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arxiv: 2405.09723 · v2 · submitted 2024-05-15 · ✦ hep-ph · astro-ph.CO· gr-qc· hep-th

Gravitational Wave-Induced Freeze-In of Fermionic Dark Matter

Azadeh Maleknejad , Joachim Kopp This is my paper

Pith reviewed 2026-05-24 01:05 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COgr-qchep-th
keywords gravitational wavesfermionic dark matterWeyl fermionsfreeze-in productionstochastic backgroundgravitational productionin-in formalism
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0 comments X

The pith

Stochastic gravitational wave backgrounds can produce massless Weyl fermions that later become dark matter if they acquire mass.

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

The paper shows that minimal gravitational coupling alone cannot produce massless fermions from cosmic expansion, but realistic stochastic gravitational wave backgrounds change this by enabling production at the one-loop level. The authors compute the resulting fermion energy density with the in-in formalism and argue that the process can yield the observed dark matter density once the particles gain mass. This channel may operate more efficiently than standard gravitational production of superheavy fermions. A sympathetic reader would care because it ties a potentially observable background of gravitational waves to the origin of dark matter without requiring new particles or interactions beyond gravity.

Core claim

The central claim is that the presence of stochastic gravitational wave backgrounds induces one-loop production of Weyl fermions through their gravitational coupling, generating an energy density that, after the fermions acquire mass, can account for the full dark matter abundance and does so more efficiently than conventional gravitational production of superheavy fermions.

What carries the argument

One-loop in-in formalism computation of the energy density of Weyl fermions sourced by a stochastic gravitational wave background.

If this is right

  • Fermionic dark matter can arise from initially massless particles that gain mass after production.
  • The mechanism supplies a new gravitational production channel distinct from expansion-driven effects.
  • The resulting relic density can exceed that from conventional superheavy fermion production under the same gravitational waves.
  • Detection of the relevant gravitational wave background would directly constrain the dark matter yield.

Where Pith is reading between the lines

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

  • Future gravitational wave observatories could test the mechanism by checking whether the measured background amplitude matches the dark matter density.
  • The same loop effect might apply to other light fermions if they also acquire mass at late times.
  • This production route could operate alongside or instead of standard freeze-in scenarios that rely on non-gravitational interactions.

Load-bearing premise

Realistic stochastic gravitational wave backgrounds exist with amplitudes and frequency spectra large enough to produce the observed dark matter density.

What would settle it

A measured stochastic gravitational wave spectrum whose amplitude is too low to generate the required fermion density through this one-loop process while the observed dark matter abundance remains unchanged.

Figures

Figures reproduced from arXiv: 2405.09723 by Azadeh Maleknejad, Joachim Kopp.

Figure 1
Figure 1. Figure 1: FIG. 1. The graviton–fermion cubic and quartic vertices. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. GW-induced freeze-in of dark matter for a GW back [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
read the original abstract

The minimal coupling of massless fermions to gravity does not allow for their gravitational production solely based on the expansion of the Universe. We argue that this changes in presence of realistic and potentially detectable stochastic gravitational wave backgrounds. We compute the resulting energy density of Weyl fermions at 1-loop using in--in formalism. If the initially massless fermions eventually acquire mass, this mechanism can explain the dark matter abundance in the Universe. Remarkably, it may be more efficient than conventional gravitational production of superheavy fermions.

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 / 0 minor

Summary. The manuscript proposes that stochastic gravitational wave backgrounds (SGWB) can gravitationally produce massless Weyl fermions at one loop via the in-in formalism, even though minimal coupling to gravity does not permit production from cosmic expansion alone. If these fermions later acquire mass, the resulting energy density can account for the observed dark matter abundance and may exceed the efficiency of conventional superheavy fermion production.

Significance. If the 1-loop computation is correct and realistic SGWB spectra exist with sufficient amplitude, the work identifies a new gravitational freeze-in channel for fermionic DM that does not require direct couplings beyond gravity. The result is potentially falsifiable through future GW observatories, but its explanatory power rests on an external assumption about viable SGWB sources whose viability is not demonstrated within the calculation.

major comments (2)
  1. [Abstract] Abstract: the central claim that 'realistic and potentially detectable' SGWB can produce the observed DM density is load-bearing, yet no explicit mapping is provided from concrete early-universe sources (phase transitions, inflation, etc.) to an Omega_GW(f) spectrum that simultaneously satisfies current PTA/LISA bounds and yields Omega_DM after the fermions acquire mass. The production rate scales directly with the GW power spectrum; without this mapping the mechanism's viability remains an external assumption.
  2. [Abstract] Abstract and main text: the 1-loop in-in computation of the fermion energy density is asserted but no derivation steps, Feynman rules for the graviton-fermion vertex, regularization procedure, or validation against known limits (e.g., vanishing GW amplitude or flat-space limit) are supplied. This prevents assessment of whether the result is free of divergences or correctly reduces to the expected scaling with the GW spectrum.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each major comment below and outline the revisions we will implement to improve clarity and completeness.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'realistic and potentially detectable' SGWB can produce the observed DM density is load-bearing, yet no explicit mapping is provided from concrete early-universe sources (phase transitions, inflation, etc.) to an Omega_GW(f) spectrum that simultaneously satisfies current PTA/LISA bounds and yields Omega_DM after the fermions acquire mass. The production rate scales directly with the GW power spectrum; without this mapping the mechanism's viability remains an external assumption.

    Authors: We agree that the mechanism's ability to explain the observed DM abundance depends on the existence of suitable SGWB spectra from early-universe sources. Our manuscript focuses on establishing the gravitational production channel via the in-in formalism rather than performing a comprehensive survey of source models. To address this concern, we will revise the abstract and introduction to explicitly state that the mechanism operates for any SGWB spectrum with sufficient amplitude (within current observational bounds) and add a brief discussion section referencing example sources such as first-order phase transitions or inflationary tensor modes that could generate compatible Omega_GW(f). A full end-to-end parameter mapping from specific sources is beyond the scope of this work but can be pursued in follow-up studies. revision: partial

  2. Referee: [Abstract] Abstract and main text: the 1-loop in-in computation of the fermion energy density is asserted but no derivation steps, Feynman rules for the graviton-fermion vertex, regularization procedure, or validation against known limits (e.g., vanishing GW amplitude or flat-space limit) are supplied. This prevents assessment of whether the result is free of divergences or correctly reduces to the expected scaling with the GW spectrum.

    Authors: We acknowledge that the main text presents the final result of the 1-loop in-in calculation without intermediate steps. The computation employs the standard in-in formalism for the interaction Hamiltonian derived from minimal gravitational coupling of Weyl fermions. We will add a dedicated appendix that includes: (i) the explicit graviton-fermion vertex Feynman rules obtained from the vierbein formalism, (ii) the regularization procedure (dimensional regularization with counterterms), and (iii) explicit checks that the energy density vanishes for zero GW amplitude and reduces to the expected flat-space result. These additions will confirm the absence of spurious divergences and the direct proportionality to the GW power spectrum. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation computes energy density from external GW input

full rationale

The paper's central computation is the 1-loop in-in energy density of Weyl fermions sourced by an external stochastic gravitational wave background. This is a standard perturbative calculation whose output scales directly with the input GW power spectrum; the DM abundance match is presented as conditional on the existence of sufficiently strong realistic SGWBs rather than being forced by any internal fit, self-definition, or self-citation chain. No load-bearing step reduces to a tautology or renames a fitted result as a prediction. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence of a stochastic GW background with unspecified amplitude and spectrum, the validity of the 1-loop in-in calculation, and the later acquisition of mass by the fermions. No free parameters are explicitly fitted in the abstract, but the GW background acts as an external input.

free parameters (1)
  • stochastic GW background spectrum and amplitude
    The produced fermion energy density is computed from this background; its detailed form is an input not derived in the abstract.
axioms (2)
  • domain assumption Minimal coupling of massless fermions to gravity does not allow production from universe expansion alone
    Explicitly stated as the baseline that changes only with added GW backgrounds.
  • domain assumption 1-loop in-in formalism correctly captures the production
    The computation method is invoked without further justification in the abstract.

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    Scalar metric perturbations after inflation break conformal invariance and induce quantum production of gravitons, generating a GW spectrum that peaks near GHz frequencies for standard primordial scalar power spectra.

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