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Planck data show no clear non-Gaussianity from Kaluza-Klein gravitons or the radion; a warped extra-dimension model still predicts signals of size f_NL ~ 1-50 that future surveys can reach.

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T0 review · grok-4.5

2026-07-12 07:57 UTC pith:IL3GYV34

load-bearing objection First real Planck search for the leading (dim-5) KK-graviton and radion bispectra, with a controlled 5D target that future LSS can hit.

arxiv 2607.02651 v1 pith:IL3GYV34 submitted 2026-07-02 astro-ph.CO hep-phhep-th

First Search for Kaluza-Klein Gravitons and Radion Using Planck Data

Alexander P. Cassem , Soubhik Kumar This is my paper
classification astro-ph.CO hep-phhep-th
keywords primordial non-GaussianityKaluza-Klein gravitonsradioncosmological colliderwarped extra dimensionsPlanck 2018modulated reheatingbispectrum
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.

Heavy states that live in extra dimensions, such as the radion modulus and Kaluza-Klein gravitons, can be too massive for colliders yet light enough to be produced by inflation. Because they couple gravitationally to the field that sources density perturbations, they leave a distinctive three-point correlation (bispectrum) in the cosmic microwave background. The authors compute those full bispectra from the leading dimension-5 operators and search for them for the first time in Planck 2018 temperature and polarization maps. No significant signal appears; the strongest local excess is only 1.8 sigma near m_KK ~ 1.6 H. At the same time they exhibit an explicit warped five-dimensional construction with modulated reheating in which the same operators naturally produce f_NL of order 1-50, values still allowed by Planck and accessible to future large-scale-structure surveys. The result therefore both sets the first direct cosmological limits on these extra-dimensional states and supplies concrete observational targets for the next generation of data.

Core claim

A dedicated search of Planck 2018 temperature and polarization data for the complete radion- and KK-graviton-mediated bispectra, generated by the dimension-5 operators that couple these states to the density-perturbation field, finds no significant non-Gaussianity (maximum local significance 1.8 sigma at m_KK ~ 1.6 H). An explicit warped five-dimensional model with modulated reheating simultaneously shows that the same operators can produce f_NL ~ 1-50, still consistent with the Planck bounds and within reach of future surveys.

What carries the argument

The dimension-5 interaction Lagrangian (Eq. 1) that couples the radion and the lightest KK graviton to a light IR-localized field sigma; its in-in bispectra supply the shape functions that are then constrained by CMB-BEST on Planck 2018 data and normalized to f_NL.

Load-bearing premise

The map from the light IR field sigma to the observed curvature perturbation is assumed to be the simple linear modulated-reheating relation that fixes the overall conversion factor from the measured power spectrum.

What would settle it

A future large-scale-structure bispectrum analysis that either detects the predicted radion or KK-graviton shape at |f_NL| greater than or equal to a few, or tightens the bound well below the benchmark values |f_NL| ~ 1-50 obtained from the warped model.

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

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

0 major / 5 minor

Summary. The paper computes the full bispectra mediated by the radion and the lightest KK graviton arising from the dimension-5 operators of Eq. (1) in a warped RS1 geometry, evaluates the associated scale-invariant shape functions S on a dense kinematic grid, and searches for them in Planck 2018 temperature and polarization data with CMB-BEST. No significant non-Gaussianity is found (maximum local significance 1.8σ at µ=0.5, f_NL=-58±32 at 68% CL). A concrete 5D construction with Goldberger-Wise stabilization and IR-localized σ, combined with modulated reheating, is shown to produce |f_NL|∼1–50 while remaining under theoretical control, providing a concrete target for future LSS surveys. Simultaneous three-shape constraints (local + radion + KK) are also presented.

Significance. This is the first dedicated Planck search for the leading (dimension-5) cosmological-collider signals of KK gravitons and the radion. Previous spin-2 searches used only dimension-6 EFT operators; the shapes computed here (including contact corrections from non-dynamical helicity-0 modes, App. A.2) are therefore new and parametrically larger. The observational bounds on f_NL are model-independent of the precise 5D couplings and of the σ oζ transfer function. The explicit warped + modulated-reheating construction that yields |f_NL|∼1–50 is a falsifiable, controlled target for next-generation LSS analyses. The appendices document mode functions, in-in propagators, numerical 5D background solutions with back-reaction, and the Boltzmann treatment of modulated reheating, making the calculation reproducible.

minor comments (5)
  1. Fig. 1 caption and surrounding text: the quoted maximum local significance (1.8σ) is for µ=0.5, yet the abstract and introduction highlight m_KK≈1.6H (µ≈1.1). A single clarifying sentence would remove any ambiguity for readers who only scan the abstract.
  2. Sec. V and Eq. (10): the conversion ζ=-δσ/(3M) with M fixed by A_s is used only for the theoretical target values. Explicitly stating that the Planck f_NL bounds themselves are independent of this transfer function would strengthen the presentation.
  3. Appendix A.2: the contact-term operators Δ^(ηη|ηη) etc. are correctly derived, but a short remark that they are essential for recovering the known local-shape overlap (cos=0.99) would help non-specialist readers.
  4. Fig. 3 triangle plot: the three-shape correlations (0.34, -0.18, -0.39) are quoted in the text; adding them to the figure caption would improve readability.
  5. A few typographical inconsistencies appear (e.g., “form KK” vs. “for m_KK”, occasional missing spaces around ≈). A light copy-edit pass would polish the manuscript.

Circularity Check

0 steps flagged

No significant circularity: Planck f_NL bounds come from independently computed shapes fed into a public pipeline; the 5D target values are derived from the action and Boltzmann equations, not fitted to the data.

full rationale

The observational search (Sec. III, Fig. 1) takes shape functions S obtained from the in-in evaluation of the dimension-5 operators in Eqs. (1)–(3) (App. A) and feeds them into the public CMB-BEST package on Planck 2018 T+E data; the resulting f_NL limits are therefore independent of the 5D couplings and of the modulated-reheating transfer function. The theoretical targets f_NL ~ 1–50 (Sec. V) are obtained by solving the 5D Einstein–GW system (App. C), reading off c_g/Λ_c and c_r/Λ_c from the IR-localized kinetic term (Eq. 9), and converting δσ o ζ via the linear relation ζ = −δσ/(3M) with M fixed by the observed A_s (App. D). None of these steps is a fit to the Planck f_NL values, nor does any uniqueness claim rest solely on an unverified self-citation. The only self-citations ([34, 35]) supply the operator structure and the radion action that are re-derived or re-computed in the present appendices; they are not load-bearing for the null result. Score 1 reflects ordinary, non-circular self-citation of prior technical machinery.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 1 invented entities

The observational null result rests on standard de-Sitter mode functions, the in-in formalism, and the public CMB-BEST pipeline applied to Planck 2018 data. The theoretical target f_NL ~ 1–50 additionally rests on a specific warped 5D geometry, Goldberger-Wise stabilization, IR-localized σ, and the linear modulated-reheating transfer. Free parameters are the 5D mass scales, boundary potentials, and the slow-roll velocity σ̇_0 that set the overall amplitude.

free parameters (3)
  • σ̇_0 / H^{2} = 0.5
    Benchmark value 0.5 chosen so that the derivative expansion |σ̇_0|/Λ_c^{2} ≈ 0.1 remains under control; directly multiplies f_NL.
  • 5D scales (M_5, k, H) and GW parameters (ε, λ_0, λ_L, f_0, f_L) = M_5=1.2e18 GeV, k=6.4e17 GeV, H=1.8e13 GeV, ε=-0.85, …
    Chosen in Appendix C to produce m_rad ≈ 1.8 H, m_KK ≈ 1.57 H and the quoted couplings c_g/Λ_c ≈ -0.24/H, c_r/Λ_c ≈ 0.04/H; they fix the predicted |f_NL|.
  • M (UV scale in modulated reheating) = ≈1158 H
    Fixed by the observed A_s ≈ 2.1e-9 via A_s = H^{2}/(36 π^{2} M^{2}) to M ≈ 1158 H; enters the overall f_NL prefactor.
axioms (4)
  • standard math de Sitter mode functions and in-in (Schwinger-Keldysh) formalism for the bispectrum
    Standard cosmological-collider technology used throughout Appendix A.
  • domain assumption Leading interactions are the dimension-5 operators of Eq. (1) that respect the σ shift symmetry
    Higher-dimension or shift-breaking operators are argued to be suppressed by m_σ/H ≪ 1.
  • domain assumption Density perturbations are sourced by an IR-localized composite field σ via modulated reheating, with linear transfer ζ = -δσ/(3M)
    Sec. V and Appendix D; required to convert the δσ bispectrum into an f_NL prediction.
  • ad hoc to paper Warped RS1 geometry with Goldberger-Wise stabilization and the specific boundary potentials of Eq. (C7)
    Appendix C; chosen to realize m_KK ~ H and IR-localized wave-function overlap.
invented entities (1)
  • IR-localized light composite field σ that sources ζ via modulated reheating no independent evidence
    purpose: Provides the density perturbations that couple to the radion and KK gravitons, allowing observable NG while the inflaton remains elementary.
    Standard in the modulated-reheating literature but here required to be composite and IR-localized so that the 5D wave-function overlap enhances the couplings.

pith-pipeline@v1.1.0-grok45 · 30251 in / 3362 out tokens · 28298 ms · 2026-07-12T07:57:01.693654+00:00 · methodology

0 comments
read the original abstract

Heavy moduli and Kaluza-Klein (KK) gravitons from extra dimensions may evade terrestrial probes but can be produced during inflation, generating primordial non-Gaussianity (NG) through unavoidable couplings to density perturbations. In a warped five-dimensional (5D) model, we compute the full radion- and KK-graviton-mediated bispectra and perform the first search for these signals using Planck 2018 temperature and polarization data. We find no significant evidence for NG, with the maximum significance being $1.8\sigma$ for $m_{\rm KK}\approx 1.6H$. We also identify a 5D setup which naturally generates NG with $f_{\rm NL}\sim 1-50$, within the reach of future surveys.

Figures

Figures reproduced from arXiv: 2607.02651 by Alexander P. Cassem, Soubhik Kumar.

Figure 1
Figure 1. Figure 1: FIG. 1. Estimated strength of the bispectrum ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Shape functions for the KK graviton in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Triangle plot illustrating a simultaneous search for [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

discussion (0)

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Works this paper leans on

93 extracted references · 58 linked inside Pith

  1. [1]

    M. B. Green, J. H. Schwarz, and E. Witten,SUPER- STRING THEORY. VOL. 1: INTRODUCTION, Cam- bridge Monographs on Mathematical Physics (1988)

    1988

  2. [2]

    Polchinski,String theory

    J. Polchinski,String theory. Vol. 1: An introduction to the bosonic string, Cambridge Monographs on Mathe- matical Physics (Cambridge University Press, 2007)

    2007

  3. [3]

    Arkani-Hamed, S

    N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, Phys. Lett. B429, 263 (1998), arXiv:hep-ph/9803315

    Pith/arXiv arXiv 1998

  4. [4]

    Antoniadis, N

    I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, Phys. Lett. B436, 257 (1998), arXiv:hep- ph/9804398

    arXiv 1998

  5. [5]

    Randall and R

    L. Randall and R. Sundrum, Phys. Rev. Lett.83, 3370 (1999), arXiv:hep-ph/9905221

    Pith/arXiv arXiv 1999

  6. [6]

    Randall and R

    L. Randall and R. Sundrum, Phys. Rev. Lett.83, 4690 (1999), arXiv:hep-th/9906064

    Pith/arXiv arXiv 1999

  7. [7]

    K. R. Dienes, E. Dudas, and T. Gherghetta, Nucl. Phys. B537, 47 (1999), arXiv:hep-ph/9806292

    Pith/arXiv arXiv 1999

  8. [8]

    Kawamura, Prog

    Y. Kawamura, Prog. Theor. Phys.105, 999 (2001), arXiv:hep-ph/0012125

    Pith/arXiv arXiv 2001

  9. [9]

    L. J. Hall and Y. Nomura, Phys. Rev. D64, 055003 (2001), arXiv:hep-ph/0103125

    Pith/arXiv arXiv 2001

  10. [10]

    Grossman and M

    Y. Grossman and M. Neubert, Phys. Lett. B474, 361 (2000), arXiv:hep-ph/9912408

    Pith/arXiv arXiv 2000

  11. [11]

    Gherghetta and A

    T. Gherghetta and A. Pomarol, Nucl. Phys. B586, 141 (2000), arXiv:hep-ph/0003129

    Pith/arXiv arXiv 2000

  12. [12]

    Servant and T

    G. Servant and T. M. P. Tait, Nucl. Phys. B650, 391 (2003), arXiv:hep-ph/0206071

    Pith/arXiv arXiv 2003

  13. [13]

    Cheng, J

    H.-C. Cheng, J. L. Feng, and K. T. Matchev, Phys. Rev. Lett.89, 211301 (2002), arXiv:hep-ph/0207125

    Pith/arXiv arXiv 2002

  14. [14]

    Navaset al.(Particle Data Group), Phys

    S. Navaset al.(Particle Data Group), Phys. Rev. D110, 030001 (2024)

    2024

  15. [15]

    P. A. R. Adeet al.(BICEP, Keck), Phys. Rev. Lett.127, 151301 (2021), arXiv:2110.00483 [astro-ph.CO]

    arXiv 2021

  16. [16]

    Chen and Y

    X. Chen and Y. Wang, JCAP04, 027 (2010), arXiv:0911.3380 [hep-th]

    Pith/arXiv arXiv 2010

  17. [17]

    Baumann and D

    D. Baumann and D. Green, JCAP09, 014 (2011), arXiv:1102.5343 [hep-th]

    Pith/arXiv arXiv 2011

  18. [18]

    Chen and Y

    X. Chen and Y. Wang, JCAP09, 021 (2012), arXiv:1205.0160 [hep-th]

    Pith/arXiv arXiv 2012

  19. [19]

    Noumi, M

    T. Noumi, M. Yamaguchi, and D. Yokoyama, JHEP06, 051 (2013), arXiv:1211.1624 [hep-th]

    Pith/arXiv arXiv 2013

  20. [20]

    Arkani-Hamed and J

    N. Arkani-Hamed and J. Maldacena, (2015), arXiv:1503.08043 [hep-th]

    Pith/arXiv arXiv 2015

  21. [21]

    Green, Y

    D. Green, Y. Guo, J. Han, and B. Wallisch, JCAP05, 090 (2024), arXiv:2311.04882 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  22. [22]

    Cabass, O

    G. Cabass, O. H. E. Philcox, M. M. Ivanov, K. Akitsu, S.- F. Chen, M. Simonovi´ c, and M. Zaldarriaga, Phys. Rev. D111, 063510 (2025), arXiv:2404.01894 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  23. [23]

    Goldstein, O

    S. Goldstein, O. H. E. Philcox, J. C. Hill, and L. Hui, Phys. Rev. D110, 083516 (2024), arXiv:2407.08731 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  24. [24]

    Sohn, D.-G

    W. Sohn, D.-G. Wang, J. R. Fergusson, and E. P. S. Shellard, JCAP09, 016 (2024), arXiv:2404.07203 [astro- ph.CO]

    Pith/arXiv arXiv 2024

  25. [25]

    O. H. E. Philcox, Phys. Rev. D111, 123534 (2025), arXiv:2502.06931 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  26. [26]

    Bao, L.-T

    Y. Bao, L.-T. Wang, Z.-Z. Xianyu, and Y.-M. Zhong, Phys. Rev. D112, 103536 (2025), arXiv:2504.02931 [astro-ph.CO]

    arXiv 2025

  27. [27]

    O. H. E. Philcox, K. Zhong, and S. S. Sirletti, (2025), arXiv:2511.19179 [astro-ph.CO]

    arXiv 2025

  28. [28]

    Suman, D.-G

    P. Suman, D.-G. Wang, W. Sohn, J. R. Fergusson, and E. P. S. Shellard, (2025), arXiv:2511.17500 [astro- ph.CO]

    arXiv 2025

  29. [29]

    Suman, D.-G

    P. Suman, D.-G. Wang, W. Sohn, J. R. Fergusson, and E. P. S. Shellard, (2025), arXiv:2512.22085 [astro- ph.CO]

    arXiv 2025

  30. [30]

    Green, J

    D. Green, J. Han, and B. Wallisch, (2026), arXiv:2602.12232 [astro-ph.CO]

    arXiv 2026

  31. [31]

    Kumar, Q

    S. Kumar, Q. Lu, Z.-Z. Xianyu, and Y. Zhang, (2026), arXiv:2603.15728 [hep-ph]

    arXiv 2026

  32. [32]

    O. H. E. Philcox, (2026), arXiv:2603.17004 [astro- ph.CO]

    arXiv 2026

  33. [33]

    Kumar, Q

    S. Kumar, Q. Lu, Z.-Z. Xianyu, and Y. Zhang, (2026), arXiv:2604.07434 [hep-ph]

    Pith/arXiv arXiv 2026

  34. [34]

    Kumar and R

    S. Kumar and R. Sundrum, JHEP04, 120 (2019), arXiv:1811.11200 [hep-ph]

    Pith/arXiv arXiv 2019

  35. [35]

    Kumar and M

    S. Kumar and M. Nee, JHEP04, 035 (2026), arXiv:2510.19900 [hep-ph]

    arXiv 2026

  36. [36]

    Dvali, A

    G. Dvali, A. Gruzinov, and M. Zaldarriaga, Phys. Rev. D69, 023505 (2004), arXiv:astro-ph/0303591

    Pith/arXiv arXiv 2004

  37. [37]

    J. M. Maldacena, Adv. Theor. Math. Phys.2, 231 (1998), arXiv:hep-th/9711200

    Pith/arXiv arXiv 1998

  38. [38]

    S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B428, 105 (1998), arXiv:hep-th/9802109

    Pith/arXiv arXiv 1998

  39. [39]

    Witten, Adv

    E. Witten, Adv. Theor. Math. Phys.2, 253 (1998), arXiv:hep-th/9802150

    Pith/arXiv arXiv 1998

  40. [40]

    Arkani-Hamed, M

    N. Arkani-Hamed, M. Porrati, and L. Randall, JHEP 08, 017 (2001), arXiv:hep-th/0012148

    Pith/arXiv arXiv 2001

  41. [41]

    Rattazzi and A

    R. Rattazzi and A. Zaffaroni, JHEP04, 021 (2001), arXiv:hep-th/0012248

    Pith/arXiv arXiv 2001

  42. [42]

    Bodas, S

    A. Bodas, S. Kumar, and R. Sundrum, JHEP02, 079 (2021), arXiv:2010.04727 [hep-ph]

    Pith/arXiv arXiv 2021

  43. [43]

    A. Hook, J. Huang, and D. Racco, Phys. Rev. D101, 023519 (2020), arXiv:1908.00019 [hep-ph]

    Pith/arXiv arXiv 2020

  44. [44]

    J. You, L. Song, C. Han, H.-J. He, X. Chen, and Z.-Z. Xianyu, (2026), arXiv:2605.21419 [hep-ph]

    Pith/arXiv arXiv 2026

  45. [45]

    Wang and Z.-Z

    L.-T. Wang and Z.-Z. Xianyu, JHEP11, 082 (2020), arXiv:2004.02887 [hep-ph]

    Pith/arXiv arXiv 2020

  46. [46]

    Bodas, E

    A. Bodas, E. Broadberry, and R. Sundrum, JHEP01, 115 (2025), arXiv:2409.07524 [hep-ph]

    Pith/arXiv arXiv 2025

  47. [47]

    X. Chen, R. Ebadi, and S. Kumar, JCAP08, 083 (2022), arXiv:2205.01107 [hep-ph]

    Pith/arXiv arXiv 2022

  48. [48]

    D. H. Lyth and D. Wands, Phys. Lett. B524, 5 (2002), arXiv:hep-ph/0110002

    Pith/arXiv arXiv 2002

  49. [49]

    Enqvist and M

    K. Enqvist and M. S. Sloth, Nucl. Phys. B626, 395 (2002), arXiv:hep-ph/0109214

    Pith/arXiv arXiv 2002

  50. [50]

    Moroi and T

    T. Moroi and T. Takahashi, Phys. Lett. B522, 215 (2001), [Erratum: Phys.Lett.B 539, 303–303 (2002)], arXiv:hep-ph/0110096

    Pith/arXiv arXiv 2001

  51. [51]

    Zaldarriaga, Phys

    M. Zaldarriaga, Phys. Rev. D69, 043508 (2004), arXiv:astro-ph/0306006

    Pith/arXiv arXiv 2004

  52. [52]

    Bernardeau and J.-P

    F. Bernardeau and J.-P. Uzan, Phys. Rev. D67, 121301 (2003), arXiv:astro-ph/0209330

    Pith/arXiv arXiv 2003

  53. [53]

    Bernardeau, L

    F. Bernardeau, L. Kofman, and J.-P. Uzan, Phys. Rev. D70, 083004 (2004), arXiv:astro-ph/0403315

    Pith/arXiv arXiv 2004

  54. [54]

    W. D. Goldberger, B. Grinstein, and W. Skiba, Phys. Rev. Lett.100, 111802 (2008), arXiv:0708.1463 [hep-ph]

    Pith/arXiv arXiv 2008

  55. [55]

    Witten, Nucl

    E. Witten, Nucl. Phys. B160, 57 (1979)

    1979

  56. [56]

    Weinberg, Phys

    S. Weinberg, Phys. Rev. D72, 043514 (2005), arXiv:hep- th/0506236. 7

    arXiv 2005

  57. [57]

    Cheung, P

    C. Cheung, P. Creminelli, A. L. Fitzpatrick, J. Kaplan, and L. Senatore, JHEP03, 014 (2008), arXiv:0709.0293 [hep-th]

    Pith/arXiv arXiv 2008

  58. [58]

    Tong and Z.-Z

    X. Tong and Z.-Z. Xianyu, JHEP10, 194 (2022), arXiv:2203.06349 [hep-ph]

    Pith/arXiv arXiv 2022

  59. [59]

    Hubisz, S

    J. Hubisz, S. J. Lee, H. Li, and B. Sambasivam, Phys. Rev. D111, 023543 (2025), arXiv:2408.08951 [astro- ph.CO]

    Pith/arXiv arXiv 2025

  60. [60]

    Camphuiset al.(SPT-3G), Phys

    E. Camphuiset al.(SPT-3G), Phys. Rev. D113, 083504 (2026), arXiv:2506.20707 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  61. [61]

    W. Sohn, J. R. Fergusson, and E. P. S. Shellard, Phys. Rev. D108, 063504 (2023), arXiv:2305.14646 [astro- ph.CO]

    Pith/arXiv arXiv 2023

  62. [62]

    W. D. Goldberger and M. B. Wise, Phys. Rev. Lett.83, 4922 (1999), arXiv:hep-ph/9907447

    Pith/arXiv arXiv 1999

  63. [63]

    DeWolfe, D

    O. DeWolfe, D. Z. Freedman, S. S. Gubser, and A. Karch, Phys. Rev. D62, 046008 (2000), arXiv:hep- th/9909134

    arXiv 2000

  64. [64]

    Kaloper, Phys

    N. Kaloper, Phys. Rev. D60, 123506 (1999), arXiv:hep- th/9905210

    arXiv 1999

  65. [65]

    Nihei, Phys

    T. Nihei, Phys. Lett. B465, 81 (1999), arXiv:hep- ph/9905487

    arXiv 1999

  66. [66]

    H. B. Kim and H. D. Kim, Phys. Rev. D61, 064003 (2000), arXiv:hep-th/9909053

    Pith/arXiv arXiv 2000

  67. [67]

    Cheung and D

    T. Cheung and D. Stefanyszyn, JCAP05, 022 (2026), arXiv:2509.08888 [hep-th]

    arXiv 2026

  68. [68]

    T. S. Bunch and P. C. W. Davies, Proc. Roy. Soc. Lond. A360, 117 (1978)

    1978

  69. [69]

    Baumann, inTheoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small(2011) pp

    D. Baumann, inTheoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small(2011) pp. 523–686, arXiv:0907.5424 [hep-th]

    Pith/arXiv arXiv 2011

  70. [70]

    H. Lee, D. Baumann, and G. L. Pimentel, JHEP12, 040 (2016), arXiv:1607.03735 [hep-th]

    Pith/arXiv arXiv 2016

  71. [71]

    T. D. Newton, Annals of Mathematics51, 730 (1950)

    1950

  72. [72]

    L. H. Thomas, Annals of Mathematics42, 113 (1941)

    1941

  73. [73]

    Deser and R

    S. Deser and R. I. Nepomechie, Annals Phys.154, 396 (1984)

    1984

  74. [74]

    Garidi, (2003), arXiv:hep-th/0309104

    T. Garidi, (2003), arXiv:hep-th/0309104

    Pith/arXiv arXiv 2003

  75. [75]

    L. P. S. Singh and C. R. Hagen, Phys. Rev. D9, 898 (1974)

    1974

  76. [76]

    L. P. S. Singh and C. R. Hagen, Phys. Rev. D9, 910 (1974)

    1974

  77. [77]

    Y. M. Zinoviev, (2001), arXiv:hep-th/0108192

    Pith/arXiv arXiv 2001

  78. [78]

    Deser and A

    S. Deser and A. Waldron, Nucl. Phys. B662, 379 (2003), arXiv:hep-th/0301068

    Pith/arXiv arXiv 2003

  79. [79]

    E. P. Wigner, Annals Math.40, 149 (1939)

    1939

  80. [80]

    Deser and A

    S. Deser and A. Waldron, Phys. Rev. Lett.87, 031601 (2001), arXiv:hep-th/0102166

    Pith/arXiv arXiv 2001

Showing first 80 references.