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arxiv: 2606.23787 · v1 · pith:ALFC2QE3new · submitted 2026-06-22 · ✦ hep-ph · astro-ph.CO

Multi-peaked high-frequency gravitational waves from PBH-assisted leptogenesis

Debasish Borah , Nayan Das This is my paper

Pith reviewed 2026-06-26 07:55 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords primordial black holesleptogenesisgravitational wavesright-handed neutrinoshigh-frequency gravitational wavesnon-thermal leptogenesisseesaw mechanismHawking radiation
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The pith

Primordial black holes enable non-thermal leptogenesis that produces a multi-peaked high-frequency gravitational wave spectrum.

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

This paper shows that heavy right-handed neutrinos produced by the evaporation of ultra-light primordial black holes can generate the observed lepton asymmetry via non-thermal leptogenesis. The same neutrinos emit gravitational waves through graviton bremsstrahlung during decay, while the PBH-dominated era adds separate signals from density perturbations and Hawking radiation, yielding a multi-peaked spectrum. A sympathetic reader would care because the setup avoids the strong washout that plagues high-scale thermal leptogenesis and predicts signals in the MHz-EHz band. The optimistic high-scale seesaw case consistent with neutrino masses ties early-universe particle production to potential gravitational-wave observations.

Core claim

The authors claim that right-handed neutrinos from PBH evaporation generate the lepton asymmetry needed for non-thermal leptogenesis, and the graviton bremsstrahlung from their decays produces an enhanced GW spectrum; the PBH-dominated epoch further supplies distinct GW contributions from density perturbations and Hawking evaporation, resulting in a multi-peaked spectrum whose peaks lie in the MHz-EHz range for very high-scale seesaw models consistent with neutrino mass and leptogenesis.

What carries the argument

The ultra-light PBH dominated epoch, which supplies right-handed neutrinos while keeping leptogenesis free of strong washout and sourcing multiple distinct GW signals.

If this is right

  • The GW spectrum receives separate peaks from RHN graviton bremsstrahlung, PBH density perturbations, and Hawking radiation.
  • Peak frequencies lie in the MHz-EHz range for the optimistic high-scale seesaw consistent with neutrino masses.
  • Leptogenesis proceeds without the strong washout that affects thermal scenarios at very high scales.
  • The PBH epoch produces a GW background distinct from the stochastic background of the thermal bath.

Where Pith is reading between the lines

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

  • Future detectors sensitive to MHz-EHz gravitational waves could place bounds on the seesaw scale or PBH parameters if the predicted peaks are absent.
  • The same PBH-assisted production mechanism could be applied to other heavy-particle baryogenesis scenarios.
  • Correlations between the GW peak positions and the observed baryon asymmetry might offer an independent test of the model.

Load-bearing premise

An ultra-light primordial black hole dominated era must exist that produces enough right-handed neutrinos for successful leptogenesis without triggering strong washout.

What would settle it

A search for multi-peaked gravitational wave signals whose frequencies and amplitudes match the relations set by the right-handed neutrino mass and the PBH mass scale in the MHz-EHz band.

Figures

Figures reproduced from arXiv: 2606.23787 by Debasish Borah, Nayan Das.

Figure 1
Figure 1. Figure 1: FIG. 1: Allowed regions in the [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Feynman diagrams for graviton bremsstrahlung induced by RHN decay. [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: GW spectra via RHN bremsstrahlung corresponding to the benchmark points BP1 [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Parameter-space plots for hierarchical leptogenesis in the [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Parameter-space plots for resonant leptogenesis in the [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: CGMB spectra corresponding to the benchmark points BP1, BP2, and BP3. Since [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: GW spectra sourced by PBH-induced scalar density perturbations for the benchmark [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: GW spectra generated from graviton emission during PBH evaporation. Similar [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Total GW spectrum, including all relevant contributions, for the hierarchical lepto [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Total GW spectrum, including all relevant contributions, for the resonant leptoge [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: GW spectra from graviton bremsstrahlung via the decay of thermal RHN, shown [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗
read the original abstract

We study the possibility of probing non-thermal leptogenesis with multi-peaked high-frequency gravitational waves (GW) by considering heavy right-handed neutrino (RHN) produced from primordial black hole (PBH) evaporation to be responsible for generating the required lepton asymmetry. The decay of RHN also produces a GW spectrum due to graviton bremsstrahlung with the corresponding amplitude being enhanced for heavier RHN. The presence of an ultra-light PBH dominated epoch not only ensures sufficient production of RHNs, but also keeps the leptogenesis scenario free from strong washout problem of thermal leptogenesis at very high scale. In addition, the PBH dominated epoch also helps in generating a gravitational bremsstrahlung spectrum distinct from the stochastic GW background from the thermal bath. Finally, PBH evaporation also brings two separate sources of GW via density perturbation and graviton emission via Hawking evaporation. For the most optimistic scenario with very high scale seesaw consistent with neutrino mass and leptogenesis, this leads to a multi-peaked GW spectrum with peak frequencies lying in the MHz-EHz range.

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 proposes that evaporation of ultra-light primordial black holes (PBHs) produces heavy right-handed neutrinos (RHNs) that drive non-thermal leptogenesis, generating the observed baryon asymmetry while evading the strong washout that rules out thermal leptogenesis at seesaw scales ≳10^14 GeV. The PBH-dominated epoch is also claimed to source a distinctive multi-peaked stochastic gravitational-wave background via graviton bremsstrahlung from RHN decays, density perturbations, and Hawking radiation, with peaks spanning the MHz–EHz range in optimistic parameter choices consistent with neutrino masses.

Significance. If the central claims are substantiated, the work would link PBH cosmology, high-scale leptogenesis, and high-frequency GW phenomenology in a falsifiable way, offering a potential observational window on seesaw scales otherwise inaccessible to colliders or low-energy probes. The multi-source GW spectrum is a concrete, potentially distinctive signature.

major comments (2)
  1. [Abstract / leptogenesis section] Abstract and § on leptogenesis mechanism: the claim that the ultra-light PBH epoch 'keeps the leptogenesis scenario free from strong washout problem of thermal leptogenesis at very high scale' is load-bearing for the viability at seesaw scales ≳10^14 GeV, yet no explicit Boltzmann evolution, integrated washout factor, or parameter scan is shown demonstrating that the final Y_B remains O(10^{-10}) when inverse decays and ΔL=2 scatterings remain active during the matter-dominated phase.
  2. [GW production section] GW spectrum section: the assertion of a 'multi-peaked' spectrum with distinct contributions from bremsstrahlung, density perturbations, and Hawking evaporation requires quantitative demonstration that the peaks are separable and that the bremsstrahlung amplitude is indeed enhanced for the heavier RHN masses needed for high-scale leptogenesis; no explicit spectra or peak-frequency formulas are referenced in the available text.
minor comments (2)
  1. [Abstract] Notation for frequency units (MHz-EHz) and RHN mass scale should be defined consistently with standard conventions (e.g., explicit relation to M_N).
  2. [Results section] The optimistic scenario parameters (PBH mass/abundance, RHN scale) should be tabulated with the resulting peak frequencies and amplitudes for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the major comments point by point below, agreeing that additional quantitative support is needed for the central claims.

read point-by-point responses

  1. Referee: [Abstract / leptogenesis section] Abstract and § on leptogenesis mechanism: the claim that the ultra-light PBH epoch 'keeps the leptogenesis scenario free from strong washout problem of thermal leptogenesis at very high scale' is load-bearing for the viability at seesaw scales ≳10^14 GeV, yet no explicit Boltzmann evolution, integrated washout factor, or parameter scan is shown demonstrating that the final Y_B remains O(10^{-10}) when inverse decays and ΔL=2 scatterings remain active during the matter-dominated phase.

    Authors: We agree that the manuscript would be strengthened by explicit calculations. In the revised version we will add the Boltzmann equations governing the lepton asymmetry evolution during the PBH-dominated phase, including inverse decays and ΔL=2 scatterings. We will present numerical results showing that Y_B reaches O(10^{-10}) for seesaw scales ≳10^14 GeV, with washout suppressed by the non-thermal RHN production and the matter-dominated expansion history, together with a limited parameter scan consistent with neutrino masses. revision: yes

  2. Referee: [GW production section] GW spectrum section: the assertion of a 'multi-peaked' spectrum with distinct contributions from bremsstrahlung, density perturbations, and Hawking evaporation requires quantitative demonstration that the peaks are separable and that the bremsstrahlung amplitude is indeed enhanced for the heavier RHN masses needed for high-scale leptogenesis; no explicit spectra or peak-frequency formulas are referenced in the available text.

    Authors: We acknowledge that explicit formulas and spectra are required. In the revision we will derive and quote the peak-frequency expressions for graviton bremsstrahlung from RHN decays, PBH-induced density perturbations, and Hawking radiation. We will include plots of the total GW spectrum demonstrating that the peaks remain separable in the MHz–EHz range for optimistic parameters, and we will show the enhancement of the bremsstrahlung amplitude for the heavier RHN masses needed at high-scale leptogenesis. revision: yes

Circularity Check

0 steps flagged

No circularity identified; derivation relies on external physics inputs without self-referential reduction.

full rationale

The abstract and available text describe a PBH-assisted leptogenesis scenario leading to multi-peaked GW spectra, invoking standard mechanisms for RHN production, asymmetry generation, and graviton bremsstrahlung. No equations, parameter fits, or self-citations are presented that reduce any claimed prediction to an input by construction (e.g., no fitted washout factors renamed as predictions, no uniqueness theorems imported from the authors' prior work, and no ansatzes smuggled via citation). The central claims rest on model assumptions that remain independently falsifiable outside the paper's fitted values, making the chain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Abstract-only; the ledger is populated with the minimal elements explicitly named in the abstract. Many additional free parameters (PBH mass function, RHN mass scale, branching ratios) are expected but not listed here.

free parameters (2)
  • RHN mass scale
    Amplitude of bremsstrahlung GW is stated to increase with heavier RHN; the value is therefore a free parameter chosen to produce observable signals.
  • PBH mass and abundance
    Ultra-light PBH mass and initial abundance control both the duration of the PBH-dominated epoch and the RHN yield.
axioms (1)
  • domain assumption High-scale seesaw mechanism remains consistent with observed neutrino masses and leptogenesis
    Invoked in the final sentence to define the 'most optimistic scenario'.

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discussion (0)

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Reference graph

Works this paper leans on

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    but without any connection to the origin of neutrino mass or leptogenesis. In this work, we consider a type-I seesaw leptogenesis scenario with a PBH dominating epoch such that heavy RHNs are produced non-thermally and hence does not suffer from the problem of strong∆L= 2washout [72]. Due to the early matter dominated phase of ultra-light PBH, it also sep...

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    Analytical estimation of Baryon Asymmetry In terms of the number of the lightest RHNN1 species,N N1, produced from the complete evaporation of a PBH, the Eq. (13) can be expressed as Y ∆L =ϵ ∆L 1 asph NN1nBH(aev) s(aev) .(17) The expression forN N1 is obtained from the generic expression of the number of a species with massm X and internal degrees of free...

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    Analytical estimation of GW via bremsstrahlung The Eq. (26) can be re-written as d dt dρgw dEk + 4Hdρgw dEk = dΓ1→3 dEk Ek nN1.(28) 10 In terms of scale factora, d da a5 dρgw dlnE k = a4 H dΓ1→3 dEk E2 k nN1.(29) Integrating the above equation from the evaporation of PBH,aev to the decay of RHN,aN, we get dρgw(aN) dlnE k ≃ 2 3 τN nN1(aev) aev aN 3" 1− aev...

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