Observing Leptogenesis in Action with Gravitational Waves

Bea Noether; Hitoshi Murayama; Jan Sch\"utte-Engel

REVIEW 2 major objections 3 minor 1 cited by

Observing Leptogenesis in Action with Gravitational Waves

T0 review · 2 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Heavy right-handed neutrino decays during leptogenesis are argued to emit a stochastic gravitational-wave background whose amplitude scales with neutrino mass squared and peak frequency inversely with Yukawa coupling, offering a direct…

desk verdict A careful matrix-element correction and a useful CGMB degeneracy warning, but the headline spectrum rests on an uncomputed N1 abundance and is far from detection. read the letter →

arxiv 2506.15772 v1 pith:5A4BJZT6 submitted 2025-06-18 hep-ph gr-qchep-ex

Hitoshi Murayama , Bea Noether , Jan Schütte-Engel This is my paper · ORCID

classification hep-phgr-qchep-ex

keywords leptogenesisright-handedneutrinosseesawmechanismgravitonbremsstrahlungstochasticgravitational-wavebackgroundearlymatterdominationcosmicgravitationalmicrowavehigh-frequencywaves

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the decays of the heavy right-handed neutrinos responsible for leptogenesis also emit gravitons, producing a stochastic gravitational-wave background that is a direct fossil of the decay process. If those neutrinos drove an early matter-dominated phase, the spectrum's peak amplitude scales as the square of the neutrino mass and its peak frequency scales inversely with the neutrino Yukawa coupling. The paper also shows that the same early matter era reshapes the gravitational-wave background from the thermal plasma, and that combining the two spectra can disentangle the reheating temperature, the effective number of relativistic degrees of freedom, the right-handed neutrino mass, and its Yukawa coupling. For a mass $M = 10^{15}$ GeV and coupling $Y = 10^{-4}$, the predicted peak sits near $10^{13}$ Hz with $h^2\Omega_{\rm gw}\sim 10^{-16}$, far above current detectors but within the conceptual reach of proposed high-frequency and CMB spectral-distortion techniques.

What carries the argument

The load-bearing object is the spin- and polarization-averaged squared amplitude for graviton bremsstrahlung in $N_1\to \ell H h$, computed from four Feynman diagrams and written as $|{\cal M}|^2_{\rm av} = \tfrac12 |Y|^2(\kappa/8)^2\,16M^2(1-x_G)(2-x_G-x_Gx_L)/x_G^2$, where $x_G=2k/M$ and $x_L=2q/M$ are the graviton and lepton energy fractions. The paper checks this amplitude in two limits: as $x_G\to 0$ it reproduces the soft-graviton theorem, and as $x_G\to 1$ the amplitude vanishes only linearly with $(1-x_G)$, as angular-momentum conservation demands, in contrast to earlier results that vanish quadratically. The phase-space integral then gives the spectral shape $x(x-2)^2(1-x)$, and an instantaneous-decay approximation yields the peak frequency and amplitude. For the thermal plasma contribution, the key object is the gain term $\hat\eta(T,k/T)$ from the standard CGMB calculation, modified by the scale-factor ratio $\alpha=a_D/a_{MD}$ that encodes how long the early matter-dominated phase lasted.

What would settle it

An independent recomputation of the graviton-bremsstrahlung phase-space integral would settle a decisive point: if the squared amplitude vanishes as $(1-x_G)^2$ rather than $(1-x_G)$ near the kinematic endpoint, the predicted peak amplitude and frequency would change. Observationally, a future CMB spectral-distortion survey reaching a few nK sensitivity around the predicted $10^{13}$ Hz peak for $M=10^{15}$ GeV and $Y=10^{-4}$ would either find the peak or place a direct exclusion on this leptogenesis benchmark.

Watch

Extended reading notes

Core claim

The paper's central claim is that graviton bremsstrahlung in the decay $N_1\to \ell H h$ (where $h$ is the graviton) during leptogenesis gives a stochastic gravitational-wave background whose amplitude and peak frequency carry the mass $M$ and Yukawa coupling $Y$ of the decaying right-handed neutrino. Including the early matter-dominated era that a long-lived $N_1$ induces, the spectrum peaks at $f_{\rm peak}\simeq 7.9\times 10^{12}\,{\rm Hz}\,(M/10^{15}\,{\rm GeV})^{1/2}(10^{-4}/Y)$ with $h^2\Omega_{\rm gw}(f_{\rm peak})\simeq 2.8\times 10^{-16}(M/10^{15}\,{\rm GeV})^2$. The calculation uses a newly derived spin-and-polarization averaged matrix element checked against the soft-graviton theorem and angular-momentum conservation, and it disagrees with earlier attempts at this rate. The paper further computes how an early matter-dominated era modifies the Cosmic Gravitational Microwave Background, finding that it can mimic extra relativistic degrees of freedom and a higher reheating temperature; the bremsstrahlung spectrum breaks that degeneracy. The authors do not claim this alone proves leptogenesis, but they argue that detection would make the case far more convincing when combined with other circumstantial evidence.

Load-bearing premise

The argument requires that the right-handed neutrinos actually reach thermal equilibrium in the early universe and that the lightest one, with a small enough Yukawa coupling (about $10^{-2}$ or below) and satisfying $Y^2 < 0.23\,M/m_{\rm Pl}$, lives long enough to dominate the energy density before decaying; if thermalization fails or another particle takes over the universe, the early matter-dominated phase and the predicted $M^2$ scaling do not follow.

Editorial extensions

If this is right

If the predicted spectrum exists, a single detection would be direct evidence that a heavy particle decayed in the early universe at the right time and with the right couplings to be the source of the observed baryon asymmetry.
From the observed peak frequency and amplitude one can read off the right-handed neutrino mass $M$ and Yukawa coupling $Y$; combined with the CGMB spectrum, that information fixes the reheating temperature and effective degrees of freedom and removes the degeneracy the CGMB alone has.
The early matter-dominated phase makes the bremsstrahlung peak amplitude scale as $M^2$ and its frequency shift with $1/Y$, a distinctive pattern that separates this source from cosmic strings, inflation, and other gravitational-wave backgrounds.
Smaller $Y$ moves the bremsstrahlung peak to higher frequencies while moving the CGMB peak to lower frequencies, making the two signals easier to separate observationally.
The predicted frequencies, in the GHz-to-THz range, lie beyond current broadband sensitivity, so the result gives a concrete target for future high-frequency gravitational-wave detectors and CMB spectral-distortion experiments.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper, if the bremsstrahlung background were observed together with the cosmic-string signal expected from $U(1)_{B-L}$ breaking, the two backgrounds would pin down both the symmetry-breaking scale and the decay parameters, effectively reconstructing the full early-universe history around leptogenesis.
Beyond the paper, an independent recomputation of the phase-space integral could settle the discrepancy with earlier decay-rate calculations; the two candidate scalings predict different peak amplitudes, so the check is a closed-form calculation that does not require new data.
Beyond the paper, a natural extension is to relax the single-generation assumption and include washout and flavor effects; the gravitational-wave signal would then be correlated with the surviving lepton asymmetry, turning the spectrum into a quantitative consistency check on the leptogenesis mechanism itself.
Beyond the paper, the spectrum's shape distinguishes production scenarios: if the right-handed neutrinos are not thermally populated, the early matter-dominated phase is absent and both the peak amplitude and frequency change, so an observed or absent peak can discriminate among reheating and production models.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The thing you should know first: this is a solid correction-and-extension paper, not a detection paper. The new pieces that matter are the re-derived graviton bremsstrahlung matrix element for N1 -> l H h, with consistency checks the earlier work on this process lacked, and the CGMB degeneracy argument: an early matter-dominated era shifts the thermal graviton background in a way that mimics extra relativistic species and a higher reheating temperature, and the bremsstrahlung spectrum can break that degeneracy. Both are real contributions.

The calculation deserves credit. The appendix computes the spin-averaged amplitude with explicit gauge invariance, recovers Weinberg's soft graviton theorem in the x_G -> 0 limit, and explains the (1 - x_G) vs (1 - x_G)^2 disagreement with Refs [19,20] via angular momentum conservation in the collinear limit. I could not independently verify the overall phase-space normalization in Eq. (A.45) on a quick read, but the checks are the right ones and the argument against the older results is specific rather than hand-wavy. That is worth a referee's time.

The soft spots are in proportion. First, the signal sits four to six orders of magnitude below any planned sensitivity, and the authors say this plainly; the paper is a roadmap for future high-frequency detectors, not a current observable. Second, and more concerning, the early matter domination that gives the headline M^2 scaling is assumed rather than derived. Section 3 assumes N1 stays in thermal equilibrium through gauge interactions like U(1)_B-L or SU(2)_R, but never computes the N1 yield or decoupling temperature. If those interactions keep N1 chemically coupled down to T ~ M, the abundance is Boltzmann-suppressed and there is no matter-dominated era, no M^2 spectrum, and no degeneracy breaking. The stress-test note is correct on this point. The fix is straightforward in principle — pick a gauge sector, compute decoupling — but it is load-bearing. Third, 'observing leptogenesis in action' overstates the uniqueness: any heavy decaying particle with similar mass and Yukawa coupling would produce a similar spectrum. The authors explicitly acknowledge that, so it is a framing issue, not a hidden flaw.

This is a paper for the high-frequency GW and early-universe cosmology crowd; experimentalists should read it as a target-setting exercise. Bottom line: it deserves a serious referee. The matrix-element correction and the CGMB degeneracy result are worth having, and the missing abundance calculation is fixable rather than fatal. I would cite the CGMB part, and I would tell the authors to add the N1 yield calculation before publication.

Referee Report

2 major / 3 minor

Summary. The paper studies stochastic gravitational wave backgrounds generated during seesaw leptogenesis. It computes graviton bremsstrahlung in the decays of the lightest right-handed neutrino, presents a detailed gauge-invariant matrix element calculation in Appendix A, and derives the resulting GW spectrum for a cosmological history that includes an early matter-dominated phase. The headline results are the scalings h^2 Omega_gw ~ 2.8 x 10^-16 (M/10^15 GeV)^2 and f_peak ~ 7.9 x 10^12 Hz (M/10^15 GeV)^{1/2} (10^-4/Y). The paper also re-evaluates the Cosmic Gravitational Microwave Background (CGMB) in the presence of early matter domination and argues that a joint observation of both spectra could break degeneracies among M, Y, T_rh, and g*. The central claim is that a high-frequency GW background from right-handed neutrino decays would constitute strong evidence for leptogenesis.

Significance. If the early matter-dominated phase is real, the paper provides a careful and testable prediction, with a matrix element that is checked against the soft graviton theorem and angular momentum conservation. The CGMB analysis raises an important degeneracy that is worth pointing out, and the paper is transparent about the benchmark assumptions. However, the observability is far below current and near-future sensitivities, and, more importantly, the existence of the early matter-dominated phase is assumed rather than derived from a concrete particle physics model. The significance is therefore moderate: the paper is a useful phenomenological target for high-frequency GW efforts, but its headline signal is contingent on an unestablished cosmological premise.

major comments (2)

[Sec. 3, Eq. (3.5)] The condition Y^2 < 0.23 M/m_Pl is necessary for an early matter-dominated phase only if the right-handed neutrino number density at T = M is close to the thermal relativistic value and then freezes in as matter. This is not established. If the U(1)_B-L or SU(2)_R gauge interactions invoked in Sec. 2 keep N1 in chemical equilibrium below T ~ M, the equilibrium abundance is Boltzmann-suppressed and rho_N never overtakes rho_SM; if N1 decouples earlier, the yield depends on the gauge coupling and gauge boson mass, neither of which is specified or varied. No Boltzmann equation for n_N, including annihilations and inverse decays, is presented. Because the M^2 scaling in Eq. (4.6) and the peak-frequency scaling in Eq. (4.5) are contingent on the early matter-dominated phase, the paper should either compute the N1 yield/decoupling for a concrete gauge model or state the thermal abundance as an explicit assumption and estimate the gauge couplings for which it holds.
[Sec. 4.2, Eq. (4.10)] The alpha parameter does not scale as stated. Combining Eq. (4.10) with Eq. (3.8) gives T_D proportional to M^{1/2} Y^{1/4}, whereas Eq. (2.10) gives T_D proportional to M^{1/2} Y; for M = 10^15 GeV and Y = 10^-4 the two expressions differ by about a factor 1.5 in T_D, and the discrepancy grows as Y is lowered. A direct estimate from t_D = 8 pi/(Y^2 M) and t_MD = t_M (g*_SM/g*_N)^2 gives alpha proportional to (M/m_Pl)^{2/3} Y^{-4/3}, not Y^{-1/3}. Consequently the CGMB peak scalings in Eqs. (4.12)-(4.13) and the alpha values used in Fig. 6 are not correct as written and should be revised before the degeneracy-breaking claim is assessed.

minor comments (3)

[Figs. 6 and 7] The figures use T_rh = 10^16 GeV, which exceeds the instantaneous-reheating upper bound T_rh,max = 5.7 x 10^15 GeV derived in Eq. (2.7). A more optimistic inflationary model should be cited, or the plots should use the stated bound.
[Sec. 4.1, Eq. (4.3)] The discussion of dropping the n_B(r) and n_F(q) factors is clear, but it would be helpful to state explicitly that the suppression for soft lepton or Higgs momenta is controlled by the matrix element, as the phase space alone would not justify neglecting these terms.
[General presentation] There are several typographical and readability issues, including missing parentheses in Eq. (2.13) and inconsistent formatting of g* and h^2 Omega_gw; a careful proofread is recommended.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the GW predictions are independent observables derived from the seesaw Lagrangian and standard cosmology, not from fitted GW data.

full rationale

The derivation chain is self-contained. The central new result, the graviton-bremsstrahlung spectrum from N1 decay, is computed in Appendix A from the seesaw Lagrangian (2.1) with an explicit matrix-element calculation, checked against Weinberg's soft-graviton theorem and angular-momentum conservation; no gravitational-wave datum is fitted. Equations (4.3)-(4.6) are derived rather than assumed: the M^2 magnitude follows from the early-matter-dominated cosmology and the 1/Y peak scaling follows from the decay-temperature relations (2.10) and (3.8). The benchmark values M = 10^15 GeV and Y = 10^-4 are chosen to satisfy neutrino-mass and baryon-asymmetry constraints, Eqs. (2.4) and (2.13), and the predicted GW spectrum is an independent observable. The CGMB section uses the eta-hat function from Ref. [18], which shares an author with the present paper; however, eta-hat is a parameter-free input computed in prior work for the SM plasma and does not contain the target CGMB-with-early-matter-domination spectrum. The new alpha dependence is derived analytically in Eqs. (4.9)-(4.11), not imported from the cited work. The thermalization of N1 via gauge interactions is an assumption about the cosmological scenario, not a circular step; if it fails, the signal would not be produced, but that is a physical premise, not a logical equivalence between input and prediction. There is no fitted parameter renamed as a prediction, no uniqueness theorem imported from self-citations, and no ansatz smuggled in via citation that reduces the derivation to its inputs.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The benchmark values M1, Y and T_rh are chosen by hand to be consistent with neutrino masses, the baryon asymmetry, and the existence of an early matter-dominated era; they are not fitted to the GW spectra. The derivation assumes the seesaw Lagrangian, standard Friedmann evolution, and thermalization of right-handed neutrinos via new gauge interactions. No new entities beyond the standard seesaw right-handed neutrinos are introduced.

free parameters (3)

M1 (lightest right-handed neutrino mass) = 10^15 GeV benchmark (10^14 GeV in Fig 5)
Chosen benchmark; predicted amplitude scales as M1^2, so this choice controls detectability.
Y (Yukawa coupling) = 10^-4 benchmark (10^-1 and 10^-6 in figures)
Chosen to allow out-of-equilibrium decay and early matter domination; peak frequency scales as 1/Y.
T_rh (reheating temperature) = 10^16 GeV benchmark
Set near the instantaneous reheating bound; controls CGMB amplitude and N thermal abundance.

assumptions (5)

domain assumption Right-handed neutrinos are thermally populated after reheating via U(1)B-L or SU(2)R gauge interactions.
Sec 2 and Sec 3; without this, the early matter-dominated phase and thermal decay history do not follow.
domain assumption The universe enters an early matter-dominated phase before N1 decay, requiring Y^2 < 0.23 M/m_Pl.
Eq (3.5); the M^2 scaling and CGMB modification depend on this epoch.
domain assumption N2 and N3 contributions can be neglected: their CP asymmetries are washed out and their gravitons redshift away.
Sec 2; reduces the analysis to a single right-handed neutrino generation.
domain assumption Vacuum graviton emission is a valid description; thermal masses only affect soft and collinear limits in the way argued in Appendix A.3.
Appendix A.3; the authors argue the soft singularity persists and there is no collinear divergence.
standard math The seesaw Lagrangian (Eq 2.1) with linearized gravity Feynman rules from Ref [43] is the correct effective theory.
Background for the matrix element; gauge invariance is checked explicitly.

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Pith. "Pith review of Observing Leptogenesis in Action with Gravitational Waves." pith.science (2026). https://pith.science/paper/5A4BJZT6

@misc{pith2026250615772,
  author       = {Pith},
  title        = {Pith review of: Observing Leptogenesis in Action with Gravitational Waves},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5A4BJZT6}},
  note         = {Machine review of arXiv:2506.15772}
}

read the original abstract

Leptogenesis is arguably the best motivated theory of baryogenesis given the discovery of finite neutrino masses, yet its experimental test is elusive given its high energy scale. We discuss gravitational waves (GWs) produced via graviton bremsstrahlung in right-handed neutrino decays during leptogenesis. The presence of right-handed neutrinos in the early universe can lead to a period of early matter domination. In this context, the resultant GW spectrum scales quadratically with the right-handed neutrino mass, while its peak frequency scales inversely with the Yukawa coupling. Detecting such a spectrum would provide strong evidence for leptogenesis and the existence of heavy right-handed neutrinos. We also discuss how the GW spectrum emitted from the thermal plasma is altered by an era of early matter domination. We show that it can mimic the effects of additional relativistic degrees of freedom and a higher reheating temperature, and that information from the graviton bremsstrahlung GW spectrum can break this degeneracy.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Gravitational Wave Spectrum from the Production of Dark Matter via the freeze-in Mechanism
hep-ph 2025-08 conditional novelty 4.0 of 10

Graviton bremsstrahlung during freeze-in dark matter production yields a high-frequency gravitational wave background peaking near 5.35 x 10^10 Hz, with UV freeze-in amplitudes up to Omega_GW h^2 ~ 1e-17.

Reference graph

Works this paper leans on

46 extracted references · 4 canonical work pages · cited by 1 Pith paper

[1]

Guth,The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys

A.H. Guth,The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D23 (1981) 347

1981
[2]

Sato,First-order phase transition of a vacuum and the expansion of the Universe, Mon

K. Sato,First-order phase transition of a vacuum and the expansion of the Universe, Mon. Not. Roy. Astron. Soc.195 (1981) 467. – 27 –

work page 1981
[3]

Starobinsky,Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations, Phys

A.A. Starobinsky,Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations, Phys. Lett. B117 (1982) 175

work page 1982
[4]

Sakharov,Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh

A.D. Sakharov,Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz.5 (1967) 32

1967
[5]

Riotto,Theories of baryogenesis, inICTP Summer School in High-Energy Physics and Cosmology, pp

A. Riotto,Theories of baryogenesis, inICTP Summer School in High-Energy Physics and Cosmology, pp. 326–436, 7, 1998 [hep-ph/9807454]

arXiv 1998
[6]

Fukugita and T

M. Fukugita and T. Yanagida,Baryogenesis Without Grand Unification, Phys. Lett. B174 (1986) 45

1986
[7]

Super-Kamiokande collaboration, Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett.81 (1998) 1562 [hep-ex/9807003]

arXiv 1998
[8]

Minkowski,µ→eγ at a Rate of One Out of109 Muon Decays?, Phys

P. Minkowski,µ→eγ at a Rate of One Out of109 Muon Decays?, Phys. Lett. B67 (1977) 421

work page 1977

Show all 46 references

[9]

Yanagida,Horizontal gauge symmetry and masses of neutrinos, Conf

T. Yanagida,Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C7902131 (1979) 95

1979
[10]

Gell-Mann, P

M. Gell-Mann, P. Ramond and R. Slansky,Complex Spinors and Unified Theories, Conf. Proc. C 790927 (1979) 315 [1306.4669]

1979 arXiv
[11]

Kuzmin, V.A

V.A. Kuzmin, V.A. Rubakov and M.E. Shaposhnikov,On the Anomalous Electroweak Baryon Number Nonconservation in the Early Universe, Phys. Lett. B155 (1985) 36

1985
[12]

Buchmüller, P

W. Buchmüller, P. Di Bari and M. Plümacher,Leptogenesis for pedestrians, Annals Phys. 315 (2005) 305 [hep-ph/0401240]

2005 arXiv
[13]

J.A. Dror, T. Hiramatsu, K. Kohri, H. Murayama and G. White,Testing the Seesaw Mechanism and Leptogenesis with Gravitational Waves, Phys. Rev. Lett.124 (2020) 041804 [1908.03227]

2020 arXiv
[14]

Zurek,Cosmological Experiments in Superfluid Helium?, Nature 317 (1985) 505

W.H. Zurek,Cosmological Experiments in Superfluid Helium?, Nature 317 (1985) 505

1985
[15]

Murayama and J

H. Murayama and J. Shu,Topological Dark Matter, Phys. Lett. B686 (2010) 162 [0905.1720]

2010 arXiv
[16]

Ghiglieri and M

J. Ghiglieri and M. Laine,Gravitational wave background from Standard Model physics: Qualitative features, JCAP 07 (2015) 022 [1504.02569]

2015 arXiv
[17]

Ghiglieri, G

J. Ghiglieri, G. Jackson, M. Laine and Y. Zhu,Gravitational wave background from Standard Model physics: Complete leading order, JHEP 07 (2020) 092 [2004.11392]

2020 arXiv
[18]

Ringwald, J

A. Ringwald, J. Schütte-Engel and C. Tamarit,Gravitational Waves as a Big Bang Thermometer, JCAP 03 (2021) 054 [2011.04731]

2021 arXiv
[19]

Datta and A

A. Datta and A. Sil,Probing Leptogenesis through Gravitational Waves, 2410.01900

arXiv
[20]

K.-Y. Choi, E. Lkhagvadorj and S. Mahapatra,Cosmological Origin of the KM3-230213A event and associated Gravitational Waves, 2503.22465
[21]

Borboruah, L

Z.A. Borboruah, L. Malhotra, F.F. Deppisch and A. Ghoshal,Inflationary Gravitational Waves and Laboratory Searches as Complementary Probes of Right-handed Neutrinos, 2504.15374

arXiv
[22]

Chianese, G

M. Chianese, G. Domènech, T. Papanikolaou, R. Samanta and N. Saviano,Induced Gravitational Waves as Cosmic Tracers of Leptogenesis, 2504.20135

arXiv
[23]

DESI collaboration, DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations, JCAP 02 (2025) 021 [2404.03002]. – 28 –

2025 arXiv
[24]

Tristram et al.,Improved limits on the tensor-to-scalar ratio using BICEP and Planck data, Phys

M. Tristram et al.,Improved limits on the tensor-to-scalar ratio using BICEP and Planck data, Phys. Rev. D105 (2022) 083524 [2112.07961]

2022 arXiv
[25]

Domcke and J

V. Domcke and J. Heisig,Constraints on the reheating temperature from sizable tensor modes, Phys. Rev. D92 (2015) 103515 [1504.00345]

2015 arXiv
[26]

L. Covi, E. Roulet and F. Vissani,CP violating decays in leptogenesis scenarios, Phys. Lett. B 384 (1996) 169 [hep-ph/9605319]

1996 arXiv
[27]

Davidson and A

S. Davidson and A. Ibarra,A Lower bound on the right-handed neutrino mass from leptogenesis, Phys. Lett. B535 (2002) 25 [hep-ph/0202239]

2002 arXiv
[28]

Ghiglieri, J

J. Ghiglieri, J. Schütte-Engel and E. Speranza,Freezing-in gravitational waves, Phys. Rev. D 109 (2024) 023538 [2211.16513]

2024 arXiv
[29]

Ghiglieri, M

J. Ghiglieri, M. Laine, J. Schütte-Engel and E. Speranza,Double-graviton production from Standard Model plasma, JCAP 04 (2024) 062 [2401.08766]

2024 arXiv
[30]

F. Muia, F. Quevedo, A. Schachner and G. Villa,Testing BSM physics with gravitational waves, JCAP 09 (2023) 006 [2303.01548]

2023 arXiv
[31]

Abbott et al.,Sensitivity of the Advanced LIGO detectors at the beginning of gravitational wave astronomy, Phys

B.P. Abbott et al.,Sensitivity of the Advanced LIGO detectors at the beginning of gravitational wave astronomy, Phys. Rev. D93 (2016) 112004 [1604.00439]

2016 arXiv
[32]

Kuroyanagi, K

S. Kuroyanagi, K. Nakayama and J. Yokoyama,Prospects of determination of reheating temperature after inflation by DECIGO, PTEP 2015 (2015) 013E02 [1410.6618]

2015 arXiv
[33]

Ringwald, K

A. Ringwald, K. Saikawa and C. Tamarit,Primordial gravitational waves in a minimal model of particle physics and cosmology, JCAP 02 (2021) 046 [2009.02050]

2021 arXiv
[34]

Tito D’Agnolo and S.A.R

R. Tito D’Agnolo and S.A.R. Ellis,Classical (and quantum) heuristics for gravitational wave detection, JHEP 04 (2025) 164 [2412.17897]

2025 arXiv
[35]

Y. He, S.K. Giri, R. Sharma, S. Mtchedlidze and I. Georgiev,Inverse Gertsenshtein effect as a probe of high-frequency gravitational waves, JCAP 05 (2024) 051 [2312.17636]

2024 arXiv
[36]

Berlin, D

A. Berlin, D. Blas, R. Tito D’Agnolo, S.A.R. Ellis, R. Harnik, Y. Kahn et al.,Detecting high-frequency gravitational waves with microwave cavities, Phys. Rev. D105 (2022) 116011 [2112.11465]

2022 arXiv
[37]

Domcke, C

V. Domcke, C. García-Cely and N.L. Rodd,Novel Search for High-Frequency Gravitational Waves with Low-Mass Axion Haloscopes, Phys. Rev. Lett.129 (2022) 041101 [2202.00695]

2022 arXiv
[38]

Berlin, D

A. Berlin, D. Blas, R. Tito D’Agnolo, S.A.R. Ellis, R. Harnik, Y. Kahn et al.,Electromagnetic cavities as mechanical bars for gravitational waves, Phys. Rev. D108 (2023) 084058 [2303.01518]

2023 arXiv
[39]

Y. Kahn, J. Schütte-Engel and T. Trickle,Searching for high-frequency gravitational waves with phonons, Phys. Rev. D109 (2024) 096023 [2311.17147]

2024 arXiv
[40]

Domcke, S.A.R

V. Domcke, S.A.R. Ellis and N.L. Rodd,Magnets are Weber Bar Gravitational Wave Detectors, Phys. Rev. Lett.134 (2025) 231401 [2408.01483]

2025 arXiv
[41]

Kharzeev, A

D.E. Kharzeev, A. Maleknejad and S. Shalamberidze,QuGrav: Bringing gravitational waves to light with Qumodes, 2506.09459. – 29 –
[42]

Aggarwal et al.,Challenges and Opportunities of Gravitational Wave Searches above 10 kHz, 2501.11723

N. Aggarwal et al.,Challenges and Opportunities of Gravitational Wave Searches above 10 kHz, 2501.11723
[43]

Holstein,Graviton Physics, Am

B.R. Holstein,Graviton Physics, Am. J. Phys.74 (2006) 1002 [gr-qc/0607045]

2006 arXiv
[44]

Choi, J.S

S.Y. Choi, J.S. Shim and H.S. Song,Factorization and polarization in linearized gravity, Phys. Rev. D 51 (1995) 2751 [hep-th/9411092]

1995 arXiv
[45]

Weinberg,Infrared photons and gravitons, Phys

S. Weinberg,Infrared photons and gravitons, Phys. Rev. 140 (1965) B516

1965
[46]

W. Hu, K. Nakayama, V. Takhistov and Y. Tang,Gravitational wave probe of Planck-scale physics after inflation, Phys. Lett. B856 (2024) 138958 [2403.13882]. – 30 –

2024 arXiv

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Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

Guth,The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys

A.H. Guth,The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D23 (1981) 347

1981

[2] [2]

Sato,First-order phase transition of a vacuum and the expansion of the Universe, Mon

K. Sato,First-order phase transition of a vacuum and the expansion of the Universe, Mon. Not. Roy. Astron. Soc.195 (1981) 467. – 27 –

work page 1981

[3] [3]

Starobinsky,Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations, Phys

A.A. Starobinsky,Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations, Phys. Lett. B117 (1982) 175

work page 1982

[4] [4]

Sakharov,Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh

A.D. Sakharov,Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz.5 (1967) 32

1967

[5] [5]

Riotto,Theories of baryogenesis, inICTP Summer School in High-Energy Physics and Cosmology, pp

A. Riotto,Theories of baryogenesis, inICTP Summer School in High-Energy Physics and Cosmology, pp. 326–436, 7, 1998 [hep-ph/9807454]

arXiv 1998

[6] [6]

Fukugita and T

M. Fukugita and T. Yanagida,Baryogenesis Without Grand Unification, Phys. Lett. B174 (1986) 45

1986

[7] [7]

Super-Kamiokande collaboration, Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett.81 (1998) 1562 [hep-ex/9807003]

arXiv 1998

[8] [8]

Minkowski,µ→eγ at a Rate of One Out of109 Muon Decays?, Phys

P. Minkowski,µ→eγ at a Rate of One Out of109 Muon Decays?, Phys. Lett. B67 (1977) 421

work page 1977