Pith. sign in

REVIEW 2 major objections 5 minor 76 references

Dark-matter abundance fixes the amplitude of a MHz gravitational-wave signal from the same primordial peak.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-14 10:30 UTC pith:ZKJTIFVE

load-bearing objection Clean algebraic closure that removes free scalar amplitude from SIGW templates and ties MHz peaks to conformal-fermion mass; solid under its stated assumptions. the 2 major comments →

arxiv 2607.10607 v1 pith:ZKJTIFVE submitted 2026-07-12 astro-ph.CO hep-ph

Conformal dark matter and MHz gravitational waves

Imtiaz Khan , Niamat Ullah , Salvatore Capozziello , G. Mustafa , Farruh Atamurotov This is my paper
classification astro-ph.CO hep-ph
keywords conformal dark matterscalar-induced gravitational wavesMHz gravitational wavesprimordial curvature spectrumsuperheavy fermionsinflationary small-scale featuresrelic abundance normalization
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

A localized bump in the primordial curvature spectrum can create two relics at once: superheavy conformal-fermion dark matter produced gravitationally from the cubic moment of the spectrum, and a stochastic gravitational-wave background induced at second order from its quadratic convolution. The observed dark-matter density therefore fixes the overall scalar normalization, so the usual free amplitude in scalar-induced gravitational-wave templates is removed. The remaining peak height, frequency, and width of the MHz signal are then predicted from the dark-matter mass, the peak scale, and the spectral shape of one primordial feature. A concrete single-field inflationary evolution produces a broad laboratory-band signal that stays safely below the Gaussian primordial-black-hole threshold. A null high-frequency search becomes a lower bound on the fermion mass; a detection must simultaneously match the relic density, peak frequency, amplitude, and width.

Core claim

Once the dark-matter abundance is used to fix the integrated area of a localized primordial curvature peak through its cubic moment, the peak amplitude of the scalar-induced gravitational-wave spectrum is completely determined by the same peak’s mass scale, frequency, width, and shape factors. There is no free scalar normalization left in the tensor prediction, so a MHz laboratory signal is tied directly to the conformal-fermion mass.

What carries the argument

Abundance-normalized closure relation: the cubic moment that sets the conformal-fermion yield is eliminated against the quadratic radiation-era convolution that sets the induced tensor amplitude, yielding an explicit formula for the peak gravitational-wave density in terms of dark-matter mass, peak frequency, width, and shape factors only.

Load-bearing premise

The calculation assumes the MHz modes re-enter the horizon only after the universe has already reheated into radiation, so the standard radiation-era transfer functions apply; a much later reheating would replace those kernels and change the predicted amplitude.

What would settle it

A laboratory MHz stochastic search that either (a) sets a limit stronger than the mass-reach curve implied by the observed dark-matter density at the measured peak frequency and width, or (b) detects a peak whose amplitude, frequency, and width cannot be reproduced by any single curvature spectrum that also yields the correct relic density.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper argues that a localized small-scale peak in the primordial curvature spectrum P_ζ simultaneously produces conformal-fermion dark matter through a cubic moment of P_ζ and a scalar-induced gravitational-wave (SIGW) background through a quadratic radiation-era convolution. By fixing the integrated scalar area A_ζ from the observed relic density Ω_χ h^{2} (Eq. 14), the free normalization of ordinary SIGW templates is eliminated, yielding the closed relation h^{2}Ω_pk_GW = C_V (Ω_χ h^{2})^{2}/(M_χ/GeV)^{2} (f_0/MHz)^{6} imes Δ^{-2} exp(9Δ^{2})/R_3^{2} (Eq. 1 / Eq. 23). A concrete single-field Mukhanov–Sasaki realization with a transient slow-roll dip generates a broad MHz peak (f_pk_GW ≈ 2.63 MHz, h^{2}Ω_pk_GW ≈ 5.3 imes10^{-12}) that lies far below the Gaussian PBH threshold; null HFGW searches then become lower bounds on M_χ while a detection is overconstrained by abundance, frequency, amplitude and width.

Significance. If the radiation-era kernel and the adopted production coefficient A_χ hold, the result supplies a genuinely predictive link between superheavy conformal dark matter and laboratory MHz gravitational-wave searches. The algebraic elimination of A_ζ is clean, the numerical pipeline (Mukhanov–Sasaki spectrum, cubic shape factor R_3 = 1.6287, radiation-era convolution with documented convergence in Table II) is reproducible, and the closure converts existing and projected HFGW sensitivities into concrete mass reach (Eq. 25) and an inverted mass inference (Eq. 26). The construction therefore turns a free-normalization SIGW template into a falsifiable multi-observable test of one primordial feature.

major comments (2)
  1. Sec. VII.A, Eqs. (36)–(38): the entire numerical prediction and mass-reach translation rest on the radiation-era kernel, which requires T_reh ≳ 1.12 imes10^{14} GeV. The paper correctly notes that delayed reheating replaces the amplitude by an unspecified factor S_reh, yet provides neither a concrete evaluation of S_reh for any standard reheating history nor a quantitative band on how large the correction can be. Because the central claim is a definite MHz amplitude and mass bound, this external condition should be either justified more tightly or accompanied by an explicit range of S_reh so that the predicted signal and M_lim_χ can be assessed under realistic post-inflationary evolution.
  2. Sec. II.B, Eq. (11): the production coefficient A_χ ≃ 0.015 is taken from the external conformal-fermion calculation of Refs. [10,11] and is never recomputed or varied for the specific Mukhanov–Sasaki peak used here. Because A_χ enters C_χ and therefore C_V, any O(1) uncertainty in the kernel (spin sum, constraint normalization, or time integral) rescales the entire predicted h^{2}Ω_pk_GW and the inferred mass. A short sensitivity scan or an explicit statement of the uncertainty inherited from the cited production calculation is needed before the closure can be treated as quantitatively robust.
minor comments (5)
  1. Table I is useful but the final column is somewhat repetitive; a single sentence in the introduction already states the same point.
  2. Fig. 2 (right panel) labels a “local quadratic support proxy” without defining the proxy function; a one-line formula would help the reader.
  3. Several arXiv preprints in the reference list carry future dates (2026); these should be updated or flagged as “in preparation” if they remain unpublished.
  4. Notation for the shape factors switches between R_3 and R3, and between C_GW and CGW; a uniform choice would improve readability.
  5. Eq. (21) gives a convenient analytic fit for C_LN_GW(Δ), but the maximum fractional deviation of 1.6 % is stated without showing the underlying scan; a brief appendix plot would strengthen the claim.

Circularity Check

0 steps flagged

No significant circularity: central closure is algebraic elimination of A_ζ between independent cubic (DM) and quadratic (SIGW) moments of one P_ζ; shape factors are measured, not fitted to the target.

full rationale

The load-bearing claim (Eq. 1/Eq. 23) follows by direct elimination of the free scalar area A_ζ between the conformal-fermion abundance (Eq. 12, linear in A_ζ via the cubic moment M_3 and R_3) and the radiation-era SIGW peak (Eq. 20, quadratic in A_ζ via C_GW). Both kernels are standard or externally cited (A_χ ≃ 0.015 from Garani et al. [10,11]; SIGW transfer from Ananda/Baumann et al.); the single-field Mukhanov–Sasaki ansatz supplies a concrete P_num_ζ from which R_3 and C_GW are recomputed once, after which the algebra is forced. This is a genuine relation among observables (M_χ, f_0, Δ, Ω_χ h^{2} o h^{2}Ω_pk_GW), not a tautology that renames an input as a prediction. Inflationary parameters (D, σ, N_pk) are chosen to realize a localized peak and then held fixed while both channels are evaluated; they are not fitted to the GW amplitude. Mild self-consistency arises only because the same numerical spectrum sources both moments, but that is the intended demonstration of a single primordial feature, not circular reduction. No self-citation is load-bearing for the kernels, no uniqueness theorem is imported, and no fitted parameter is re-labeled a prediction. Score 1 reflects only the shared-spectrum bookkeeping; the derivation is otherwise self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 2 invented entities

The central claim rests on two external kernels (conformal cubic production and radiation-era SIGW), a high-scale reheating assumption, an engineered single-field feature, and a minimal dark-sector completion. Free parameters control the height, width and location of that feature; the shape factors R_3 and C_GW are derived but still spectrum-dependent. No new fundamental force or particle is required beyond the conformal fermion already discussed in the 2025 literature, yet the late mass-generation scalar and Z_2 symmetry are introduced without independent evidence.

free parameters (5)
  • D (slow-roll suppression depth) = 18.0 (fiducial)
    Controls the integrated scalar area A_ζ; fiducial D=18.0, nearby family 17.2–18.8 chosen by hand to produce a usable peak while remaining sub-PBH.
  • σ (feature width in e-folds) = 1.4
    Sets logarithmic width Δ of the curvature peak; chosen σ=1.4.
  • N_pk (feature location) = 53.2
    Fixes comoving scale k_0 / f_0; set to 53.2 so that f_0≈3 MHz.
  • A_χ (production coefficient) = ≃0.015
    Overall factor in the cubic fermion yield; taken as ≃0.015 from external references without re-derivation.
  • Δ (log-width of peak) = 0.92096
    Extracted from numerical spectrum but treated as free when scanning mass reach; fiducial 0.92096.
axioms (4)
  • domain assumption Conformal fermions are produced solely by curvature inhomogeneities with number density n_χ a³ = (A_χ/4π²) ∫ k³ P_ζ(k) d ln k
    Taken from Garani, Redi, Tesi (2025); the entire cubic-moment normalization rests on this kernel (Sec. II.B).
  • domain assumption Radiation-era second-order tensor kernel (Eqs. 15–17) applies for the MHz modes
    Requires T_reh ≳ 1.12×10^14 GeV; otherwise a free S_reh factor appears (Sec. VII.A).
  • domain assumption Gaussian Press–Schechter estimate with δ_c≈0.4–0.5 is a sufficient PBH-tail diagnostic
    Used to claim the benchmark is safe; non-Gaussian corrections are acknowledged but not computed (Sec. VII.B).
  • ad hoc to paper Late mass generation via a dark scalar S with exact Z_2 and crossover potential produces no additional stochastic GW background
    Minimal completion (Eqs. 43–45) introduced to convert conformal fermions into cold DM without spoiling the SIGW signal.
invented entities (2)
  • Stable conformal fermion χ with late mass M_χ = y_S v_S no independent evidence
    purpose: Provides the dark-matter candidate whose abundance fixes the scalar area
    Builds on prior conformal-production literature but the concrete Z_2 + crossover scalar completion is introduced here without collider or other independent handle.
  • Localized single-field slow-roll feature (Gaussian dip in ε(N)) no independent evidence
    purpose: Generates the required small-scale curvature peak while leaving the CMB band untouched
    Engineered ansatz (Eq. 30) with free depth, width and location; not derived from a UV-complete potential.

pith-pipeline@v1.1.0-grok45 · 22788 in / 3578 out tokens · 46677 ms · 2026-07-14T10:30:34.104561+00:00 · methodology

0 comments
Cite this review

Pith. "Pith review of Conformal dark matter and MHz gravitational waves." pith.science (2026). https://pith.science/paper/ZKJTIFVE

@misc{pith2026260710607,
  author       = {Pith},
  title        = {Pith review of: Conformal dark matter and MHz gravitational waves},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZKJTIFVE}},
  note         = {Machine review of arXiv:2607.10607}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

A localized enhancement of the primordial curvature spectrum can leave two distinct relics: gravitationally produced conformal-fermion dark matter and a scalar-induced stochastic gravitational-wave background. We show that the dark-matter abundance fixes the scalar normalization through the cubic moment of the curvature spectrum, while the induced tensor signal probes its quadratic convolution. This closes the usual normalization freedom in scalar-induced gravitational-wave templates and ties the MHz signal directly to the dark-matter mass, peak scale, and spectral width. A concrete single-field realization demonstrates this mechanism: a Mukhanov--Sasaki evolution produces a broad MHz background that sits safely below the Gaussian primordial-black-hole threshold. In this construction, a null high-frequency search becomes a lower bound on the conformal-fermion mass, while a detection has to reproduce the relic abundance, peak frequency, amplitude, and width from one primordial feature. The result is a testable link between small-scale inflationary structure, superheavy dark matter, and laboratory MHz gravitational-wave searches

Figures

Figures reproduced from arXiv: 2607.10607 by Farruh Atamurotov, G. Mustafa, Imtiaz Khan, Niamat Ullah, Salvatore Capozziello.

Figure 1
Figure 1. Figure 1: FIG. 1. Relic-normalized MHz signature. Left: predicted tensor peak after imposing [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Scalar spectrum and moment weights. Left: Mukhanov-Sasaki curvature spectrum around the amplified band and its [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Induced gravitational-wave spectrum and MHz sensitivity comparison. Left: direct radiation-era convolution for the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Relic-normalized prediction in the [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Control checks. Left: Gaussian PBH tail estimate as a function of scalar peak height, with the benchmark marked; [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Response to controlled feature deformations. Left: direct Mukhanov–Sasaki/SIGW family generated by varying [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Current search band and projected reach. Left: ABRACADABRA-10 cm is shown as a published search interval [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Closure diagnostic for a stochastic MHz detection. Left: inferred conformal-fermion mass from Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

76 extracted references · 23 canonical work pages

  1. [1]

    (11), Eq

    Combining Eq. (11), Eq. (6), and Eq. (3) yields Ωχh2 =C χ (Mχ GeV ) ( f0 MHz )3 Aζexp (9∆ 2 2 ) R3,(12) which relates the relic density to the integrated peak area and the cubic shape factor. The normalization constant is Cχ= Aχ 4π2 (1.546×10−21)−3 (3.0856776×1024)3 1 ρc/h2 = 3.3206×10−10, (13) withρc/h2 = 1.05375×10−5GeV cm−3. The factors con- vert the f...

  2. [2]

    Aghanim et al

    N. Aghanim et al. Planck 2018 results. vi. cosmologi- cal parameters.Astron. Astrophys., 641:A6, 2020. doi: 10.1051/0004-6361/201833910

    doi:10.1051/0004-6361/201833910 2018

  3. [3]

    Shifted Hybrid Realization of Non-Minimal Higgs Inflation in Light of ACT DR6 and Planck Data

    Nadir Ijaz, Pirzada, and Mansoor Ur Rehman. Shifted Hybrid Realization of Non-Minimal Higgs Inflation in Light of ACT DR6 and Planck Data. 7 2026

    2026

  4. [4]

    Pri- mordial black holes from single field models of in- flation.Phys

    Juan García-Bellido and Ester Ruiz Morales. Pri- mordial black holes from single field models of in- flation.Phys. Dark Univ., 18:47–54, 2017. doi: 10.1016/j.dark.2017.09.007

    doi:10.1016/j.dark.2017.09.007 2017

  5. [5]

    On primor- dial black holes from an inflection point.Phys

    Cristiano Germani and Tomislav Prokopec. On primor- dial black holes from an inflection point.Phys. Dark Univ., 18:6–10, 2017. doi:10.1016/j.dark.2017.09.001

    doi:10.1016/j.dark.2017.09.001 2017

  6. [8]

    Controlled penumbral inflation from monodromic valleys, 5 2026

    Pirzada and Tianjun Li. Controlled penumbral inflation from monodromic valleys, 5 2026

    2026

  7. [9]

    Dilaton-flattened axion inflation, 4 2026

    Pirzada, Ali Muhammad, Tianjun Li, Imtiaz Khan, and Mussawir Khan. Dilaton-flattened axion inflation, 4 2026

    2026

  8. [10]

    Non-minimal dilaton inflation from the effective gluodynamics, 2 2026

    Pirzada, Imtiaz Khan, Mussawair Khan, Tianjun Li, and Ali Muhammad. Non-minimal dilaton inflation from the effective gluodynamics, 2 2026

    2026

  9. [11]

    Stochastic dark matter from curvature perturba- tions.Phys

    Raghuveer Garani, Michele Redi, and Andrea Tesi. Stochastic dark matter from curvature perturba- tions.Phys. Rev. Lett., 134:101005, 2025. doi: 10.1103/PhysRevLett.134.101005

    work page doi:10.1103/physrevlett.134.101005 2025

  10. [12]

    Par- ticle production from inhomogeneities: general met- ric perturbations.JHEP, 2025(08):037, 2025

    Raghuveer Garani, Michele Redi, and Andrea Tesi. Par- ticle production from inhomogeneities: general met- ric perturbations.JHEP, 2025(08):037, 2025. doi: 10.1007/JHEP08(2025)037

    work page doi:10.1007/jhep08(2025)037 2025

  11. [13]

    Second order cosmological pertur- bations from inflation.Nucl

    Viviana Acquaviva, Nicola Bartolo, Sabino Matarrese, and Antonio Riotto. Second order cosmological pertur- bations from inflation.Nucl. Phys. B, 667:119–148, 2003. 13 doi:10.1016/S0550-3213(03)00550-9

    doi:10.1016/s0550-3213(03)00550-9 2003

  12. [14]

    Cmb polarization from secondary vector and tensor modes.Phys

    Silvia Mollerach, Diego Harari, and Sabino Matar- rese. Cmb polarization from secondary vector and tensor modes.Phys. Rev. D, 69:063002, 2004. doi: 10.1103/PhysRevD.69.063002

    doi:10.1103/physrevd.69.063002 2004

  13. [15]

    Ananda, Chris Clarkson, and David Wands

    Kishore N. Ananda, Chris Clarkson, and David Wands. The cosmological gravitational wave background from primordial density perturbations.Phys. Rev. D, 75: 123518, 2007. doi:10.1103/PhysRevD.75.123518

    doi:10.1103/physrevd.75.123518 2007

  14. [16]

    Steinhardt, Keitaro Takahashi, and Kiyotomo Ichiki

    Daniel Baumann, Paul J. Steinhardt, Keitaro Takahashi, and Kiyotomo Ichiki. Gravitational wave spectrum in- duced by primordial scalar perturbations.Phys. Rev. D, 76:084019, 2007. doi:10.1103/PhysRevD.76.084019

    doi:10.1103/physrevd.76.084019 2007

  15. [17]

    Gravitational-wave background as a probe of the primordial black-hole abundance.Phys

    Ryo Saito and Jun’ichi Yokoyama. Gravitational-wave background as a probe of the primordial black-hole abundance.Phys. Rev. Lett., 102:161101, 2009. doi: 10.1103/PhysRevLett.102.161101

    work page doi:10.1103/physrevlett.102.161101 2009

  16. [18]

    Semiana- lytic calculation of gravitational wave spectrum non- linearly induced from primordial curvature pertur- bations.Phys

    Kazunori Kohri and Takahiro Terada. Semiana- lytic calculation of gravitational wave spectrum non- linearly induced from primordial curvature pertur- bations.Phys. Rev. D, 97:123532, 2018. doi: 10.1103/PhysRevD.97.123532

    doi:10.1103/physrevd.97.123532 2018

  17. [20]

    Scalar induced gravitational waves review.Universe, 7:398, 2021

    Guillem Domènech. Scalar induced gravitational waves review.Universe, 7:398, 2021. doi: 10.3390/universe7110398

    doi:10.3390/universe7110398 2021

  18. [21]

    Iovino, Gabriele Perna, Davide Perrone, Da- vide Racco, and Antonio Riotto

    Antonio J. Iovino, Gabriele Perna, Davide Perrone, Da- vide Racco, and Antonio Riotto. Understanding the na- ture of scalar-induced gravitational waves.JCAP, 03: 001, 2026. doi:10.1088/1475-7516/2026/03/001

    work page doi:10.1088/1475-7516/2026/03/001 2026

  19. [22]

    Exploring pri- mordial black holes and gravitational waves with R- symmetric GUT Higgs inflation.Phys

    Nadir Ijaz and Mansoor Ur Rehman. Exploring pri- mordial black holes and gravitational waves with R- symmetric GUT Higgs inflation.Phys. Lett. B, 861: 139229, 2025. doi:10.1016/j.physletb.2024.139229

    work page doi:10.1016/j.physletb.2024.139229 2025

  20. [23]

    Daniel J. H. Chung, Edward W. Kolb, and Antonio Ri- otto. Superheavy dark matter.Phys. Rev. D, 59:023501,

  21. [24]

    doi:10.1103/PhysRevD.59.023501

    work page doi:10.1103/physrevd.59.023501

  22. [25]

    Daniel J. H. Chung, Edward W. Kolb, and An- tonio Riotto. Nonthermal supermassive dark mat- ter.Phys. Rev. Lett., 81:4048–4051, 1998. doi: 10.1103/PhysRevLett.81.4048

    work page doi:10.1103/physrevlett.81.4048 1998

  23. [26]

    Giudice, Edward W

    Gian F. Giudice, Edward W. Kolb, and Antonio Riotto. Largest temperature of the radiation era and its cosmo- logical implications.Phys. Rev. D, 64:023508, 2001. doi: 10.1103/PhysRevD.64.023508

    doi:10.1103/physrevd.64.023508 2001

  24. [27]

    Mathias Garny, McCullen Sandora, and Martin S. Sloth. Planckian interacting massive particles as dark matter.Phys. Rev. Lett., 116:101302, 2016. doi: 10.1103/PhysRevLett.116.101302

    work page doi:10.1103/physrevlett.116.101302 2016

  25. [28]

    Pro- duction of purely gravitational dark matter.JHEP, 09: 135, 2018

    Yohei Ema, Kazunori Nakayama, and Yong Tang. Pro- duction of purely gravitational dark matter.JHEP, 09: 135, 2018. doi:10.1007/JHEP09(2018)135

    work page doi:10.1007/jhep09(2018)135 2018

  26. [29]

    Pro- duction of purely gravitational dark matter: the case of fermion and vector boson.JHEP, 07:060, 2019

    Yohei Ema, Kazunori Nakayama, and Yong Tang. Pro- duction of purely gravitational dark matter: the case of fermion and vector boson.JHEP, 07:060, 2019. doi: 10.1007/JHEP07(2019)060

    work page doi:10.1007/jhep07(2019)060 2019

  27. [30]

    Gravi- tational production of a conformal dark sector.JHEP, 2021(05):010, 2021

    Michele Redi, Andrea Tesi, and Hugues Tillim. Gravi- tational production of a conformal dark sector.JHEP, 2021(05):010, 2021. doi:10.1007/JHEP05(2021)010

    work page doi:10.1007/jhep05(2021)010 2021

  28. [31]

    Jump starting the dark sectorwithaphasetransition.JHEP,2023(01):085, 2023

    Michele Redi and Andrea Tesi. Jump starting the dark sectorwithaphasetransition.JHEP,2023(01):085, 2023. doi:10.1007/JHEP01(2023)085

    work page doi:10.1007/jhep01(2023)085 2023

  29. [32]

    Imtiaz Khan, Pirzada, and G. Mustafa. Post-inflationary quenched production of axion su(2) dark matter, 4 2026

    2026

  30. [33]

    Parametric-resonance production of qcd axions, 2 2026

    Pirzada, Yu Gao, and Qiaoli Yang. Parametric-resonance production of qcd axions, 2 2026

    2026

  31. [34]

    Challenges and opportunities of gravitational wave searches above 10 khz.Living Rev

    Nancy Aggarwal et al. Challenges and opportunities of gravitational wave searches above 10 khz.Living Rev. Rel., 28:10, 2025. doi:10.1007/s41114-025-00060-5

    doi:10.1007/s41114-025-00060-5 2025

  32. [35]

    HFGWplotter_Omega: High frequency gravitational wave plotter for stochastic signals and power-law- integrated sensitivities

    Francesco Muia, Andreas Ringwald, and Carlos Tamarit. HFGWplotter_Omega: High frequency gravitational wave plotter for stochastic signals and power-law- integrated sensitivities. Zenodo software release, 2025. Version v1, published June 25, 2025

    2025

  33. [36]

    HFGWplotter_Sh: High frequency gravitational wave plotter for noise-equivalent strain

    Francesco Muia, Andreas Ringwald, and Carlos Tamarit. HFGWplotter_Sh: High frequency gravitational wave plotter for noise-equivalent strain. Zenodo software re- lease, 2025. Version v1, published June 25, 2025

    2025

  34. [37]

    Kaliroe M. W. Pappas, Jessica T. Fry, Sabrina Cheng, Arianna Colon Cesani, Jonathan L. Ouellet, Chiara P. Salemi, Inoela Vital, Lindley Winslow, Valerie Dom- cke, Sung Mook Lee, Joshua W. Foster, Reyco Hen- ning, Yonatan Kahn, Nicholas L. Rodd, and Benjamin R. Safdi. High-frequency gravitational wave search with abracadabra-10 cm, 2025

    2025

  35. [38]

    Potential of radio telescopes as high-frequency gravitational wave detectors.Phys

    Valerie Domcke and Camilo Garcia-Cely. Potential of radio telescopes as high-frequency gravitational wave detectors.Phys. Rev. Lett., 126:021104, 2021. doi: 10.1103/PhysRevLett.126.021104

    work page doi:10.1103/physrevlett.126.021104 2021

  36. [39]

    Valerie Domcke, Camilo Garcia-Cely, and Nicholas L. Rodd. Novel search for high-frequency gravita- tional waves with low-mass axion haloscopes. Phys. Rev. Lett., 129(4):041101, 2022. doi: 10.1103/PhysRevLett.129.041101

    work page doi:10.1103/physrevlett.129.041101 2022

  37. [40]

    Rapidis et al

    Nicholas M. Rapidis et al. Status of dmradio-50l and dmradio-m3, 2022

    2022

  38. [41]

    Overview of the dmradio series of experiments

    Alexander Droster. Overview of the dmradio series of experiments. APS April Meeting abstract, 2025. URL https://archive.aps.org/smt/2025/apr-d10/1/

    2025

  39. [42]

    Electromagnetic modeling and science reach of dmradio-m3.Phys

    Abrar AlShirawi et al. Electromagnetic modeling and science reach of dmradio-m3.Phys. Rev. D, 112:052001,

  40. [43]

    doi:10.1103/bwgd-kxsb

    work page doi:10.1103/bwgd-kxsb

  41. [44]

    Valerie Domcke, Sebastian A. R. Ellis, and Nicholas L. Rodd. Magnets are weber bar gravitational wave de- tectors.Phys. Rev. Lett., 134:231401, 2025. doi: 10.1103/PhysRevLett.134.231401

    work page doi:10.1103/physrevlett.134.231401 2025

  42. [45]

    Flash conceptual design report

    FLASH Collaboration. Flash conceptual design report. Conceptual design report, 2024. URLhttps://agenda. infn.it/category/1192/attachments/134864/201897/ FLASH_Conceptual_Design_Report.pdf

    2024

  43. [46]

    Wenskat, B

    M. Wenskat, B. Giaccone, J. Branlard, V. Chouhan, C. Dokuyucu, L. Fischer, I. Gonin, A. Grassellino, W. Hillert, T. Khabiboulline, T. Krokotsch, et al. De- tection of high-frequency gravitational waves using srf cavities, 2026

    2026

  44. [48]

    Navarro Madrid, Diego Blas, Alejandro Díaz Morcillo, Igor García Irastorza, Benito Gimeno, and Juan Monzó Cabrera

    José Reina Valero, Jose R. Navarro Madrid, Diego Blas, Alejandro Díaz Morcillo, Igor García Irastorza, Benito Gimeno, and Juan Monzó Cabrera. High- frequency gravitational waves detection with the babyi- axo haloscopes.Phys. Rev. D, 111:043024, 2025. doi: 10.1103/PhysRevD.111.043024. 14

    work page doi:10.1103/physrevd.111.043024 2025

  45. [49]

    High-frequency gravitational waves on bread, 2025

    Rodolfo Capdevilla, Roni Harnik, Taegyun Kim, and Tom Krokotsch. High-frequency gravitational waves on bread, 2025

    2025

  46. [50]

    Cavity multimodes as an array for high- frequency gravitational waves, 2026

    Diego Blas, Yifan Chen, Yuxin Liu, Yanfei Shang, and Jing Shu. Cavity multimodes as an array for high- frequency gravitational waves, 2026

    2026

  47. [51]

    Global detector network to search for high-frequency gravitational waves (gravnet): conceptual design, 2026

    Dorian Amaral, Diego Blas, Yuliia Borysenkova, et al. Global detector network to search for high-frequency gravitational waves (gravnet): conceptual design, 2026

    2026

  48. [52]

    Detecting gravitational waves with spin systems, 2025

    Jiamin Liang, Mingqiu Li, Yu Gao, Wei Ji, Sichun Sun, and Qi-Shu Yan. Detecting gravitational waves with spin systems, 2025

    2025

  49. [53]

    Kharzeev, Azadeh Maleknejad, and Saba Sha- lamberidze

    Dmitri E. Kharzeev, Azadeh Maleknejad, and Saba Sha- lamberidze. Qugrav: Bringing gravitational waves to light with qumodes.Phys. Rev. Research, 8:013140, 2026. doi:10.1103/nbzp-1yn7

    work page doi:10.1103/nbzp-1yn7 2026

  50. [54]

    High-frequency gravitational waves from first-order phase transitions, 2025

    Wen-Yuan Ai, Francesco Muia, Andreas Ringwald, and Carlos Tamarit. High-frequency gravitational waves from first-order phase transitions, 2025

    2025

  51. [55]

    Reconstructing primor- dial curvature perturbations via scalar-induced gravita- tional waves with lisa.JCAP, 2025(05):062, 2025

    Jonas El Gammal, Aya Ghaleb, Gabriele Franciolini, Theodoros Papanikolaou, Marco Peloso, Gabriele Perna, Mauro Pieroni, Angelo Ricciardone, Robert Rosati, Gi- anmassimo Tasinato, et al. Reconstructing primor- dial curvature perturbations via scalar-induced gravita- tional waves with lisa.JCAP, 2025(05):062, 2025. doi: 10.1088/1475-7516/2025/05/062

    doi:10.1088/1475-7516/2025/05/062 2025

  52. [56]

    Constraints on the sharpness of the curvature power spectrum, 2025

    Keisuke Inomata and Xuheng Luo. Constraints on the sharpness of the curvature power spectrum, 2025

    2025

  53. [57]

    Eric Thrane and Joseph D. Romano. Sensitiv- ity curves for searches for gravitational-wave back- grounds.Phys. Rev. D, 88(12):124032, 2013. doi: 10.1103/PhysRevD.88.124032

    doi:10.1103/physrevd.88.124032 2013

  54. [58]

    HFGWplotter_Omega: Gravitational waves plotter for stochastic signals and power-law-integrated sensitivi- ties

    Francesco Muia, Andreas Ringwald, and Carlos Tamarit. HFGWplotter_Omega: Gravitational waves plotter for stochastic signals and power-law-integrated sensitivi- ties. GitHub repository, 2025.https://github.com/ ctamaritd/HFGWPlotter_Omega, accessed April 13, 2026

    2025

  55. [59]

    Lidsey, Andrew R

    James E. Lidsey, Andrew R. Liddle, Edward W. Kolb, Edmund J. Copeland, T. Barreiro, and M. Ab- ney. Reconstructing the inflaton potential — an overview.Rev. Mod. Phys., 69:373–410, 1997. doi: 10.1103/RevModPhys.69.373

    work page doi:10.1103/revmodphys.69.373 1997

  56. [60]

    Mukhanov, H

    Viatcheslav F. Mukhanov, H. A. Feldman, and Robert H. Brandenberger. Theory of cosmological perturbations. Phys. Rept., 215:203–333, 1992. doi:10.1016/0370- 1573(92)90044-Z

    doi:10.1016/0370- 1992

  57. [61]

    E. D. Stewart and D. H. Lyth. A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation.Phys. Lett. B, 302:171–175,

  58. [62]

    doi:10.1016/0370-2693(93)90379-V

    doi:10.1016/0370-2693(93)90379-v

  59. [63]

    Linde, and Alexei A

    Lev Kofman, Andrei D. Linde, and Alexei A. Starobin- sky. Towards the theory of reheating after infla- tion.Phys. Rev. D, 56:3258–3295, 1997. doi: 10.1103/PhysRevD.56.3258

    doi:10.1103/physrevd.56.3258 1997

  60. [64]

    Tristram et al

    M. Tristram et al. Improved limits on the tensor-to-scalar ratio using bicep and planck data.Phys. Rev. D, 105(8): 083524, 2022. doi:10.1103/PhysRevD.105.083524

    work page doi:10.1103/physrevd.105.083524 2022

  61. [65]

    Gravitational waves induced by scalar perturbations during a gradual transition from an early matter era to the radiation era.JCAP, 10:071,

    Keisuke Inomata, Kazunori Kohri, Tomohiro Nakama, and Takahiro Terada. Gravitational waves induced by scalar perturbations during a gradual transition from an early matter era to the radiation era.JCAP, 10:071,

  62. [66]

    doi:10.1088/1475-7516/2019/10/071

    work page doi:10.1088/1475-7516/2019/10/071 2019

  63. [67]

    Enhancement of gravitational waves induced by scalar perturbations due to a sud- den transition from an early matter era to the radi- ation era.Phys

    Keisuke Inomata, Kazunori Kohri, Tomohiro Nakama, and Takahiro Terada. Enhancement of gravitational waves induced by scalar perturbations due to a sud- den transition from an early matter era to the radi- ation era.Phys. Rev. D, 100(4):043532, 2019. doi: 10.1103/PhysRevD.100.043532

    doi:10.1103/physrevd.100.043532 2019

  64. [68]

    The role of non-gaussianities in primordial black hole forma- tion.Phys

    Vicente Atal and Cristiano Germani. The role of non-gaussianities in primordial black hole forma- tion.Phys. Dark Univ., 24:100275, 2019. doi: 10.1016/j.dark.2019.100275

    doi:10.1016/j.dark.2019.100275 2019

  65. [69]

    Primordial black hole formation with non- gaussian curvature perturbations.JCAP, 09:073, 2019

    Vicente Atal, Jaume Garriga, and Airam Marcos- Caballero. Primordial black hole formation with non- gaussian curvature perturbations.JCAP, 09:073, 2019. doi:10.1088/1475-7516/2019/09/073

    doi:10.1088/1475-7516/2019/09/073 2019

  66. [70]

    Non-gaussianities for primordial black hole formation.JCAP, 08:016, 2021

    Marco Taoso and Alfredo Urbano. Non-gaussianities for primordial black hole formation.JCAP, 08:016, 2021. doi:10.1088/1475-7516/2021/08/016

    work page doi:10.1088/1475-7516/2021/08/016 2021

  67. [71]

    Non-gaussian features of primordial fluctuations in single field inflationary models.JHEP, 05:013, 2003

    Juan Martin Maldacena. Non-gaussian features of primordial fluctuations in single field inflationary models.JHEP, 05:013, 2003. doi:10.1088/1126- 6708/2003/05/013

    doi:10.1088/1126- 2003

  68. [72]

    De Luca, G

    V. De Luca, G. Franciolini, A. Kehagias, M. Peloso, A. Riotto, and C. Ünal. The ineludible non-gaussianity of the primordial black hole abundance.JCAP, 07:048,

  69. [73]

    doi:10.1088/1475-7516/2019/07/048

    doi:10.1088/1475-7516/2019/07/048 2019

  70. [74]

    Sam Young, Ilia Musco, and Christian T. Byrnes. Pri- mordial black hole formation and abundance: contribu- tion from the non-linear relation between the density and curvature perturbation.JCAP, 11:012, 2019. doi: 10.1088/1475-7516/2019/11/012

    doi:10.1088/1475-7516/2019/11/012 2019

  71. [75]

    Kovetz, and Marc Kamionkowski

    Gabriela Sato-Polito, Ely D. Kovetz, and Marc Kamionkowski. Constraints on the primordial curvature power spectrum from primordial black holes.Phys. Rev. D, 100(6):063521, 2019. doi: 10.1103/PhysRevD.100.063521

    work page doi:10.1103/physrevd.100.063521 2019

  72. [76]

    The threshold for primordial black hole formation: a simple analytic prescription.Phys

    Ilia Musco, Valerio De Luca, Gabriele Franciolini, and Antonio Riotto. The threshold for primordial black hole formation: a simple analytic prescription.Phys. Rev. D, 103(6):063538, 2021. doi:10.1103/PhysRevD.103.063538

    doi:10.1103/physrevd.103.063538 2021

  73. [77]

    Iovino, Gabriele Perna, Ville Vaskonen, and Hardi Veermäe

    Bernard Carr, Antonio J. Iovino, Gabriele Perna, Ville Vaskonen, and Hardi Veermäe. Primordial black holes: constraints, potential evidence and prospects, 2026

    2026

  74. [78]

    Revisiting con- straints on primordial curvature power spectrum from primordial black holes, 2026

    Ashu Kushwaha and Teruaki Suyama. Revisiting con- straints on primordial curvature power spectrum from primordial black holes, 2026

    2026

  75. [79]

    Colin Hill

    Samuel Goldstein and J. Colin Hill. A 2% determina- tion ofn eff from primordial element abundance, cosmic microwave background, and baryon acoustic oscillation measurements, 2026

    2026

  76. [80]

    Dorsch, Mark Hindmarsh, Stephan J

    Chiara Caprini, Mikael Chala, Glauber C. Dorsch, Mark Hindmarsh, Stephan J. Huber, Thomas Konstandin, Jonathan Kozaczuk, Germano Nardini, Jose Miguel No, Kari Rummukainen, Pedro Schwaller, Geraldine Servant, Anders Tranberg, and David J. Weir. Detecting gravi- tational waves from cosmological phase transitions with lisa: an update.JCAP, 03:024, 2020. doi:...

    doi:10.1088/1475- 2020