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Classical gravitational waves, treated as coherent graviton states, decay in vacuum into photon pairs—an effect forbidden classically and boosted by the square of the graviton number.

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2026-07-31 05:33 UTC pith:WMV73VYZ

load-bearing objection Real N^{2}-enhanced gg oγγ rate for coherent GW states, carefully derived, but the absolute normalization rests on an angular profile the paper never specifies. the 3 major comments →

arxiv 2607.24930 v1 pith:WMV73VYZ submitted 2026-07-27 hep-ph gr-qc

Gravitational waves decay in vacuum: a low energy effect of quantized gravitation

Diego Blas , Jos\'e Antonio Oller This is my paper
classification hep-ph gr-qc
keywords gravitational wavescoherent graviton statesgraviton-photon fusionquantum gravity phenomenologyCMB spectral distortionsultralight dark matterphoton injection bounds
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.

Classical gravitational waves are stable in empty space. This paper argues that once they are described as coherent states of gravitons, they can fuse into photon pairs through a tree-level quantum process that vanishes both classically and in the semiclassical limit, and that scales with the square of the average graviton number. The authors compute the resulting photon luminosity for compact-binary inspirals and mergers and for a stochastic background, including stimulated emission into the cosmic microwave background, and show that an analogous channel into ultralight dark-matter bosons can be enormously enhanced by occupation number. They then turn the predicted photon injection into the first observational bounds on cosmological gravitational-wave sources, using CMB spectral distortions, extragalactic backgrounds, and light-nuclei photofission. If the effect is real, it supplies a new—though still extremely challenging—electromagnetic handle on gravitational-wave sources that can exist only if gravity itself is quantized.

Core claim

When a gravitational wave is represented as a narrow-band coherent state of gravitons, the tree-level graviton–graviton fusion amplitude into two photons yields a nonzero decay probability per unit time proportional to G squared times N squared times frequency cubed times bandwidth squared. The process is absent from both classical general relativity and semiclassical particle production on a fixed wave background, vanishes as Planck’s constant goes to zero, and therefore constitutes a low-energy signature of quantized gravity.

What carries the argument

The Skobelev tree amplitude for gg→γγ evaluated on a narrow-band coherent-state profile, with coherent-mode propagation in the intermediate graviton propagator discarded because it forces the Mandelstam variable s to zero; the resulting rate is dP/dt = 3 G² N² ω_s³ σ_ω² / 25π.

Load-bearing premise

That evaluating the known two-graviton fusion amplitude on a simple coherent-state wave packet in flat space, while throwing away the coherent piece of the graviton propagator, correctly describes a physical depletion of a real outgoing gravitational wave rather than an artifact cancelled by gauge constraints or higher-order effects.

What would settle it

A laboratory or astrophysical measurement that either detects the predicted photon luminosity scaling as G² N² ω³ σ² from a well-characterized gravitational-wave burst, or demonstrates that no such photons appear at a sensitivity that rules out the calculated rate.

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

If this is right

  • Compact-binary mergers produce a modest photon luminosity (roughly comparable to the Hawking luminosity of a black hole of the same total mass) that is further enhanced by stimulated emission into the CMB at low frequencies.
  • A stochastic gravitational-wave background depletes at a volume rate proportional to the square of its energy density, but the effect remains negligible under present N_eff bounds.
  • In the presence of ultralight dark matter the same fusion channel can convert gravitational-wave energy into dark-matter quanta at rates that can reach stellar luminosities inside dense galactic cores.
  • Photon injection from a cosmological population of gravitational-wave sources is already constrained by CMB μ- and y-distortions, the UV/X-ray and γ-ray backgrounds, and deuterium and helium-4 photofission.
  • Any future detection of the predicted photons would constitute direct evidence that the gravitational field is quantized.

Where Pith is reading between the lines

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

  • Because the rate scales with N² and with the inverse square of the wavefront width, sources that are both extremely energetic and extremely coherent (for example certain cosmic-string bursts) could produce far larger electromagnetic counterparts than ordinary binaries.
  • The same coherent-state logic should apply to any light boson or fermion that couples to gravity, opening a systematic search for ‘gravitational-wave decay’ into dark sectors beyond ultralight scalars.
  • If the effect survives a full curved-space, gauge-invariant treatment, it supplies a new infrared consistency condition that any ultraviolet completion of gravity must reproduce.

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

3 major / 7 minor

Summary. The paper argues that classical gravitational waves, treated as coherent states of gravitons in the EFT of gravity, decay in vacuum via the tree-level process gg→γγ (Skobelev amplitude), with a rate per unit time dP/dt = 3G²N²ω_s³σ_ω²/25π (Eq. 8) that is forbidden classically and semiclassically, vanishes as ℏ→0, and is enhanced by N². The authors estimate photon luminosities for inspiral and merger phases of compact binaries (Fig. 2), derive a depletion equation for the stochastic GW background (Eqs. 14–15), compute the analogous decay into ultralight dark matter with Bose enhancement from large occupation numbers (Eqs. 16–18), and derive constraints on homogeneous populations of recurrent GW sources from CMB μ and y distortions, the UV/X-ray and γ-ray backgrounds, and BBN photofission (Fig. 3). A Supplement provides the propagator-cancellation argument (SA), the phase-space integrations (SB), the SGWB depletion (SC), scalar amplitudes (SD), and the injection/cascade formulas (SE–SF).

Significance. If the result holds, this is a conceptually important observation: a genuinely quantum (vanishing as ℏ→0), tree-level EFT effect by which gravitational waves lose energy to photons, with the appealing feature that the same machinery yields concrete, falsifiable constraints on populations of cosmological GW sources (Fig. 3) and a stimulated channel into ultralight dark matter. The paper deserves credit for shipping checkable derivations: the coherent-state construction, the propagator-cancellation argument (SM SA), the phase-space integrations (SM SB), the SGWB depletion equation with its formal solution (SM SC), the scalar helicity amplitudes and full rate integral (SM SD), and the cosmological injection formulas including μ/y distortions and photofission (SM SE–SF) are all written out in sufficient detail to be verified. The authors are also commendably honest about the smallness of the effect (e.g. the Hawking-luminosity comparison, Eq. (13), and the negligible SGWB depletion). No target observable is inserted as a fit parameter and re-predicted.

major comments (3)
  1. [SM §SB / Eq. (8)] SM §SB, Eqs. (S6)–(8): the derivation specifies the coherent-state profile f_s(k) only through its magnitude (top-hat in |k|), and the final |K| integral runs over 0 ≤ |K| ≤ 2ω_s, i.e. over effectively all relative angles of the annihilated pair (s = 4ω_s² − K²). The entire effect lives at s ≠ 0, yet for an outgoing spherical wave packet from a localized source the gravitons overlapping at a given spacetime point far from the source are nearly collinear (radial), with relative angle set by wavefront curvature/antenna pattern, Δθ ~ (kr)^{-1}, not by σ_ω. The parameter that regulates the evasion of the plane-wave no-go theorems (Refs. 20–25) is thus the angular spread of f_s, which is never written down. The paper's own remark after Eq. (14) — that the effective volume for the coherent state is ~ λ_s³ — suggests the conversion is in fact localized to a near-zone, wavelength-sized region, w
  2. [Merger phase / Fig. 2b] §'Application to binary systems', merger phase (Fig. 2b): if, per the effective-volume argument after Eq. (14), the conversion is localized near the source within r ~ λ_s, then for the nominal merger scaling (ν ≈ 150 Hz × 65M_⊙/M) one has λ_s ~ r_s and the field in the conversion region is strong (h ~ O(1), r_m/r ~ O(1)). The whole setup — Minkowski-background EFT, Eq. (1)–(5), and the flat-space Skobelev amplitude Eq. (6) — is then being applied outside its regime of validity precisely where the reaction is supposed to occur. The inspiral-phase results are not affected in the same way (r_m/λ ≪ 1). The merger-phase luminosities of Fig. 2b should either be justified against strong-field and curvature corrections or explicitly restricted to the regime where the conversion region is weak-field.
  3. [SM §SB / Eqs. (19)–(20)] SM §SB, after Eq. (S6): the replacement 2πδ(0) → T with T ~ 1/σ_ω, together with the requirement τ ≪ δt ~ 1/σ_ω imposed throughout, makes the constant-rate description applicable only within one coherence time of the wave train. For the inspiral the steady-state binning in ϵ plausibly handles this, but for burst-like configurations (merger, and implicitly the cosmological populations of §'Phenomenological bounds') the manuscript never states how many coherence times the reaction acts over as the packet propagates, nor what fraction is converted when τ ≫ δt (perturbatively, P ~ δt/τ per packet should still be definable). Since Eqs. (19)–(20) and Fig. 3 integrate the emission over cosmological source populations, the assumed recurrence of the rate is load-bearing for the bounds and should be stated and justified.
minor comments (7)
  1. [Discussion] Discussion, first sentence: decay into 'light fermions' is advertised but never computed anywhere in the paper (only photons and scalars, SM §SD). Either add the estimate or soften the sentence.
  2. [Eq. (10)] Eq. (10): please double-check the printed powers; dimensional analysis and consistency with Eqs. (S7)–(9) require τ = 25π/(6G² E_rel ω_s² σ_ω²).
  3. [Grammar/typos] 'Application to binary systems', inspiral paragraph: 'a close equation for ρ_GW' should read 'a closed equation'; earlier, 'the validity of this approximations for each source we shall considered' needs grammar fixes.
  4. [Figures 2–3] Fig. 2 caption: define the hatched region and the colored boundary lines (blue/orange/red/green/brown) in the caption itself rather than only in the text; likewise Fig. 3 should define Γ and ϵ in its caption.
  5. [Footnote 2 / Eq. (11) vicinity] Footnote 2: the statement 'stimulated emission/absorption effects are relevant only for ω_s ≲ k_BT' appears with the inequality seemingly reversed in one clause; please recheck the wording, and state explicitly whether the (1+2f_γ) factor in Fig. 2 uses today's CMB temperature or the source-frame temperature for the inspiral/merger cases.
  6. [After Eq. (7)] The claim 'g → gγγ has a vanishing rate' (after Eq. 7) is important for isolating the two-body channel; a one-line justification or reference would help, since in a coherent background three-body final states are not obviously forbidden.
  7. [Eq. (13)] The comparison W_H/W_γ in Eq. (13) is one of the most memorable estimates in the paper; please state whether it uses the same ϵ and bandwidth conventions as Fig. 2b, and give the strain h_r used for GW150914 in Eq. (12)'s preceding relation.

Circularity Check

0 steps flagged

No circularity: the N²-enhanced gg→γγ rate and cosmological bounds follow from external tree amplitudes, coherent-state kinematics, and independent observational limits, not from fitted or self-defined inputs.

full rationale

The central result (Eq. 8) is obtained by evaluating the external Skobelev tree amplitude (Ref. [29], Eq. 6) on a narrow-band coherent-state profile constructed from the linearized EFT source (Eqs. 1–5), then performing the phase-space integral in SM SB. No parameter is fitted to a target observable and re-predicted; bandwidth choices such as ϵ≈0.1 only set conservative lower bounds on emissivity. Cosmological constraints in Fig. 3 compare the derived photon injection to external FIRAS μ/y limits, IGRB, UV/X-ray backgrounds, and BBN photofission cascades. Self-citations ([26] for conventions and multiparticle phase-space suppression) are incidental and not load-bearing for the decay rate or the bounds. The skeptic concern about angular support of f^s(k) is a possible correctness issue, not a circular reduction of outputs to inputs. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

The central claim rests on standard gravitational EFT, the identification of classical GWs with coherent graviton states generated by a linearized source, tree-level Skobelev amplitudes, and a set of narrow-band and cosmological modeling choices. No new particles are required for the photon channel. Free parameters are few and mostly binning/threshold choices; the large occupation numbers for ULDM are taken from standard fuzzy-DM estimates rather than fitted here.

free parameters (2)
  • fractional bandwidth ϵ = 0.1 (fiducial)
    Chosen by hand (ϵ=0.1 in Fig. 2a; ϵ≈0.15 referenced for GW150914 ringdown) to define frequency bins and the coherence-time cut τ≪1/(ϵ ω_s). Controls which binary parameter space is ‘allowed’ and the lower-bound emissivity.
  • source start redshift / rate model (z_a, Γ=ñ κ)
    Cosmological bounds treat comoving density and recurrence rate as free phenomenological parameters packaged into √(Γ ϵ) E_rel; not fitted to data but scanned to produce Fig. 3 upper limits.
axioms (5)
  • domain assumption General relativity is a valid EFT of gravitons coupled to the Standard Model below the Planck scale, with linearized coupling of a classical source producing a coherent graviton state (Eqs. 1–5).
    Stated in the opening and ‘Coherent states of gravitons’ section; standard but load-bearing for identifying classical GWs with |f⟩.
  • domain assumption The tree-level Skobelev helicity amplitudes (Eq. 6) plus free graviton propagators correctly describe gg→γγ when the external gravitons are taken from a coherent state, and coherent-mode intermediate lines do not contribute (SM SA).
    Core dynamical input; SA argues on-shell s=0 and helicity obstruction cancel coherent propagation.
  • ad hoc to paper Narrow-band top-hat profile f_s(k) with width σ_ω≪ω_s adequately models astrophysical wave packets for the purpose of computing dP/dt.
    Introduced explicitly after Eq. 5 for convenience; used throughout binary and rate formulas.
  • domain assumption No-production theorems for classical/semiclassical plane-wave backgrounds do not forbid the coherent-state fusion process computed here.
    Paper cites Refs. 20–25 for the semiclassical prohibition and claims the full quantum propagator plus N² coherence evade it; this separation is assumed rather than derived from a complete constrained quantization.
  • domain assumption Standard cosmological thermal history, FIRAS μ/y limits, IGRB measurements, and BBN photofission cascade methodology apply to continuous photon injection from homogeneous recurrent GW sources (SM SE–SF).
    Used to convert Δρ_γ into the bounds of Fig. 3.

pith-pipeline@v1.2.0-grok45-kimik3 · 25525 in / 3819 out tokens · 93985 ms · 2026-07-31T05:33:26.552149+00:00 · methodology

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read the original abstract

Classical gravitational waves (GWs) are stable in vacuum. We show that treated as coherent graviton states, they decay into photon pairs, a quantum process forbidden classically and semiclassically and enhanced by the graviton number squared $N^2$. We estimate the resulting rates for compact binaries and a stochastic background, including the effect from stimulated decay to the CMB. In theories with light degrees of freedom, an analogous decay into them is also possible, and more relevant for ultralight dark matter, as it can entail huge occupation numbers. We derive first constraints on cosmological GW sources by the corresponding injection of photons from CMB spectral distortions, extragalactic backgrounds, and light-nuclei photofission. In summary, the decay of GWs into photons offers a new (challenging) handle into the detection of GW sources, with the extra appealing feature of being only possible by the quantum nature of the gravitational field.

Figures

Figures reproduced from arXiv: 2607.24930 by Diego Blas, Jos\'e Antonio Oller.

Figure 1
Figure 1. Figure 1: FIG. 1. Feynman diagrams for the scattering amplitude [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Photon luminosity [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Log–log plot showing the upper bounds on [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

68 extracted references · 9 canonical work pages

  1. [1]

    B. P. Abbott et al. Observation of Gravitational Waves from a Binary Black Hole Merger.Phys. Rev. Lett., 116(6):061102, 2016.arXiv:1602.03837,doi:10.1103/ PhysRevLett.116.061102

    Pith/arXiv arXiv 2016

  2. [2]

    A. G. Abac et al. Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M ⊙ Compact Ob- ject and a Neutron Star.Astrophys. J. Lett., 970(2):L34, 2024.arXiv:2404.04248,doi:10.3847/2041-8213/ ad5beb

    Pith/arXiv arXiv 2024

  3. [3]

    The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background.As- trophys

    Gabriella Agazie et al. The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background.As- trophys. J. Lett., 951(1):L8, 2023.arXiv:2306.16213, doi:10.3847/2041-8213/acdac6

    Pith/arXiv arXiv 2023

  4. [4]

    K. G. Arun et al. New horizons for fundamental physics with LISA.Living Rev. Rel., 25(1):4, 2022.arXiv:2205. 01597,doi:10.1007/s41114-022-00036-9

    doi:10.1007/s41114-022-00036-9 2022

  5. [5]

    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(1):10, 2025.arXiv:2501.11723,doi:10.1007/ s41114-025-00060-5

    arXiv 2025

  6. [6]

    Figueroa

    Chiara Caprini and Daniel G. Figueroa. Cosmological backgrounds of gravitational waves.Class. Quant. Grav., 35(16):163001, 2018.arXiv:1801.04268,doi:10.1088/ 1361-6382/aac608

    Pith/arXiv arXiv 2018

  7. [7]

    Is a graviton detectable?Int

    Freeman Dyson. Is a graviton detectable?Int. J. Mod. Phys. A, 28:1330041, 2013.doi:10.1142/ S0217751X1330041X

    2013

  8. [8]

    Quantum Mechanics of Gravitational Waves.Phys

    Maulik Parikh, Frank Wilczek, and George Zahariade. Quantum Mechanics of Gravitational Waves.Phys. Rev. Lett., 127(8):081602, 2021.arXiv:2010.08205,doi:10. 1103/PhysRevLett.127.081602

    Pith/arXiv arXiv 2021

  9. [9]

    Manikandan, Thomas Bei- tel, and Igor Pikovski

    Germain Tobar, Sreenath K. Manikandan, Thomas Bei- tel, and Igor Pikovski. Detecting single gravitons with quantum sensing.Nature Commun., 15(1):7229, 2024. arXiv:2308.15440,doi:10.1038/s41467-024-51420-8

    Pith/arXiv arXiv 2024

  10. [10]

    Daniel Carney, Valerie Domcke, and Nicholas L. Rodd. Graviton detection and the quantization of gravity.Phys. Rev. D, 109(4):044009, 2024.arXiv:2308.12988,doi: 10.1103/PhysRevD.109.044009

    Pith/arXiv arXiv 2024

  11. [11]

    Coher- ent State Description of Gravitational Waves from Bi- nary Black Holes.Phys

    Sugumi Kanno, Jiro Soda, and Akira Taniguchi. Coher- ent State Description of Gravitational Waves from Bi- nary Black Holes.Phys. Rev. Lett., 136(6):061404, 2026. arXiv:2508.17947,doi:10.1103/kv1t-j27m

    arXiv 2026

  12. [12]

    Consistent canonical quantization of gravity: Recovery of classical GR from BRST-invariant coherent states

    Lasha Berezhiani, Gia Dvali, and Otari Sakhelashvili. Consistent canonical quantization of gravity: Recovery of classical GR from BRST-invariant coherent states. Phys. Rev. D, 113(12):125032, 2026.arXiv:2409.18777, doi:10.1103/652w-ym62

    Pith/arXiv arXiv 2026

  13. [13]

    Absorption of Gravitational Waves from Distant Sources.Phys

    Raphael Flauger and Steven Weinberg. Absorption of Gravitational Waves from Distant Sources.Phys. Rev. D, 99(12):123030, 2019.arXiv:1906.04853,doi:10.1103/ 7 PhysRevD.99.123030

    Pith/arXiv arXiv 2019

  14. [14]

    Wen-Yuan Ai, Sebastian A. R. Ellis, and Josef Pradler. Soft Gravitons, Hard Truths: Infrared Safety of Particle Processes in a Gravitational-Wave Background. 10 2025. arXiv:2510.27690

    arXiv 2025

  15. [15]

    R. F. Sawyer. Quantum break in high intensity gravitational wave interactions.Phys. Rev. Lett., 124(10):101301, 2020.arXiv:1910.08835,doi:10.1103/ PhysRevLett.124.101301

    Pith/arXiv arXiv 2020

  16. [16]

    John W. Moffat. Stochastic fluctuations and Brown- ian motion detection of gravitons.Eur. Phys. J. C, 85(2):166, 2025.arXiv:2409.02948,doi:10.1140/epjc/ s10052-025-13882-y

    Pith/arXiv arXiv 2025

  17. [17]

    Noah M. MacKay. Effective Field Theory Calculation of LIGO-like Compton Scattering. 12 2024.arXiv:2412. 20169

    2024

  18. [18]

    Donoghue, Mikhail M

    John F. Donoghue, Mikhail M. Ivanov, and Andrey Shk- erin. EPFL Lectures on General Relativity as a Quantum Field Theory. 2 2017.arXiv:1702.00319

    Pith/arXiv arXiv 2017

  19. [19]

    C. P. Burgess. Quantum gravity in everyday life: General relativity as an effective field theory.Living Rev. Rel., 7:5–56, 2004.arXiv:gr-qc/0311082,doi:10.12942/ lrr-2004-5

    Pith/arXiv arXiv 2004

  20. [20]

    Schwinger

    Julian S. Schwinger. On gauge invariance and vac- uum polarization.Phys. Rev., 82:664–679, 1951.doi: 10.1103/PhysRev.82.664

    doi:10.1103/physrev.82.664 1951

  21. [21]

    G. W. Gibbons. Quantized Fields Propagating in Plane Wave Space-Times.Commun. Math. Phys., 45:191–202, 1975.doi:10.1007/BF01629249

    work page doi:10.1007/bf01629249 1975

  22. [22]

    Plane waves do not polarize the vacuum

    Stanley Deser. Plane waves do not polarize the vacuum. J. Phys. A, 8:1972, 1975.doi:10.1088/0305-4470/8/ 12/012

    work page doi:10.1088/0305-4470/8/ 1972

  23. [23]

    Dunne.Heisenberg-Euler effective La- grangians: Basics and extensions, pages 445–522

    Gerald V. Dunne.Heisenberg-Euler effective La- grangians: Basics and extensions, pages 445–522. 6 2004. arXiv:hep-th/0406216,doi:10.1142/9789812775344_ 0014

    Pith/arXiv arXiv 2004

  24. [24]

    Quest for particles production in the plane gravitational wave spacetime.Eur

    Nail Khusnutdinov. Quest for particles production in the plane gravitational wave spacetime.Eur. Phys. J. Plus, 141(5):532, 2026.arXiv:2508.11558,doi:10. 1140/epjp/s13360-026-07725-2

    arXiv 2026

  25. [25]

    Scattering of quan- tum particles by gravitational plane waves.Phys

    Jaume Garriga and Enric Verdaguer. Scattering of quan- tum particles by gravitational plane waves.Phys. Rev. D, 43:391–401, 1991.doi:10.1103/PhysRevD.43.391

    doi:10.1103/physrevd.43.391 1991

  26. [26]

    Unitarization of infinite-range forces: graviton- graviton scattering.JHEP, 08:266, 2022.arXiv:2010

    Diego Blas, Jorge Martin Camalich, and Jose Antonio Oller. Unitarization of infinite-range forces: graviton- graviton scattering.JHEP, 08:266, 2022.arXiv:2010. 12459,doi:10.1007/JHEP08(2022)266

    work page doi:10.1007/jhep08(2022)266 2022

  27. [27]

    Backreaction on back- ground fields: A coherent state approach.Phys

    Anton Ilderton and Daniel Seipt. Backreaction on back- ground fields: A coherent state approach.Phys. Rev. D, 97(1):016007, 2018.arXiv:1709.10085,doi:10.1103/ PhysRevD.97.016007

    Pith/arXiv arXiv 2018

  28. [28]

    Itzykson and J

    C. Itzykson and J. B. Zuber.Quantum Field Theory. In- ternational Series In Pure and Applied Physics. McGraw- Hill, New York, 1980

    1980

  29. [29]

    DDyqvSwFm5VOnpRjfdC0RtjhVTQ=

    (see also [30, 31]). The corresponding Feynman di- agrams are shown in Fig. 1, and the fusion amplitude Aλ1λ2µ1µ2 (k1, k2, p1, p2) reads A++++ =A −−−− = 8πG t2 s ,(6) A++−− =A −−++ = 8πG u2 s , where s = (k 1 +k 2)2, t = (k 1 −q 1)2, and u = (k 1 −q 2)2 are the usual Mandelstam variables. The initial gravi- tons can also scatter into gravitons outside the...

    2020

  30. [30]

    V. V. Skobelev. Graviton-photon interaction.Sov. Phys. J., 18:62–65, 1975.doi:10.1007/BF00889810

    work page doi:10.1007/bf00889810 1975

  31. [31]

    Grisaru, P

    Marcus T. Grisaru, P. van Nieuwenhuizen, and C. C. Wu. Gravitational Born Amplitudes and Kinematical Constraints.Phys. Rev. D, 12:397, 1975.doi:10.1103/ PhysRevD.12.397

    1975

  32. [32]

    N. E. J. Bjerrum-Bohr, Barry R. Holstein, Ludovic Plant´ e, and Pierre Vanhove. Graviton-Photon Scatter- ing.Phys. Rev. D, 91(6):064008, 2015.arXiv:1410.4148, doi:10.1103/PhysRevD.91.064008

    Pith/arXiv arXiv 2015

  33. [33]

    Llanes-Estrada, Jos´ e Antonio Oller, and Alexandre Salas-Bern´ ardez

    Juan Escudero-Pedrosa, Felipe J. Llanes-Estrada, Jos´ e Antonio Oller, and Alexandre Salas-Bern´ ardez. As- sessment of systematic theory uncertainties in IAM uni- tarization.Nucl. Part. Phys. Proc., 312-317:82–86, 2021. arXiv:2012.02616,doi:10.1016/j.nuclphysbps.2021. 05.022

    Pith/arXiv arXiv 2021

  34. [34]

    Effects of orbital precession on hyperbolic encounters.Phys

    Marienza Caldarola, Sachiko Kuroyanagi, Savvas Nesseris, and Juan Garcia-Bellido. Effects of orbital precession on hyperbolic encounters.Phys. Rev. D, 109(6):064001, 2024.arXiv:2307.00915,doi:10.1103/ PhysRevD.109.064001

    Pith/arXiv arXiv 2024

  35. [35]

    Michele Maggiore.Gravitational Waves. Vol. 1: Theory and Experiments. Oxford University Press, 2007.doi: 10.1093/acprof:oso/9780198570745.001.0001

    arXiv 2007

  36. [36]

    Stella Koch Ocker and James M. Cordes. NE2025: An Updated Electron Density Model for the Galactic Inter- stellar Medium.Astrophys. J., 1002(1):3, 2026.arXiv: 2602.11838,doi:10.3847/1538-4357/ae5825

    Pith/arXiv arXiv 2026

  37. [37]

    Cook, and Frans Pretorius

    Alessandra Buonanno, Gregory B. Cook, and Frans Pretorius. Inspiral, merger and ring-down of equal- mass black-hole binaries.Phys. Rev. D, 75:124018, 2007.arXiv:gr-qc/0610122,doi:10.1103/PhysRevD. 75.124018

    Pith/arXiv arXiv 2007

  38. [38]

    Flanagan and Scott A

    Eanna E. Flanagan and Scott A. Hughes. Measur- ing gravitational waves from binary black hole coales- cences: 1. Signal-to-noise for inspiral, merger, and ring- down.Phys. Rev. D, 57:4535–4565, 1998.arXiv:gr-qc/ 9701039,doi:10.1103/PhysRevD.57.4535

    doi:10.1103/physrevd.57.4535 1998

  39. [39]

    Observational Black Hole Spectroscopy: A time-domain multimode analysis of GW150914.Phys

    Gregorio Carullo, Walter Del Pozzo, and John Veitch. Observational Black Hole Spectroscopy: A time-domain multimode analysis of GW150914.Phys. Rev. D, 99(12):123029, 2019. [Erratum: Phys.Rev.D 100, 089903 (2019)].arXiv:1902.07527,doi:10.1103/PhysRevD.99. 123029

    Pith/arXiv arXiv 2019

  40. [40]

    Aghanim, et al

    Planck Collaboration, N. Aghanim, et al. Planck 2018 results. VI. Cosmological parameters.Astronomy & As- trophysics, 641:A6, 2020.arXiv:1807.06209,doi:10. 1051/0004-6361/201833910

    Pith/arXiv arXiv 2018

  41. [41]

    TASI lectures on extra dimensions and branes

    Csaba Csaki. TASI lectures on extra dimensions and branes. InTheoretical Advanced Study Institute in Ele- mentary Particle Physics (TASI 2002): Particle Physics and Cosmology: The Quest for Physics Beyond the Stan- dard Model(s), pages 605–698, 4 2004.arXiv:hep-ph/ 0404096

    2002

  42. [42]

    Black Hole Bound on the Number of Species and Quantum Gravity at LHC

    Gia Dvali and Michele Redi. Black Hole Bound on the Number of Species and Quantum Gravity at LHC. Phys. Rev. D, 77:045027, 2008.arXiv:0710.4344,doi: 10.1103/PhysRevD.77.045027

    Pith/arXiv arXiv 2008

  43. [43]

    Cold and fuzzy dark matter.Phys

    Wayne Hu, Rennan Barkana, and Andrei Gruzinov. Cold and fuzzy dark matter.Phys. Rev. Lett., 85:1158– 1161, 2000.arXiv:astro-ph/0003365,doi:10.1103/ PhysRevLett.85.1158

    Pith/arXiv arXiv 2000

  44. [44]

    Ostriker, Scott Tremaine, and Ed- ward Witten

    Lam Hui, Jeremiah P. Ostriker, Scott Tremaine, and Ed- ward Witten. Ultralight scalars as cosmological dark matter.Phys. Rev. D, 95(4):043541, 2017.arXiv: 1610.08297,doi:10.1103/PhysRevD.95.043541

    Pith/arXiv arXiv 2017

  45. [45]

    J. I. Read. The Local Dark Matter Density.J. Phys. G, 41:063101, 2014.arXiv:1404.1938,doi:10.1088/ 0954-3899/41/6/063101

    Pith/arXiv arXiv 2014

  46. [46]

    Gross and Roman Jackiw

    David J. Gross and Roman Jackiw. Low-Energy Theo- rem for Graviton Scattering.Phys. Rev., 166:1287–1292, 1968.doi:10.1103/PhysRev.166.1287

    work page doi:10.1103/physrev.166.1287 1968

  47. [47]

    Rodd, and Lian-Tao Wang

    Dhong Yeon Cheong, Nicholas L. Rodd, and Lian-Tao Wang. Quantum description of wave dark matter.Phys. 8 Rev. D, 111(1):015028, 2025.arXiv:2408.04696,doi: 10.1103/PhysRevD.111.015028

    Pith/arXiv arXiv 2025

  48. [48]

    Foster, Yonatan Kahn, Rachel Nguyen, Nicholas L

    Joshua W. Foster, Yonatan Kahn, Rachel Nguyen, Nicholas L. Rodd, and Benjamin R. Safdi. Dark Matter Interferometry.Phys. Rev. D, 103(7):076018, 2021.arXiv:2009.14201,doi:10.1103/PhysRevD.103. 076018

    Pith/arXiv arXiv 2021

  49. [49]

    Ya. B. Zeldovich and R. A. Sunyaev. The Interac- tion of Matter and Radiation in a Hot-Model Universe. Astrophys. Space Sci., 4:301–316, 1969.doi:10.1007/ BF00661821

    1969

  50. [50]

    Future Steps in Cosmology using Spectral Distortions of the Cosmic Microwave Background.Proc

    Jens Chluba. Future Steps in Cosmology using Spectral Distortions of the Cosmic Microwave Background.Proc. Int. Sch. Phys. Fermi, 200:265–309, 2020.arXiv:1806. 02915,doi:10.3254/ENFI200012

    work page doi:10.3254/enfi200012 2020

  51. [51]

    Chluba et al

    J. Chluba et al. New horizons in cosmology with spec- tral distortions of the cosmic microwave background.Ex- per. Astron., 51(3):1515–1554, 2021.arXiv:1909.01593, doi:10.1007/s10686-021-09729-5

    Pith/arXiv arXiv 2021

  52. [52]

    New constraints on a light spinless particle coupled to photons.Phys

    Eduard Masso and Ramon Toldra. New constraints on a light spinless particle coupled to photons.Phys. Rev. D, 55:7967–7969, 1997.arXiv:hep-ph/9702275,doi:10. 1103/PhysRevD.55.7967

    Pith/arXiv arXiv 1997

  53. [53]

    A cosmic UV/X-ray background model update.Mon

    Claude-Andr´ e Faucher-Gigu` ere. A cosmic UV/X-ray background model update.Mon. Not. Roy. Astron. Soc., 493(2):1614–1632, 2020.arXiv:1903.08657,doi: 10.1093/mnras/staa302

    Pith/arXiv arXiv 2020

  54. [54]

    Ackermann et al

    M. Ackermann et al. The spectrum of isotropic dif- fuse gamma-ray emission between 100 MeV and 820 GeV.Astrophys. J., 799:86, 2015.arXiv:1410.3696, doi:10.1088/0004-637X/799/1/86

    Pith/arXiv arXiv 2015

  55. [55]

    Ellis, G

    John R. Ellis, G. B. Gelmini, Jorge L. Lopez, Dim- itri V. Nanopoulos, and Subir Sarkar. Astrophysi- cal constraints on massive unstable neutral relic parti- cles.Nucl. Phys. B, 373:399–437, 1992.doi:10.1016/ 0550-3213(92)90438-H

    1992

  56. [56]

    Big bang nucleosynthesis and physics be- yond the standard model.Rept

    Subir Sarkar. Big bang nucleosynthesis and physics be- yond the standard model.Rept. Prog. Phys., 59:1493– 1610, 1996.arXiv:hep-ph/9602260,doi:10.1088/ 0034-4885/59/12/001

    Pith/arXiv arXiv 1996

  57. [57]

    Green’s function of the cosmological ther- malization problem – II

    Jens Chluba. Green’s function of the cosmological ther- malization problem – II. Effect of photon injection and constraints.Mon. Not. Roy. Astron. Soc., 454(4):4182– 4196, 2015.arXiv:1506.06582,doi:10.1093/mnras/ stv2243

    Pith/arXiv arXiv 2015

  58. [58]

    D. J. Fixsen, E. S. Cheng, J. M. Gales, John C. Mather, R. A. Shafer, and E. L. Wright. The Cosmic Microwave Background spectrum from the full COBE FIRAS data set.Astrophys. J., 473:576, 1996.arXiv:astro-ph/ 9605054,doi:10.1086/178173

    doi:10.1086/178173 1996

  59. [59]

    P. J. E. Peebles.Principles of Physical Cosmology. Princeton University Press, 2020

    2020

  60. [60]

    Galactic rotation curves versus ultralight dark matter: Implications of the soliton-host halo re- lation.Phys

    Nitsan Bar, Diego Blas, Kfir Blum, and Sergey Sibiryakov. Galactic rotation curves versus ultralight dark matter: Implications of the soliton-host halo re- lation.Phys. Rev. D, 98(8):083027, 2018.arXiv:1805. 00122,doi:10.1103/PhysRevD.98.083027

    doi:10.1103/physrevd.98.083027 2018

  61. [61]

    Roy J. Glauber. Coherent and incoherent states of the radiation field.Phys. Rev., 131:2766–2788, 1963.doi: 10.1103/PhysRev.131.2766

    doi:10.1103/physrev.131.2766 1963

  62. [62]

    E. C. G. Sudarshan. Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams.Phys. Rev. Lett., 10:277–279, 1963.doi:10.1103/ PhysRevLett.10.277

    1963

  63. [63]

    Ellis, Dimitri V

    John R. Ellis, Dimitri V. Nanopoulos, and Subir Sarkar. The Cosmology of Decaying Gravitinos.Nucl. Phys. B, 259:175–188, 1985.doi:10.1016/0550-3213(85) 90306-2

    doi:10.1016/0550-3213(85 1985

  64. [64]

    Cosmological Constraints on the Lifetime of Massive Particles.Astrophys

    David Lindley. Cosmological Constraints on the Lifetime of Massive Particles.Astrophys. J., 294:1–8, 1985.doi: 10.1086/163267

    work page doi:10.1086/163267 1985

  65. [65]

    J. M. Laget. Electromagnetic Properties of the pi n n System. 3. The gamma d –>p n Reaction.Nucl. Phys. A, 312:265–290, 1978.doi:10.1016/0375-9474(78) 90590-0

    work page doi:10.1016/0375-9474(78 1978

  66. [66]

    Sofia Quaglioni, Winfried Leidemann, Giuseppina Orlan- dini, Nir Barnea, and Victor D. Efros. Two body pho- todisintegration of He-4 with full final state interaction. Phys. Rev. C, 69:044002, 2004.arXiv:nucl-th/0311068, doi:10.1103/PhysRevC.69.044002

    Pith/arXiv arXiv 2004

  67. [67]

    Gari and H

    M. Gari and H. Hebach. Photonuclear reactions at intermediate energies (40 MeV⩽E γ⩽400 MeV). Physics Reports, 72(1):1–55, June 1981.doi:10.1016/ 0370-1573(81)90008-9

    1981

  68. [68]

    S. M. Doran et al. The 4 He(γ, 2N) reaction measured with tagged photons.Nucl. Phys. A, 559:347–367, 1993. doi:10.1016/0375-9474(93)90158-T. SUPPLEMENT AL MA TERIAL SA. Propagator of the coherent state We show that the coherent-state mode does not propagate in diagram 2) of Fig. 1, the only diagram with a graviton propagator connecting the two verticesxan...

    work page doi:10.1016/0375-9474(93)90158-t 1993