature perturbations to form a significant number of ultralight PBHs without violating constraints on primordial magnetic fields.

What would settle it

A measurement of the stochastic gravitational wave spectrum that either matches or deviates from the predicted shape determined by the magnetogenesis parameters.

Figures

Figures reproduced from arXiv: 2605.14044 by Debaprasad Maity, Subhasis Maiti.

Figure 1
Figure 1. Figure 1: FIG. 1. In the above figures, we illustrate the time evolution of the inflaton field for the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. We plot the time evolution of the mode function [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. In this figure, we plot the maximum allowed value of the coupling parameter, [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Here plotted the present-day magnetic field strength as a function of comoving present-day wavelength [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Here plotted the present-day magnetic field strength as a function of comoving present-day wavelength [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. In this figure, we have plotted the curvature power spectrum as a function of comoving wavenumber for two different [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. n these figures, we present the initial fractional energy density of primordial black holes (PBHs) for a given mass under [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. In this figure, we have plotted the evolution of the energy density as a function of cosmic time [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. In this figure, we show the evolution of the energy density as a function of cosmic time [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. In the above figure, we have plotted the total SED of the present-day GWs Ω [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Here we present the spectra of gravitational waves sourced by the evaporation of PBHs for a representative set of [PITH_FULL_IMAGE:figures/full_fig_p027_11.png] view at source ↗
read the original abstract

Ultralight primordial black holes (PBHs) provide a compelling window into early-Universe cosmology. Following our earlier work, we explore a mechanism for the formation of ultralight PBHs sourced by primordial inflationary magnetic fields, without invoking an ultra-slow-roll phase of inflation. We propose a magnetogenesis model in which large curvature perturbations are induced at small scales, leading to the efficient production of ultralight PBHs across a broad mass spectrum. We analyze the phenomenological implications of these ultralight PBHs for early-Universe cosmology, particularly during reheating. We compute the resulting stochastic gravitational wave (GW) background generated by both the electromagnetic spectrum and evaporating PBHs, which exhibits distinctive features tied to the underlying magnetogenesis model parameters. Our results demonstrate that inflationary magnetic fields can serve as a viable and testable origin for ultralight PBHs, opening new avenues for probing the interplay between inflation, magnetogenesis, PBHs, and primordial gravitational waves.

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 / 3 minor

Summary. The paper proposes a magnetogenesis scenario during inflation that generates large small-scale curvature perturbations, enabling efficient production of ultralight PBHs over a broad mass range without an ultra-slow-roll phase. It examines the resulting PBH population's effects during reheating and computes the associated stochastic GW background from both the electromagnetic sector and PBH evaporation, highlighting parameter-dependent spectral features as potential observables.

Significance. If the central mechanism is confirmed, the work establishes a direct link between inflationary magnetic fields and ultralight PBHs, supplying a concrete, testable alternative to ultra-slow-roll models and yielding distinctive GW signatures that could be probed by future detectors. The approach avoids additional ad-hoc inflationary phases and ties PBH abundance to observable magnetic-field constraints.

major comments (2)
  1. [Model and Perturbation Equations] The derivation showing how the magnetogenesis model sources curvature perturbations at small scales (presumably in the section following the model definition) must include explicit transfer functions or power-spectrum expressions to demonstrate that the amplitude reaches the threshold for significant PBH formation while remaining consistent with large-scale magnetic-field bounds.
  2. [GW Background Calculation] The computation of the GW spectrum from evaporating PBHs and the electromagnetic background (likely §4 or §5) requires a clear separation between parameter choices fixed by PBH abundance and those independently constrained by observations; otherwise the claimed 'distinctive features' risk being tuned rather than predicted.
minor comments (3)
  1. [Notation and Definitions] Clarify the notation for the magnetic-field power spectrum and its relation to the curvature perturbation; a short appendix tabulating the mapping between model parameters and observables would improve readability.
  2. [Phenomenological Implications] The abstract states the GW spectrum 'exhibits distinctive features' but the main text should add a brief comparison plot against current PTA or LISA sensitivity curves to make the testability claim concrete.
  3. [Reheating Analysis] A few typographical inconsistencies appear in the reheating-era discussion (e.g., inconsistent use of 'reheating temperature' versus 'reheat scale'); a final proofreading pass is recommended.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments and positive recommendation for minor revision. We address each major comment below and will incorporate the necessary revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: The derivation showing how the magnetogenesis model sources curvature perturbations at small scales (presumably in the section following the model definition) must include explicit transfer functions or power-spectrum expressions to demonstrate that the amplitude reaches the threshold for significant PBH formation while remaining consistent with large-scale magnetic-field bounds.

    Authors: We agree with this suggestion. In the revised version, we will explicitly derive and present the transfer function relating the inflationary magnetic fields to the curvature perturbations at small scales. We will provide the analytical expression for the power spectrum of curvature perturbations induced by the magnetic fields and demonstrate numerically that it reaches amplitudes sufficient for PBH formation (exceeding the critical threshold) while respecting the constraints from large-scale magnetic field observations. This will be added to the section immediately following the model definition, including relevant plots. revision: yes

  2. Referee: The computation of the GW spectrum from evaporating PBHs and the electromagnetic background (likely §4 or §5) requires a clear separation between parameter choices fixed by PBH abundance and those independently constrained by observations; otherwise the claimed 'distinctive features' risk being tuned rather than predicted.

    Authors: We acknowledge the need for clearer separation. In the revised manuscript, we will explicitly state which parameters are fixed by the requirement of a specific PBH abundance (e.g., to account for a fraction of dark matter or to match reheating dynamics) and which are varied within observational bounds from magnetogenesis constraints. We will recompute the GW spectra for different parameter sets to highlight the model-specific features as genuine predictions. A dedicated subsection or table will clarify the parameter choices. revision: yes

Circularity Check

0 steps flagged

Derivation chain is self-contained with no circular reductions

full rationale

The paper constructs a magnetogenesis model that induces curvature perturbations at small scales, computes the PBH production from the resulting power spectrum, and then derives the GW background from both the magnetic fields and the evaporating PBHs. Each step follows from the model equations without reducing the outputs to fitted inputs by construction. The parameters are chosen to satisfy observational constraints, but the GW features are genuine predictions from the same dynamics rather than tautological fits. No self-citation load-bearing or ansatz smuggling is evident in the derivation chain.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on a proposed magnetogenesis model whose specific implementation and parameter choices are not detailed in the provided abstract.

free parameters (1)
  • magnetogenesis model parameters
    Parameters of the magnetogenesis model that determine the magnetic field spectrum and strength, adjusted to induce the required curvature perturbations for PBH formation.
axioms (1)
  • domain assumption Standard inflationary background and reheating dynamics
    Assumes conventional slow-roll inflation (except for the magnetogenesis addition) and standard reheating to calculate PBH formation and GW production.

pith-pipeline@v0.9.0 · 5472 in / 1269 out tokens · 61399 ms · 2026-05-15T02:05:55.540216+00:00 · methodology

discussion (0)

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Reference graph

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