REVIEW 4 major objections 4 minor 61 references
Aspects of massive gauge fields
T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash
Pith's one-line read Massive Yang-Mills theory has a smooth massless limit: beyond a strong-coupling scale the longitudinal modes decouple from the transverse ones, making the apparent discontinuity an artifact of perturbation theory.
desk verdict A clear proceedings summary of the author's own program on smooth massless limits, but the central mYM claim leans on an unproven Vainshtein analogy and never confronts the one-loop factor-of-1/2. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The organising device is a non-linear decomposition of the spatial vector field, $A_i = \zeta A^T_i \zeta^\dagger + (i/g)\zeta_{,i}\zeta^\dagger$, which keeps the transverse modes gauge-invariant to all orders and packages the longitudinal mode in the unitary matrix $\zeta = e^{-ig\chi}$. Solving the constraint that eliminates the temporal component and substituting back yields an action in which the longitudinal and transverse modes carry different kinetic normalisations; estimating quantum fluctuations gives $\delta\chi_L \sim 1/(mL)$, and the dominant quartic self-interaction $\sim g^2 m^2 \chi^4$ becomes of order one at $L_{\rm str} \sim g/m$. This scale coincides with the unitarity-violation scale and is where the perturbative description must be replaced by the non-linear form of the Lagrangian, which is what makes the decoupling visible.
What would settle it
Compute the full, resummed contribution of the longitudinal mode to the transverse-mode propagator in the strong-coupling regime and take the $m\to0$ limit; if the imaginary part retains the factor of $1/2$ found at one loop, the massless limit would not be smooth.
Extended reading notes
Core claim
The paper's central claim is that the massless limit of massive Yang-Mills theory is smooth, not discontinuous as perturbative calculations suggest. By decomposing the field into transverse and longitudinal modes through the non-linear unitary $\zeta = e^{-ig\chi}$, solving the temporal constraint, and estimating quantum fluctuations, the longitudinal mode is found to have fluctuation amplitude $\delta\chi_L \sim 1/(mL)$ and to generate self-interactions that grow as $g^2/(mL)^2$. At the strong-coupling scale $L_{\rm str} \sim g/m$ the perturbative expansion breaks down; the non-linear form of the action valid at shorter scales then shows the longitudinal mode decoupling from the transverse modes, so that in the $m\to0$ limit the transverse modes remain weakly coupled and match the massless theory. The residual one-loop discrepancy is thus identified as an artifact of perturbation theory, by analogy with the screening mechanism of massive gravity.
Load-bearing premise
The load-bearing premise is that beyond the strong-coupling scale the longitudinal mode truly decouples from the transverse modes; this decoupling is assumed by analogy with the screening mechanism of massive gravity rather than demonstrated, and the residual factor-of-1/2 one-loop discrepancy is not shown to vanish.
Editorial extensions
If this is right
- The smooth massless limit makes massive Yang-Mills a viable effective framework for massive non-Abelian vectors, with no discontinuity in observables as the mass is taken to zero.
- The apparent discontinuity between massive and massless predictions should be treated as a perturbative artifact, resolved by strong coupling of the longitudinal mode in the same way that massive gravity's screening mechanism resolves its own apparent discontinuity.
- For self-interacting Proca and Kalb-Ramond fields, the two theories behave oppositely: the longitudinal mode of Proca and the transverse modes of Kalb-Ramond become strongly coupled, so proposed dualities between them must fail whenever self-interactions are included.
- In Proca theory with non-minimal coupling to gravity, a Ricci-tensor coupling makes gravitational tensor modes strongly coupled at $(\beta/(M_{pl} m^2))^{1/3}$; adding a suitable disformal coupling removes this and leaves only the longitudinal mode strongly coupled.
Reading between the lines
- The common pattern across all four theories suggests a general principle: in a mass-deformed gauge theory, every degree of freedom that disappears in the massless limit becomes strongly coupled at a scale set by the mass and the coupling, and it is that strong coupling, not any linear perturbative effect, which restores the massless limit.
- The strong-coupling scale $L_{\rm str} \sim g/m$ marks the boundary of validity of the perturbative effective field theory; calculations of unitarity violation or scattering amplitudes in massive Yang-Mills should be recast in the non-linear regime, and lattice or numerical methods could test the decoupling claim directly.
- If the disformal frame is the physical one, then cosmological studies of vector inflation and gravitational production of dark photons should be formulated in that frame, which may remove the runaway modes without altering low-energy predictions.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This is a proceedings contribution, based on an invited Corfu/DSU talk, summarizing the author's recent work on massive gauge fields with mass terms added by hand. The paper has three main parts: (i) a claim that the massless limit of massive Yang-Mills theory is smooth, with longitudinal modes becoming strongly coupled at a scale L_str ~ g/m and then decoupling from the transverse modes in analogy with the Vainshtein mechanism; (ii) a comparison of self-interacting Proca and Kalb-Ramond theories, arguing that their modes behave differently and that their claimed duality may fail; and (iii) an analysis of non-minimally coupled Proca theory, where a Ricci-tensor coupling makes tensor modes strongly coupled, followed by the proposal that a disformal frame removes this problem. The text presents explicit Lagrangians, solves constraints, and derives strong-coupling scales, but it relies throughout on the author's previous papers for the detailed derivations.
Significance. If the central claim of Section 2 were rigorously established, it would overturn the vDVZ-type discontinuity in massive Yang-Mills and connect it conceptually with the Vainshtein mechanism in massive gravity. The paper is a useful concise review of a coherent research program, and it is honest about some open questions (e.g., the duality question in Section 3 is framed cautiously). The derivations are analytic and parameter-free in the sense that no free parameters are fitted; the strong-coupling scales are obtained from the stated Lagrangians. However, the most important claim — a smooth massless limit with complete decoupling of longitudinal modes — is not proven in this manuscript, and a known one-loop discrepancy from [11] is left unaddressed. The significance is therefore conditional on future work that fills this gap.
major comments (4)
- [Section 2, final paragraph (after Eq. 19)] The central claim that 'the massless limit in massive Yang-Mills theory is smooth, with longitudinal modes completely decoupling' is not established by the argument preceding it. Equations (13)-(19) show only that a particular class of classical longitudinal-induced corrections to the transverse modes, A_T^(1) ~ (g/L^3)(L/L_str), vanishes as m -> 0. This does not prove decoupling in the quantum theory. The one-loop result of [11] — an imaginary part of the transverse propagator differing from the massless case by a factor of 1/2 that survives m -> 0 — is cited in the introduction but never re-examined. If that result is correct, the standard perturbative S-matrix limit is not smooth, and a statement to the contrary requires a direct calculation or a controlled argument showing how the Vainshtein mechanism removes the discrepancy. As written, the comparison with massive gravity is an analogy, not a derivation.
- [Section 2, Eqs. (13)-(17)] The identification of the strong-coupling scale L_str ~ g/m is obtained by comparing a second-order correction to the linear term in the equation of motion for the longitudinal mode. This is a breakdown criterion for the perturbative expansion of chi, not a demonstration that the strongly coupled longitudinal sector decouples from the transverse sector for L < L_str. The text asserts that 'one can no longer expand the matrix zeta' and that 'the constraint for the temporal component can still be resolved', but the decoupling of the longitudinal and transverse sectors beyond L_str is asserted rather than shown. The paper should either provide the missing analysis or explicitly label this step as a conjecture, and it should state precisely which observables are claimed to be smooth in the massless limit.
- [Section 4, Eqs. (39)-(41)] The resolution of the tensor-mode strong-coupling problem relies on choosing the disformal frame as the physical frame. The statement 'ensuring that in this frame the coupling with matter is minimal, thus making the frame physical' is an assumption about the coupling to matter, not a consequence of the field theory defined by Eq. (27). Without a concrete prescription for matter couplings, the removal of the tensor-mode strong coupling by the field redefinition (39) could be a frame artifact rather than a physical resolution. The paper should clarify the status of this assumption and, ideally, exhibit a matter sector that picks out the disformal frame as physical.
- [Section 3, Eqs. (25)-(26) and following paragraph] The argument that the Proca/Kalb-Ramond duality 'might not hold' is based on the different strong-coupling behavior of modes in two specific self-interacting theories. This is a legitimate and interesting observation, but it does not rule out a nonperturbative duality, nor does it establish that the perturbative duality must fail in the massless limit. The conclusion is appropriately cautious in the text, but it would be strengthened by stating explicitly that the finding is a property of the quartic interactions chosen and not a general no-duality theorem.
minor comments (4)
- [Introduction, last paragraph] The section numbering is inconsistent: the text says 'Then, in section 3, we will focus on two other theories... Then, in section 3, we will focus on Proca theory in the presence of non-minimal coupling'. The second reference should be to Section 4.
- [Equation (25)] There is a typographical error in the displayed Proca Lagrangian: 'χ,μχ,μυχ,i' should read 'χ,μχ,μχ,i' with a Greek mu rather than 'mu'.
- [Section 2, around Eq. (13)] The derivation of the fluctuation estimates δχ_L ~ 1/(mL) and δA^T_L ~ 1/L is sketched in one sentence. Since these estimates carry the subsequent strong-coupling analysis, a few steps showing how the non-canonical kinetic term in Eq. (12) leads to δχ_L would improve readability.
- [Throughout] The paper contains several informal phrases and typos (e.g., 'we we are working', 'the unitarity scale' with inconsistent capitalization, 'Where g is the coupling constant'). A careful proofreading pass is needed before publication.
Circularity Check
No significant circularity: the derivations start from explicit Lagrangians and no prediction reduces to a fitted value or to a prior definition of the same quantity.
full rationale
The paper is a proceedings summary of the author's own prior work, and self-citations to [21-24] are pervasive. However, the central claims are not definitionally circular. Section 2 begins with the explicit mYM action (3), solves the constraint (9)-(10), and obtains the effective Lagrangian (12). The smooth-massless-limit claim rests on the fluctuation estimate (13), the strong-coupling scale (17), and the explicit leading correction (19), which is stated to follow from canonical redefinitions; none of these objects is fitted to the conclusion or defined as the conclusion. The step 'similarly to the Vainshtein mechanism' is an analogy, and the one-loop factor-of-1/2 result of [11] is not re-examined, so the physical claim may be incomplete; but that is a correctness risk, not circularity. In Sections 3 and 4, the strong-coupling scales are obtained by solving equations of motion (e.g., (31)-(35)) for stated Lagrangians, again without fitting. Self-citation is used to delegate technical details, but the text reproduces the main derivation chain; there is no exhibited equation that equals its own input by construction, and no fitted parameter is renamed as a prediction. Score 0 is therefore appropriate.
Assumptions & free parameters
assumptions (5)
- ad hoc to paper The nonlinear decomposition of the vector field (Eq. 6), A_i = ζ A^T_i ζ† + (i/g) ζ,i ζ†, is assumed to be valid to all orders and to make the transverse modes gauge-invariant.
- domain assumption The minimal amplitude of quantum fluctuations for canonically normalized fields is δφ ~ 1/L, yielding δχ_L ~ 1/(mL) and δA^T_L ~ 1/L (Eq. 13).
- ad hoc to paper A strongly coupled mode decouples from the remaining modes beyond its strong coupling scale, as in the Vainshtein mechanism in massive gravity.
- domain assumption Only the most important self-interactions are retained in the Proca and Kalb-Ramond analyses (Eqs. 25, 26), and the omitted ones are assumed not to change the strong-coupling scales.
- ad hoc to paper The disformal frame (Eq. 39) is taken as the physical frame, so that removing the tensor-mode strong coupling in that frame resolves the inconsistency of the Ricci-tensor coupling.
Cite this review
Pith. "Pith review of Aspects of massive gauge fields." pith.science (2026). https://pith.science/paper/QD24BFH3
@misc{pith2026250508962,
author = {Pith},
title = {Pith review of: Aspects of massive gauge fields},
year = {2026},
howpublished = {\url{https://pith.science/paper/QD24BFH3}},
note = {Machine review of arXiv:2505.08962}
}
read the original abstract
Massive gauge fields whose mass is introduced by hand form very intriguing theories. They depart from their massless counterparts by a straightforward modification. Yet, taking the limit when the same vanishes poses a non-trivial challenge. In these notes, with a focus on vector and two-form fields, we will discuss several aspects that arise when one explores the massless limit. We will study new connections among different theories, and at times raise a question about the already established ones.
Reference graph
Works this paper leans on
-
[20]
A. I. Vainshtein and I. B. Khriplovich,On the zero-mass limit and renormalizability in the theory of massive yang-mills field,Yad. Fiz.13 (1971), 198-211
work page 1971
-
[11]
H.vanDam andM.J.G.Veltman, Massiveandmassless Yang-Millsandgravitationalfields, Nucl. Phys. B22(1970), 397-411
work page 1970
-
[1]
E. Schrödinger and L. Bass,Must the photon mass be zero?, Proc. Roy. Soc. (London) A232, (1955), 1
work page 1955
-
[2]
S. L. Glashow,Partial Symmetries of Weak Interactions,Nucl. Phys.22(1961), 579-588
work page 1961
-
[3]
R. Delbourgo and S. Twisk and G. Thompson,MASSIVE YANG-MILLS THEORY: RENOR- MALIZABILITY VERSUS UNITARITY, Int. J. Mod. Phys. A3 (1988), 435
work page 1988
-
[4]
C.M.NietoandY.Rodriguez, MassiveGauge-flation, Mod.Phys.Lett.A 31,no.21,1640005 (2016) doi:10.1142/S0217732316400058 [arXiv:1602.07197 [gr-qc]]
work page Pith review arXiv 2016
-
[5]
G.’tHooft, RenormalizationofMasslessYang-MillsFields, Nucl.Phys.B 33(1971),173-199
work page 1971
-
[6]
G.’t Hooft,Renormalizable Lagrangians for Massive Yang-Mills Fields,Nucl. Phys. B35 (1971), 167-188
work page 1971
Show all 61 references
-
[7]
Komar and A
A. Komar and A. Salam,Renormalization problem for vector meson theories,Nucl. Phys.21 (1960), 624-630
1960
-
[8]
23(1961),399-429
H.UmezawaandS.Kamefuchi, Equivalencetheoremsandrenormalizationprobleminvector fieldtheory(TheYang–Millsfieldwithnon-vanishingmasses) Nucl.Phys. 23(1961),399-429
1961
-
[9]
Reiff, M.J.G
J. Reiff, M.J.G. Veltman,Massive Yang-Mills fields, Nucl. Phys. B13(1969), 545-564
1969
-
[10]
Veltman,Generalized ward identities and yang-mills fields, Nucl
M.J.G. Veltman,Generalized ward identities and yang-mills fields, Nucl. Phys. B21 (1970), 288-302
1970
-
[12]
Fierz and W
M. Fierz and W. Pauli,On relativistic wave equations for particles of arbitrary spin in an electromagnetic field,Proc. Roy. Soc. Lond. A173 (1939), 211-232
1939
-
[13]
12(1970),312
V.I.Zakharov,Linearizedgravitationtheoryandthegravitonmass JETPLett. 12(1970),312
1970
-
[14]
A. I. Vainshtein,To the problem of nonvanishing gravitation mass,Phys. Lett. B39 (1972), 393-394
1972
-
[15]
Deffayet, G
C. Deffayet, G. R. Dvali, G. Gabadadze and A. I. Vainshtein,Nonperturbative continuity in graviton mass versus perturbative discontinuity,Phys. Rev. D65 (2002), 044026 [arXiv:hep- th/0106001]
2002
-
[16]
10(2005),311-314[arXiv:astro-ph/0112246 [astro-ph]]
A.Gruzinov, Onthegravitonmass, NewAstron. 10(2005),311-314[arXiv:astro-ph/0112246 [astro-ph]]
2005 arXiv
-
[17]
D.G.BoulwareandS.Deser, Cangravitationhaveafiniterange?, Phys.Rev.D 6,3368-3382 (1972) doi:10.1103/PhysRevD.6.3368 14 Aspects of massive gauge fields Anamaria Hell
1972 doi
-
[18]
de Rham, G
C. de Rham, G. Gabadadze and A. J. Tolley,Resummation of Massive Gravity,Phys. Rev. Lett.106, 231101 (2011) doi:10.1103/PhysRevLett.106.231101 [arXiv:1011.1232 [hep-th]]
2011 arXiv
-
[19]
A. H. Chamseddine and V. Mukhanov,Mimetic Massive Gravity: Beyond Linear Approxima- tion,JHEP06 (2018), 062 [arXiv:1805.06598 [hep-th]]
2018 arXiv
-
[21]
A.Hell, OnthedualityofmassiveKalb-RamondandProcafields, JCAP01,no.01,056(2022) doi:10.1088/1475-7516/2022/01/056 [arXiv:2109.05030 [hep-th]]
2022 arXiv
-
[22]
Hell, The strong couplings of massive Yang-Mills theory, JHEP 03, 167 (2022) doi:10.1007/JHEP03(2022)167 [arXiv:2111.00017 [hep-th]]
A. Hell, The strong couplings of massive Yang-Mills theory, JHEP 03, 167 (2022) doi:10.1007/JHEP03(2022)167 [arXiv:2111.00017 [hep-th]]
2022 arXiv
-
[23]
Hell,The massless limit of massive gauge theories,doi:10.5282/edoc.30317
A. Hell,The massless limit of massive gauge theories,doi:10.5282/edoc.30317
-
[24]
A.Hell, UnveilingtheInconsistencyoftheProcaTheorywithNonminimalCouplingtoGravity, PTEP2025, no.1, 013E01 (2025) doi:10.1093/ptep/ptae188 [arXiv:2403.18673 [gr-qc]]
2025 arXiv
-
[25]
A. Hell, D. Lust and G. Zoupanos,On the degrees of freedom of R2 gravity in flat spacetime, JHEP02, 039 (2024) doi:10.1007/JHEP02(2024)039 [arXiv:2311.08216 [hep-th]]
2024 arXiv
-
[26]
G.Dvali,S.HofmannandJ.Khoury, Degravitationofthecosmologicalconstantandgraviton width, Phys. Rev. D76(2007), 084006 [arXiv:hep-th/0703027 [hep-th]]
2007 arXiv
-
[27]
A.DeFelice,L.Heisenberg,R.Kase,S.Tsujikawa,Y.l.ZhangandG.B.Zhao, Screeningfifth forcesingeneralizedProcatheories, Phys.Rev.D 93(2016)no.10,104016[arXiv:1602.00371 [gr-qc]]
2016 arXiv
-
[28]
A. H. Chamseddine and V. Mukhanov,Massive hermitian gravity, JHEP 08 (2012), 036 [arXiv:1205.5828]
2012 arXiv
-
[29]
De Felice and A
A. De Felice and A. Hell,On the cosmological degrees of freedom of Proca field with non- minimal coupling to gravity,[arXiv:2503.07454 [gr-qc]]
-
[30]
Capanelli, L
C. Capanelli, L. Jenks, E. W. Kolb and E. McDonough,Runaway Gravitational Production of Dark Photons,Phys. Rev. Lett.133, no.6, 6 (2024) doi:10.1103/PhysRevLett.133.061602 [arXiv:2403.15536 [hep-th]]
2024 arXiv
-
[31]
M. Kalb, P. Ramond,Classical Direct Interstring Action, Phys. Rev. D9 (1974) 2273-2284
1974
-
[32]
A.Proca, Surlatheorieondulatoiredeselectronspositifsetnegatifs ,J.Phys.Radium 7(1936), 347-353
1936
-
[33]
Kawai,A Dual Transformation of the Nielsen-Olesen Model, Prog
H. Kawai,A Dual Transformation of the Nielsen-Olesen Model, Prog. Theor. Phys.65(1981), 351
1981
-
[34]
B 501 (1997), 143-172 [arXiv:hep-th/9604196]
F.QuevedoandC.A.Trugenberger,Phases of antisymmetric tensor field theories,Nucl.Phys. B 501 (1997), 143-172 [arXiv:hep-th/9604196]. 15 Aspects of massive gauge fields Anamaria Hell
1997 arXiv
-
[35]
Quevedo,Duality and global symmetries, Nucl
F. Quevedo,Duality and global symmetries, Nucl. Phys. B Proc. Suppl.61 (1998), 23-41 [arXiv:hep-th/9706210]
1998 arXiv
-
[36]
Smailagic and E
A. Smailagic and E. Spallucci,The Dual phases of massless / massive Kalb-Ramond fields: Letter to the editorJ. Phys. A34(2001), L435-L440 [arXiv:hep-th/0106173]
2001 arXiv
-
[37]
Casini, R
H. Casini, R. Montemayor and L. F. Urrutia,Duality for symmetric second rank tensors: The massive case, Phys. Rev. D66(2002), 085018 [arXiv:hep-th/0206129]
2002 arXiv
-
[38]
R.D’AuriaandS.Ferrara, DyonicmassesfromconformalfieldstrengthsinDevendimensions , Phys. Lett. B606 (2005), 211-217 [arXiv:hep-th/0410051]
2005 arXiv
-
[39]
I. L. Buchbinder, E. N. Kirillova, and N. G. Pletnev,Quantum Equivalence of Massive Antisymmetric Tensor Field Models in Curved Space, Phys. Rev. D 78 (2008), 084024 [arXiv:0806.3505]
2008 arXiv
-
[40]
D.DalmaziandR.C.Santos, Spin-1dualityin 𝐷-dimensions,Phys.Rev.D 84(2011),045027 [arXiv:1105.4364]
2011 arXiv
-
[41]
Shifman and A
M. Shifman and A. Yung,Hadrons ofN = 2Supersymmetric QCD in Four Dimensions from Little String Theory, Phys. Rev. D98 (2018) no.8, 085013 [arXiv:1805.10989]
2018 arXiv
-
[42]
G. B. De Gracia,Spin jumping in the context of a QCD effective model, Int. J. Mod. Phys. A 32 (2017) no.06n07, 1750041 [arXiv:1703.05352]
2017 arXiv
-
[43]
S. M. Kuzenko and K. Turner,Effective actions for dual massive (super)𝑝-forms, JHEP01 (2021), 040 [arXiv:2009.08263]
2021 arXiv
-
[44]
Louis and A
J. Louis and A. Micu,Type 2 theories compactified on Calabi-Yau threefolds in the presence of background fluxes, Nucl. Phys. B635 (2002), 395-431 [arXiv:hep-th/0202168]
2002 arXiv
-
[45]
Y.M.Zinoviev,Ondualformulationsofmassivetensorfields ,JHEP 10(2005),075[arXiv:hep- th/0504081]
2005
-
[46]
M.Gunaydin,S.McReynoldsandM.Zagermann, TheR-mapandthecouplingofN=2tensor multiplets in 5 and 4 dimensions, JHEP01 (2006), 168
2006
-
[47]
Aurilia, P
A. Aurilia, P. Gaete, J. A. Helayël-Neto and E. Spallucci,The bosonized version of the Schwinger model in four dimensions: a blueprint for confinement?, EPL117 (2017) no.6, 61001 [arXiv:1702.07294]
2017 arXiv
-
[48]
Markou, F
C. Markou, F. J. Rudolph and A. Schmidt-May,Vierbein interactions with antisymmetric components, J. Phys. Comm.3 (2019) no.7, 075013 [arXiv:1812.07580]
2019 arXiv
-
[49]
C.Markou,F.J.RudolphandA.Schmidt-May, Gravitywithantisymmetriccomponents ,Class. Quant. Grav.36(2019) no.9, 095014 [arXiv:1811.12419]
2019 arXiv
-
[50]
Heisenberg and G
L. Heisenberg and G. Trenkler,Generalization of the 2-form interactions, JCAP05 (2020), 019 [arXiv:1908.09328]. 16 Aspects of massive gauge fields Anamaria Hell
2020 arXiv
-
[51]
Smailagic and E
A. Smailagic and E. Spallucci,Cornell potential in Kalb-Ramond scalar QED via Higgs mechanism, Phys. Lett. B803 (2020), 135304 [arXiv:2002.12750]
2020 arXiv
-
[52]
F. A. d. Barbosa,Canonical analysis of Kalb–Ramond–Proca duality,Eur. Phys. J. Plus137, no.6, 678 (2022) doi:10.1140/epjp/s13360-022-02856-8 [arXiv:2203.08867 [hep-th]]
2022 arXiv
-
[53]
TurnerandL
M.S. TurnerandL. M.Widrow, InflationProduced, Large ScaleMagneticFields, Phys.Rev. D 37, 2743 (1988) doi:10.1103/PhysRevD.37.2743
1988 doi
-
[54]
Golovnev, V
A. Golovnev, V. Mukhanov and V. Vanchurin,Vector Inflation, JCAP 06, 009 (2008) doi:10.1088/1475-7516/2008/06/009 [arXiv:0802.2068 [astro-ph]]
2008 arXiv
-
[55]
Himmetoglu, C
B. Himmetoglu, C. R. Contaldi and M. Peloso, Instability of anisotropic cosmo- logical solutions supported by vector fields, Phys. Rev. Lett. 102, 111301 (2009) doi:10.1103/PhysRevLett.102.111301 [arXiv:0809.2779 [astro-ph]]
2009 arXiv
-
[56]
Dimopoulos and M
K. Dimopoulos and M. Karciauskas,Non-minimally coupled vector curvaton,JHEP 07, 119 (2008) doi:10.1088/1126-6708/2008/07/119 [arXiv:0803.3041 [hep-th]]
2008 arXiv
-
[57]
Dimopoulos, Statistical Anisotropy and the Vector Curvaton Paradigm,Int
K. Dimopoulos, Statistical Anisotropy and the Vector Curvaton Paradigm,Int. J. Mod. Phys. D 21, 1250023 (2012) [erratum: Int. J. Mod. Phys. D 21, 1292003 (2012)] doi:10.1142/S021827181250023X [arXiv:1107.2779 [hep-ph]]
2012 arXiv
-
[58]
J. A. R. Cembranos, L. J. Garay, Á. Parra-López and J. M. Sánchez Velázquez,Vector dark matter production during inflation and reheating,JCAP 02, 013 (2024) doi:10.1088/1475- 7516/2024/02/013 [arXiv:2310.07515 [gr-qc]]
2024 arXiv
-
[59]
E. W. Kolb and A. J. Long, Completely dark photons from gravitational particle pro- duction during the inflationary era,JHEP 03, 283 (2021) doi:10.1007/JHEP03(2021)283 [arXiv:2009.03828 [astro-ph.CO]]
2021 arXiv
-
[60]
Özsoy and G
O. Özsoy and G. Tasinato,Vector dark matter, inflation, and non-minimal couplings with gravity,JCAP06,003(2024)doi:10.1088/1475-7516/2024/06/003[arXiv:2310.03862[astro- ph.CO]]
2024 arXiv
-
[61]
Grzadkowski and A
B. Grzadkowski and A. Socha,Gravitational production of massive vectors non-minimally coupled to gravity,[arXiv:2411.07222 [hep-ph]]. 17
Reviewed August 15, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.