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REVIEW 4 major objections 5 minor 50 references

Particles, Forces and the Early Universe

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Pith's one-line read This paper claims that supersymmetric preons, the no-boundary universe, and Chern-Simons quantum gravity form one scenario.

desk verdict Raitio's scenario is an honest, readable synthesis, but the preon binding mechanism is a 3D-to-4D leap that the paper never makes. read the letter →

arxiv 2507.08057 v1 pith:BUWYRBM4 submitted 2025-07-10 hep-ph gr-qc

classification hep-phgr-qc
keywords preoncompositenesssupersymmetryChern-SimonsquantumgravityHartle-Hawkingno-boundarywavefunctionbaryonasymmetryparity-violatinggravitationalwavesMaxwell-Chern-SimonspotentialbeyondtheStandardModel
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 three independent ideas—supersymmetric preons as the constituents of quarks and leptons, the Hartle-Hawking no-boundary condition for the universe's start, and a three-dimensional Chern-Simons quantum gravity—are actually parts of one scenario for the very early universe. In that scenario, the universe begins as a topological, supersymmetric preon gas bound by a Maxwell-Chern-Simons interaction, and the quarks, leptons, and dark matter of the Standard Model are composites formed from these preons. The scenario offers concrete paths beyond the Standard Model: a statistical mechanism for the observed baryon asymmetry and a prediction that the two circular polarization states of primordial gravitational waves have different intensities. If the scenario is right, the singular big bang is replaced by a smooth no-boundary beginning, and the preon sector is in principle testable through composite superpartners and gravitational-wave polarization.

What carries the argument

The load-bearing object is the gauge-invariant effective potential of Eq. (2.8), $$V_{\rm MCS}(r)=\frac{$e^{2}$}{2\pi}\left[\left(1-\frac{\$\theta$}{m_e}\right)K_0(\$\theta$ r)+\frac{1}{m_e $r^{2}$}\left(l-\frac{$e^{2}$}{2\pi\$\theta$}[1-\$\theta$ r K_1(\$\theta$ r)]\right)^2\right],$$ obtained from nonrelativistic two-particle scattering in a spontaneously broken Maxwell-Chern-Simons QED$_3$. In the paper's regime $\theta \gg m_e$ the potential is negative and Yukawa-like, giving an attractive force that overcomes Coulomb repulsion between like-charge preons. This potential is what makes bound preons possible at all; the other load-bearing elements are the Hartle-Hawking path integral (3.2) for the initial state and the Einstein-Hilbert-Chern-Simons action (4.12) whose Cotton tensor $C_{\mu\nu}$ produces parity-violating gravitational waves.

What would settle it

Compute the two-body potential obtained by embedding the Maxwell-Chern-Simons QED$_3$ action into the Einstein-Hilbert-Chern-Simons action (4.12); if the 4D potential is repulsive or admits no two-preon bound states, the binding mechanism is falsified. An observational check is a stochastic gravitational-wave background with equal intensities in the two circular polarizations, which would falsify the parity-violation prediction.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that global supersymmetry of preons, the Hartle-Hawking no-boundary wave function, and Chern-Simons quantum gravity share enough conceptual structure to form a single cosmological narrative. The paper proposes that at energies above $\Lambda_{\rm cr}\sim 10^{10}{-}10^{16}$ GeV, preons are free; below that scale they bind into Standard Model fermions and sfermions through the gauge-invariant Maxwell-Chern-Simons potential $V_{\rm MCS}(r)$ of Eq. (2.8), taken over from QED$_3$ with spontaneously broken U(1). The no-boundary state supplies the non-singular initial condition, and the Wilson-spool Chern-Simons gravity supplies an all-order calculable quantum gravity whose parity-violating term makes left- and right-handed gravitational-wave polarizations differ. The paper also claims a baryon-asymmetry mechanism: with $B=L=0$ at the preon level, hydrogen and antihydrogen atoms form in statistically fluctuating amounts, leaving a small excess after annihilation.

Load-bearing premise

Everything in the preon-binding picture depends on the assumption that the attractive force derived in a (1+2)-dimensional model, Eq. (2.8), still binds preons when the early universe is described as four-dimensional; the paper states this transfer without supplying the dimensional-reduction or embedding proof.

Editorial extensions

If this is right

  • Quarks and leptons are not elementary: each Standard Model fermion is a bound state of three preons, and each sfermion is a bound state of scalar preon superpartners.
  • The initial singularity of the big bang is replaced by a smooth Euclidean 'South Pole' start, with time behaving as a spatial dimension near the beginning.
  • The baryon asymmetry follows from a statistical fluctuation in the numbers of hydrogen and antihydrogen atoms formed from preons, leaving $n_B/n_\gamma \ll 1$.
  • Primordial gravitational waves produced by preon scattering above $\Lambda_{\rm cr}$ should have different intensities in their two polarization states, a signal potentially visible in CMB B-modes.
  • Dark matter consists of preon composites such as the $\sigma^0_R\sigma^0_G\sigma^0_B$ scalar bound state and axino-like particles, with both dark and anti-dark clumps expected.

Reading between the lines

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

  • If the 3D binding potential does not survive the embedding into 4D general relativity—a step the paper asserts rather than derives in Sec. 2.2—the preon model loses its only binding mechanism; constructing that 4D uplift of Eq. (2.8) is the decisive calculation.
  • The baryon-asymmetry mechanism is statistical, so the predicted $n_B/n_\gamma$ should depend on the number of independently formed hydrogen/antihydrogen regions; comparing that scaling with the observed value near $10^{-10}$ could distinguish this scenario from dynamical baryogenesis.
  • Because the quantum-gravity sector is three-dimensional, the scenario implicitly assumes the very early universe is effectively 3D during the topological phase; identifying the mechanism that suppresses the fourth dimension above $\Lambda_{\rm cr}$ would turn this assumption into a prediction.
  • The parity-violating gravitational-wave signal could be sought as a chiral stochastic background; a null observation of chirality at pulsar-timing or space-interferometer frequencies would constrain the Chern-Simons coupling rather than the compositeness idea.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript proposes a unified early-universe scenario in which supersymmetric preons form Standard Model fermions through a Maxwell–Chern–Simons (MCS) binding force, the universe originates from a Hartle–Hawking no-boundary state, and three-dimensional Chern–Simons quantum gravity provides parity-violating gravitational waves and a baryon asymmetry. The paper reviews the QED3 MCS potential (2.8) and asserts that the regime θ ≫ m_e makes it attractive for preons; it then transfers this (1+2)-dimensional result to the 4D early universe, referring to §4.2 for an embedding that in fact concerns only the gravitational Chern–Simons term. Sections 3 and 4 are largely recapitulations of existing literature, and §3.4 argues for baryon asymmetry at a purely statistical level without computing n_B/n_γ. The conclusions present a tentative scenario and explicitly state that many details remain to be determined.

Significance. If established, the scenario would be a notable unification of compositeness, quantum cosmology, and Chern–Simons gravity, with concrete phenomenological targets: dark-sector composite states, unequal intensities of gravitational-wave polarizations, and a non-thermal baryon asymmetry. The preon assignments in Table 2 do reproduce the SM quantum numbers of the first generation, and the paper is candid about its tentative status and about unresolved items such as SUSY breaking. However, the paper contains no parameter-free derivation, no quantitative computation of the baryon asymmetry, and no independent determination of the binding parameters; the central mechanism is currently an assertion rather than a demonstrated result. No machine-checked proofs, reproducible code, or falsifiable numerical predictions accompany the manuscript.

major comments (4)
  1. [§2.2, Eq. (2.8)] The claim that preons bind via the MCS potential rests on transferring a (1+2)-dimensional result to 3+1 dimensions. The text says the embedding is described in §4.2, but §4.2 embeds only the gravitational Chern–Simons term (Eqs. (4.7)–(4.14)); it does not embed the matter action (2.4) nor derive a 4D analogue of the potential (2.8). Because the modified Bessel function K0(θr), the nonrelativistic approximation, and the cancellation structure of (2.8) are specific to QED3, the existence of attractive preon binding in 4D at Λcr ~ 10^10–10^16 GeV is unsupported. This step is load-bearing for the entire preon sector.
  2. [§2.2, Eq. (2.8)] The sign of the potential is made attractive by choosing θ ≫ m_e, but the paper gives no independent origin or numerical values for θ and m_e in the preon context. The 'prediction' of bound preons is therefore a restatement of the chosen regime rather than a consequence of the model. A concrete test would be to specify how θ and m_e follow from the Lagrangian parameters in (2.4)–(2.7) and to compute the resulting bound-state spectrum and masses.
  3. [§3.4] The baryon asymmetry mechanism is only argued statistically. The text states that n_B/n_γ is 'thus predicted to be ≪ 1', but it does not provide a fluctuation amplitude, a causal-patch size, or an annihilation calculation, nor does it connect the result to the observed value ~6×10^-10. Without such a calculation the mechanism is not a quantitative prediction.
  4. [§3.3] The compatibility of Chern–Simons quantum gravity with the Hartle–Hawking no-boundary proposal, which is part of the paper's unification claim, is explicitly set aside: 'For now, we set aside the Kodama state, CS-HH compatibility, and other interesting problems, treating sections 3 and 4 as phenomenological tools for the present.' The cited literature (Louko, Magueijo, Alexander et al.) is relevant, but within this manuscript the claimed common conceptual basis is not developed beyond quotation.
minor comments (5)
  1. [§2.2] 'The the Einstein-Hilbert action must be added to (2.4)' contains a duplicated article; also 'Möller scattering' should be 'Møller scattering'.
  2. [§3.4] 'The rationB/nγ' is a typo for 'ratio'; the symbol n_B/n_γ should be typeset consistently throughout.
  3. [Eq. (2.8)] Please define r, θ, m_e, and the Chern–Simons coefficient; θ is also used for the would-be Goldstone boson in (2.6), which makes the notation confusing.
  4. [§4.1, Eq. (4.6)] The path-ordered exponential is written 'TrRPexp'; please use conventional notation (e.g., Tr_R P exp) and define the representation R, which is not specified in the text.
  5. [References] Reference [42] is given only as 'NANOGraph'; please supply a full collaboration name, title, and arXiv/DOI, and check reference [45] for typographical issues in the author list.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the three frameworks are imported from external prior work; the theta >> m_e choice in the preon potential is an explicit model assumption, not a fitted prediction.

full rationale

This paper does not exhibit circularity in the prohibited sense. Its three ingredients are taken from prior literature: the Maxwell-Chern-Simons potential (2.8) is imported from Belich et al. and from the author's previous preon papers [2,5] for particle content. The sign choice theta >> m_e in section 2.2 is an explicit model-building assumption, not a parameter fitted to data and renamed as a prediction; Eq. (2.8) is an external formula, and the attractive regime is a condition of the scenario, not an output derived from it. The Hartle-Hawking wave function and the Chern-Simons gravity sections are reviews of external work (Lehners, Jackiw-Pi, Alexander et al., Castro et al.), and the 'common concepts' claim is an observation that these frameworks all involve Chern-Simons structures, not a derivation of one from the other. Self-citations [2,5] supply the composite-particle correspondence and the baryon-asymmetry idea, but these are presented as prior published proposals and are externally falsifiable (for example, sparticles at the lepton/hadron mass scale 'should be detectable with present accelerator experiments'); hence they are independent support, not circular justification. The main weakness, as the paper itself asserts, is that 'the embedding of the CS action into the four-dimensional action is described in subsection 4.2', yet subsection 4.2 embeds only the gravitational Chern-Simons term, not the matter action (2.4); this missing derivation is a correctness gap or risk, not a circular step. No equation in the paper is defined in terms of its own output, and no fitted parameter is relabeled as a prediction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 2 invented entities

The central scenario rests on free parameters in the preon binding potential (θ/m_e, Λcr, preon stoichiometry), on domain assumptions inherited from prior literature (no-boundary proposal, CS quantum gravity), and on invented entities (preons, dark composites) without independent experimental handles.

free parameters (3)
  • θ/m_e ratio in MCS potential = θ >> m_e (chosen to make potential attractive)
    In Eq. (2.8), the sign of the potential depends on this ratio; the paper selects θ >> m_e in section 2.2 to obtain attraction, and this selection is what enables preon binding.
  • Λcr (preon free scale) = 10^10 - 10^16 GeV
    Chosen by order of magnitude to match the reheating/GUT scale; not derived.
  • Preon composition: number of preons per hydrogen atom = 12
    The baryon asymmetry mechanism rests on groups of 12 preons (4 m+, 4 m-, 4 m0) forming H or anti-H; this stoichiometry is introduced ad hoc from table 2.
assumptions (5)
  • ad hoc to paper Preons exist and form composite SM fermions via Chern-Simons binding
    The entire particle model assumes preons as fundamental constituents; no evidence beyond qualitative assignments in tables 1 and 2.
  • domain assumption The Hartle-Hawking no-boundary wave function describes the initial state of the universe
    Taken as given from Hartle & Hawking 1983; used to justify a singularity-free beginning.
  • domain assumption The Chern-Simons quantum gravity model of Castro et al. is correct and applicable
    Paper relies on [37,38] for the Wilson spool and finite quantum gravity; no independent check is provided in this paper.
  • domain assumption The Kodama/CSK state is physically viable despite Witten's 2003 critique
    Paper cites Randono's generalization to overcome the critique, but does not adjudicate the debate (section 3.3).
  • ad hoc to paper Baryon and lepton numbers are zero at the preon level
    Stated in section 2.1 ('In the preon model, B = L = 0') and used for the baryon asymmetry; no derivation.
invented entities (2)
  • Preons (m±, m^0_i, s±, σ^0_i, etc.)
    purpose: Fundamental constituents forming all SM and dark particles
    No predicted masses or cross sections; only composite assignments in tables 1 and 2.
  • Dark sector composites (e', γ', σ^0_R σ^0_G σ^0_B, axino)
    purpose: Dark matter candidates
    Qualitative dark matter candidates; no masses or interactions specified.

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Cite this review

Pith. "Pith review of Particles, Forces and the Early Universe." pith.science (2026). https://pith.science/paper/BUWYRBM4

@misc{pith2026250708057,
  author       = {Pith},
  title        = {Pith review of: Particles, Forces and the Early Universe},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BUWYRBM4}},
  note         = {Machine review of arXiv:2507.08057}
}
read the original abstract

This article reveals the unexpected result that three a priori distinct ideas--global supersymmetry of preons, Hartle-Hawking cosmology, and Chern-Simons quantum gravity--share common concepts that offer paths beyond the Standard Model. Differences from the MSSM are discussed.

Figures

Figures reproduced from arXiv: 2507.08057 by the authors.

Figure 1
Figure 1. Big Bang Universe and Hartle-Hawking Universe. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗

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Works this paper leans on

50 extracted references · 28 canonical work pages

  1. [1]

    The Supersymmetric Standard Model

    Pierre Fayet, The Supersymmetric Standard Model, Essays to Celebrate CERN’s 60th Anniversary, World Scientific (2016). https://doi.org/10.1142/9878. arXiv:1506.08277

  2. [2]

    doi:10.1016/j.nuclphysb.2018.04.021

    Risto Raitio, Supersymmetric preons and the standard model, Nuclear Physics B931, 283–290 (2018). doi:10.1016/j.nuclphysb.2018.04.021. arXiv:1805.03013

  3. [3]

    Belich, O

    H. Belich, O. M. Del Cima, M. M. Ferreira Jr. and J. A. Helayël-Neto, Electron-Electron Bound States in Maxwell-Chern-Simons-Proca QED3, Eur. Phys. J. B 32, 145–155 (2003).arXiv:hep-th/0212285

  4. [4]

    J. Wess, B. Zumino, Nucl. Phys. B 70 (1974) 39

  5. [5]

    doi: 10.1016/j.nuclphysb.2023.116174

    Risto Raitio, A Chern-Simons model for baryon asymme- try, Nuclear Physics B Volume 990, May 2023, 116174. doi: 10.1016/j.nuclphysb.2023.116174. arXiv:2301.10452

  6. [6]

    Peccei and Helen R

    Roberto D. Peccei and Helen R. Quinn, CP Conservation in the Presence of Pseudoparticles, Phys. Rev. Lett. 38 (25) 1440–1443 (1977)

  7. [7]

    doi: 10.1103/PhysRevLett.40.223

    Weinberg, Steven, A New Light Boson?, Physical Review Letters 40 (4) 223–226 (1978). doi: 10.1103/PhysRevLett.40.223

  8. [8]

    Physical Review Letters 40 (5): 279–282 (1978)

    Wilczek, Frank, Problem of Strong P and T Invariance in the Pres- ence of Instantons". Physical Review Letters 40 (5): 279–282 (1978). doi: 10.1103/PhysRevLett.40.279

Show all 50 references
  1. [9]

    doi: 10.48550/arXiv.1302.2164

    Anton Kapustin and Brian Willet, Wilson loops in supersymmetric Chern-Simons-matter theories and duality. doi: 10.48550/arXiv.1302.2164. arXiv:1302.2164

  2. [10]

    Belich, O.M

    H. Belich, O.M. Del Cima, M. M. Ferreira Jr and J.A. Helayël-Neto, Electron-electron attractive interaction in Maxwell-Chern-Simons QED3 at zero temperature, Int. J. Modern Phys. A16, 4939 (2001)

  3. [11]

    Ferreira Jr., Ph.D

    M.M. Ferreira Jr., Ph.D. Thesis: Investigation of Electron-Electron Bound States in the Framework of the QED3, in Portuguese, CBPF-DCP (De- cember 2001)

  4. [12]

    De Andrade, O.M

    M.A. De Andrade, O.M. Del Cima and J.A. Helayël-Neto, Il Nuovo Ci- mento 111, 1145 (1998)

  5. [13]

    Del Cima, D.H.T

    O.M. Del Cima, D.H.T. Franco, J.A. Helayël-Neto and O. Piguet, Phys. Lett. B 410, 250 (1997) and Phys. Lett. B 416, 402 (1998)

  6. [14]

    Binegar, J

    B. Binegar, J. Math. Phys. 23, 1511 (1982); S. Deser and R. Jackiw, Phys. Lett. B263, 431 (1991); R. Jackiw and V. P. Nair, Phys. Rev. D43, 1933 (1991); J. Fröhlich and P. A. Marchetti, Lett. Math. Phys. 16, 347 (1988)

  7. [15]

    Dobroliubov, D

    M.I. Dobroliubov, D. Eliezer, I.I. Kogan, G.W. Semenoff and R.J. Szabo, Mod. Phys. Lett. A 8, 2177 (1993). 17

  8. [16]

    Kogan, JETP Lett

    Ya.I. Kogan, JETP Lett. 49, 225 (1989)

  9. [17]

    doi: 10.1103/PhysRevD.28.2960

    Hartle, J.; Hawking, S., Wave function of the Universe, Physical Review D, 28 (12) 2960. doi: 10.1103/PhysRevD.28.2960

  10. [18]

    doi: 10.1016/j.physrep.2023.06.002

    Jean-Luc Lehners, Review of the No-Boundary Wave Function, Physics Reports, 1022, 1-82 (2023). doi: 10.1016/j.physrep.2023.06.002. arXiv:2303.08802

  11. [19]

    Stephon Alexander, Gabriel Herczeg and João Magueijo, Ageneralized Hartle-Hawking wave function, Classical and Quantum Gravity, 2021, Vol- ume 38, Number 9.arXiv:2012.08603

  12. [20]

    and Deser, Stanley and Misner, Charles W., The Dynamics of general relativity, Gen

    Arnowitt, Richard L. and Deser, Stanley and Misner, Charles W., The Dynamics of general relativity, Gen. Rel. Grav., 40, 1997-2027 (2008). doi: 10.1007/s10714-008-0661-1

  13. [21]

    DeWitt, Bryce S., Quantum Theory of Gravity. 1. The Canonical Theory, Phys. Rev., 160, 1148 (1967). doi: 10.1103/PhysRev.160.1113

  14. [22]

    Dewitt, C. M. and Wheeler, J. A., Battelle rencontres - 1967 lectures in mathematics and physics, Seattle, WA, USA, July 1967 (1968)

  15. [23]

    Kodama, Holomorphic wave function of the Universe, Phys

    H. Kodama, Holomorphic wave function of the Universe, Phys. Rev. D 42, 2548 (1990)

  16. [24]

    A Note on the Chern-Simons and Kodama Wave- functions

    Edward Witten (2003). "A Note on the Chern-Simons and Kodama Wave- functions". arXiv:gr-qc/0306083

  17. [25]

    Generalizing the Kodama State I: Construc- tion

    Andrew Randono (2006). "Generalizing the Kodama State I: Construc- tion". arXiv:gr-qc/0611073

  18. [26]

    Generalizing the Kodama State II: Properties and Physical Interpretation

    Andrew Randono (2006). "Generalizing the Kodama State II: Properties and Physical Interpretation". arXiv:gr-qc/0611074

  19. [27]

    S. W. MacDowell and F. Mansouri, Unified geometric theory of gravity and supergravity, Phys. Rev. Lett. 38 (1977), 739742. Erratum, ibid. 38 (1977), 1376

  20. [28]

    Derek Wise, MacDowell-Mansouri gravity and Cartan geometry, Class. Quant. Grav. 27:155010,2010. doi: 10.1088/0264-9381/27/15/155010. arXiv:gr-qc/0611154

  21. [29]

    Jorma Louko, Chern-Simons functional and the no-boundary proposal in Bianchi IX quantum cosmology, Phys. Rev. D51, 586-590 (1995). doi: https://doi.org/10.1103/PhysRevD.51.586. gr-qc/9408033

  22. [30]

    Newman, L

    E. Newman, L. Tamburino, and T. Unti, Empty-space generalization of the Schwarzschild metric, Journal of Mathematical Physics, 4(7), 915-923 (1963). doi: https://doi.org/10.1063/1.1704018

  23. [31]

    Stephon Alexander, Tatsuya Daniel, and João Magueijo, The Ashtekar Variables and a Varying Cosmological Constant from Dynamical Chern- Simons Gravity.2207.08885 18

  24. [32]

    Ashtekar, Phys

    A. Ashtekar, Phys. Rev. Lett. 57, 2244 (1986). Phys. Rev. Lett. 57. 2244

  25. [33]

    Stephon Alexander, Tatsuya Daniel, Marcell Howard, Morgane Konig, An Exact Fermionic Chern-Simons-Kodama State in Quantum Gravity, Phys. Rev. D 106, 10612 (2022). doi: 10.1103/PhysRevD.106.106012

  26. [34]

    Ichiro Oda, A Relation Between Topological Quantum Field Theory and the Kodama State (2003).hep-th/0311149

  27. [35]

    Cartas-Fuentevilla, J.F

    R. Cartas-Fuentevilla, J.F. Tlapanco-Limón, The Kodama state for topo- logical quantum field theory beyond instantons, Physics Letters B 623 (2005) 165–170. hep-th/0504120

  28. [36]

    Joao Magueijo, Equivalence of the Chern-Simons state and the Hartle- Hawking and Vilenkin wave functions, Phys. Rev. D 102, 044034 (2020) doi: https://doi.org/10.1103/PhysRevD.102.044034. 2005.03381

  29. [37]

    Fliss, and Claire Zukowski, Coupling Fields to 3D Quantum Gravity via Chern-Simons Theory, Phys

    Alejandra Castro, Ioana Coman, Jackson R. Fliss, and Claire Zukowski, Coupling Fields to 3D Quantum Gravity via Chern-Simons Theory, Phys. Rev. Lett. 131, 171602 (2023). doi: 10.1103/PhysRevLett.131.171602

  30. [38]

    Fliss, Spinning up the spool: Massive spinning fields in 3D quantum gravity, J

    Robert Bourne, Alejandra Castro, and Jackson R. Fliss, Spinning up the spool: Massive spinning fields in 3D quantum gravity, J. Phys. A: Math. Theor. 58 (2025) 025402 (42pp). https://doi.org/10.1088/1751- 8121/ad9e55. arXiv:2407.09608

  31. [39]

    Marcos Mariño, Lectures on localization and matrix models in supersym- metric Chern–Simons–matter theories, J. Phys. A: Math. Theor. 44 463001 (2011). doi: 10.1088/1751-8113/44/46/463001

  32. [40]

    Castro, I

    A. Castro, I. Coman, J. R. Fliss, and C. Zukowski, Keeping matter in the loop in dS3 quantum gravity, JHEP 07 (2023) 120.arXiv:2302.12281

  33. [41]

    83 (1999) 1506-1509

    Arthur Lue, Limin Wang, Marc Kamionkowski, Cosmological Sig- nature of New Parity-Violating Interactions, Phys.Rev.Lett. 83 (1999) 1506-1509. doi: https://doi.org/10.1103/PhysRevLett.83.1506. arXiv:astro-ph/9812088

  34. [42]

    NANOGraph

    NANOGraph. NANOGraph

  35. [44]

    https://doi.org/10.1038/35010242

    Wayne Hu, Ringing in the New Cosmology, Nature 404, 939–940 (2000). https://doi.org/10.1038/35010242

  36. [45]

    F. B. M. dos Santosa G. Rodriguesa R. de Souzaa J. S. Alcaniz, Stage IV CMB forecasts for warm inflation.2412.02696

  37. [46]

    Maximiliano Isi, Parametrizing gravitational-wave polarizations, Class. Quant. Grav. 40, 20, 203001 (2023). doi: 10.1088/1361-6382/acf28c. arXiv:2208.03372

  38. [47]

    Jackiw and S.-Y

    R. Jackiw and S.-Y. Pi, Chern-Simons Modification of General Relativ- ity, Phys. Rev. D68:104012 (2003). doi: 10.1103/PhysRevD.68.104012. gr-qc/0308071 19

  39. [48]

    Alexander and N

    S. Alexander and N. Yunes, Chern-Simons Modified General Relativity, Phys. Rept. 480 (2009) 1–55.0907.2562

  40. [49]

    Stephon Alexander and Cyril Creque-Sarbinowski, Chern-Simons Gravity and Neutrino Self-Interactions.2207.05094

  41. [50]

    Stephon Alexander, Heliudson Bernardo, Yiya Selina Li, Cooper Niu, Vac- uum Amplification of Chiral Gravitational Waves and the Stochastic Grav- itational Wave Background.2411.04233

  42. [51]

    David Grabovsky, Chern-Simons Theory in a Knotshell (2022).CS Theory 20

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