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Infrared foundations for quantum geometry. II. Catalog of all torsionlike theories including new ghost-tachyon-free cases

Will Barker1,*, Carlo Marzo2,†, and Alessandro Santoni3,4,‡

  • 1Central European Institute for Cosmology and Fundamental Physics, Institute of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, 182 00 Prague 8, Czechia
  • 2Laboratory for High Energy and Computational Physics, NICPB, Rävala 10, Tallinn 10143, Estonia
  • 3Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstrasse 8–10, A-1040 Vienna, Austria
  • 4Facultad de Física, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago, Chile

  • *Contact author: barker@fzu.cz
  • †Contact author: carlo.marzo@kbfi.ee
  • ‡Contact author: asantoni@uc.cl
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Phys. Rev. D 114, 084099 – Published 30 October, 2026

DOI: https://doi.org/10.1103/dwfl-y5bj

Abstract

The construction of consistent effective field theories in the infrared suggests that models be defined by their underlying gauge symmetries, rather than by a tuning of couplings of operators which may not be stable against radiative corrections. Adhering to this principle, we systematically derive all linear, parity-conserving models that propagate a pair-antisymmetric rank-three field on a Minkowski background. Such models are relevant not only to torsion, but to many areas in high-energy physics ranging from dual graviton formulations to string theory and higher-spin theories. Starting from the general 12-parameter quadratic action, we obtain 206 gauge-symmetric specializations, of which 22 are free of ghosts and tachyons. Following this exhaustive classification, none of the unitary models are found to propagate scalar or pseudoscalar torsion, in stark contrast to the literature focus on spin-zero torsion. Instead, all models propagate one or more vector torsion modes.

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See Also

Infrared foundations for quantum geometry. I. Catalog of totally symmetric rank-three field theories

Will Barker, Carlo Marzo, and Alessandro Santoni
Phys. Rev. D 114, 084098 (2026)

Article Text

References (201)

  1. W. Barker, C. Marzo, and A. Santoni, Can metric-affine gravity be saved?, Phys. Rev. D 112, 044032 (2025).
  2. W. Barker, C. Marzo, and A. Santoni, preceding paper, Infrared foundations for quantum geometry. I. Catalog of totally symmetric rank-three field theories, Phys. Rev. D 114, 084098 (2026).
  3. G. Barnich and M. Henneaux, Consistent couplings between fields with a gauge freedom and deformations of the master equation, Phys. Lett. B 311, 123 (1993).
  4. H. Georgi, Effective field theory, Annu. Rev. Nucl. Part. Sci. 43, 209 (1993).
  5. C. P. Burgess, Introduction to effective field theory, Annu. Rev. Nucl. Part. Sci. 57, 329 (2007).
  6. J. Bijnens, Chiral perturbation theory beyond one loop, Prog. Part. Nucl. Phys. 58, 521 (2007).
  7. A. V. Manohar, Effective field theories, Lect. Notes Phys. 479, 311 (1997).
  8. D. B. Kaplan, Effective field theories, in 7th Summer School in Nuclear Physics Symmetries (1995), .
  9. A. Pich, Chiral perturbation theory, Rep. Prog. Phys. 58, 563 (1995).
  10. G. Ecker, Chiral perturbation theory, Prog. Part. Nucl. Phys. 35, 1 (1995).
  11. A. Dobado and M. J. Herrero, Phenomenological Lagrangian approach to the symmetry breaking sector of the standard model, Phys. Lett. B 228, 495 (1989).
  12. A. Dobado, M. J. Herrero, and T. N. Truong, Study of the strongly interacting Higgs sector, Phys. Lett. B 235, 129 (1990).
  13. S. Weinberg, Phenomenological Lagrangians, Physica A (Amsterdam) 96, 327 (1979).
  14. S. R. Coleman, J. Wess, and B. Zumino, Structure of phenomenological Lagrangians. 1., Phys. Rev. 177, 2239 (1969).
  15. C. G. Callan, Jr., S. R. Coleman, J. Wess, and B. Zumino, Structure of phenomenological Lagrangians. 2., Phys. Rev. 177, 2247 (1969).
  16. A. Danehkar, Electric-magnetic duality in gravity and higher-spin fields, Front. Phys. 6, 146 (2018).
  17. T. L. Curtright, Generalized gauge fields, Phys. Lett. 165B, 304 (1985).
  18. S. Deser, W. Siegel, and P. K. Townsend, Higher rank representations of lower spin, Nucl. Phys. B184, 333 (1981).
  19. C. M. Hull, Duality in gravity and higher-spin gauge fields, J. High Energy Phys. 09 (2001) 027.
  20. T. L. Curtright and P. G. O. Freund, Massive dual fields, Nucl. Phys. B172, 413 (1980).
  21. C. Hull, U. Lindström, and M. L. Velásquez Cotini Hutt, Gauge-invariant charges of the dual graviton, J. High Energy Phys. 02 (2025) 198.
  22. C. Bunster, M. Henneaux, and S. Hörtner, Gravitational electric-magnetic duality, gauge invariance and twisted self-duality, J. Phys. A 46, 214016 (2013).
  23. C. Bunster, S. Cnockaert, M. Henneaux, and R. Portugués, Monopoles for gravitation and for higher spin fields, Phys. Rev. D 73, 105014 (2006).
  24. C. Lanczos, The splitting of the Riemann tensor, Rev. Mod. Phys. 34, 379 (1962).
  25. A. Sagnotti and M. Tsulaia, On higher spins and the tensionless limit of string theory, Nucl. Phys. B682, 83 (2004).
  26. A. Campoleoni, D. Francia, J. Mourad, and A. Sagnotti, Unconstrained higher spins of mixed symmetry. I. Bose fields, Nucl. Phys. B815, 289 (2009).
  27. X. Bekaert and N. Boulanger, On geometric equations and duality for free higher spins, Phys. Lett. B 561, 183 (2003).
  28. P. C. West, E11 and m-theory, Classical Quantum Gravity 18, 4443 (2001).
  29. A. Einstein, Die feldgleichungen der gravitation, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 18, 844 (1915).
  30. R. Utiyama, Invariant theoretical interpretation of interaction, Phys. Rev. 101, 1597 (1956).
  31. T. W. B. Kibble, Lorentz invariance and the gravitational field, J. Math. Phys. (N.Y.) 2, 212 (1961).
  32. D. W. Sciama, On the analogy between charge and spin in general relativity, in Recent Developments in General Relativity (Pergamon Press, Oxford, 1962), p. 415.
  33. Y.-C. Lin, M. P. Hobson, and A. N. Lasenby, Ghost and tachyon free Poincaré gauge theories: A systematic approach, Phys. Rev. D 99, 064001 (2019).
  34. Y.-C. Lin, M. P. Hobson, and A. N. Lasenby, Power-counting renormalizable, ghost-and-tachyon-free Poincaré gauge theories, Phys. Rev. D 101, 064038 (2020).
  35. R. Percacci and E. Sezgin, New class of ghost- and tachyon-free metric affine gravities, Phys. Rev. D 101, 084040 (2020); 11, 109902(E) (2025).
  36. W. Barker, C. Marzo, and C. Rigouzzo, PSALTer: Particle spectrum for any tensor Lagrangian, Phys. Rev. D 112, 016018 (2025).
  37. W. Barker, G. K. Karananas, and H. Tu, The particle spectra of parity-violating theories: A less radical approach and an upgrade of PSALTer, Phys. Rev. D 112, 084041 (2025).
  38. J. Gasser and H. Leutwyler, Chiral perturbation theory to one loop, Ann. Phys. (N.Y.) 158, 142 (1984).
  39. É. Cartan, Sur une généralisation de la notion de courbure de Riemann et les espaces à torsion, C. R, Acad. Sc. Paris 174, 593 (1922).
  40. É. Cartan, Sur les variétés à connexion affine et la théorie de la relativité généralisée (première partie), in Annales scientifiques de l’École normale supérieure (Gauthier-Villars, Paris, 1923), Vol. 40, pp. 325–412.
  41. É. Cartan, Sur les variétés à connexion affine, et la théorie de la relativité généralisée (première partie) (suite), in Annales scientifiques de l’École Normale Supérieure (Gauthier-Villars, Paris, 1924), Vol. 41, pp. 1–25.
  42. É. Cartan, Sur les variétés à connexion affine, et la théorie de la relativité généralisée (deuxième partie), in Annales scientifiques de l’École normale supérieure (Gauthier-Villars, Paris, 1925), Vol. 42, pp. 17–88.
  43. A. Einstein, Einheitliche Feldtheorie von Gravitation und Elektrizität, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 22, 414 (1925).
  44. A. Einstein, Riemanngeometrie mit aufrechterhaltung des begriffes des Fern-Parallelismus, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 17, 217 (1928).
  45. A. Einstein, Neue Möglichkeit für eine einheitliche Feldtheorie von Gravitation und Elektrizität, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 18, 224 (1928).
  46. V. I. Rodichev, Twisted space and nonlinear field equations, Zh. Eksp. Teor. Fiz. 40, 1469 (1961).
  47. L. Freidel, D. Minic, and T. Takeuchi, Quantum gravity, torsion, parity violation and all that, Phys. Rev. D 72, 104002 (2005).
  48. S. Alexandrov, Immirzi parameter and fermions with non-minimal coupling, Classical Quantum Gravity 25, 145012 (2008).
  49. M. Shaposhnikov, A. Shkerin, I. Timiryasov, and S. Zell, Einstein-Cartan gravity, matter, and scale-invariant generalization, J. High Energy Phys. 10 (2020) 177.
  50. G. K. Karananas, M. Shaposhnikov, A. Shkerin, and S. Zell, Matter matters in Einstein-Cartan gravity, Phys. Rev. D 104, 064036 (2021).
  51. C. Rigouzzo and S. Zell, Coupling metric-affine gravity to the standard model and dark matter fermions, Phys. Rev. D 108, 124067 (2023).
  52. F. Bauer and D. A. Demir, Inflation with non-minimal coupling: Metric versus palatini formulations, Phys. Lett. B 665, 222 (2008).
  53. N. J. Poplawski, Matter-antimatter asymmetry and dark matter from torsion, Phys. Rev. D 83, 084033 (2011).
  54. D. Diakonov, A. G. Tumanov, and A. A. Vladimirov, Low-energy general relativity with torsion: A systematic derivative expansion, Phys. Rev. D 84, 124042 (2011).
  55. I. B. Khriplovich, Gravitational four-fermion interaction on the Planck scale, Phys. Lett. B 709, 111 (2012).
  56. J. a. Magueijo, T. G. Zlosnik, and T. W. B. Kibble, Cosmology with a spin, Phys. Rev. D 87, 063504 (2013).
  57. I. B. Khriplovich and A. S. Rudenko, Gravitational four-fermion interaction and dynamics of the early universe, J. High Energy Phys. 11 (2013) 174.
  58. T. Markkanen, T. Tenkanen, V. Vaskonen, and H. Veermäe, Quantum corrections to quartic inflation with a non-minimal coupling: Metric vs Palatini, J. Cosmol. Astropart. Phys. 03 (2018) 029.
  59. P. Carrilho, D. Mulryne, J. Ronayne, and T. Tenkanen, Attractor behaviour in multifield inflation, J. Cosmol. Astropart. Phys. 06 (2018) 032.
  60. V.-M. Enckell, K. Enqvist, S. Rasanen, and L.-P. Wahlman, Inflation with R2 term in the Palatini formalism, J. Cosmol. Astropart. Phys. 02 (2019) 022.
  61. S. Rasanen and E. Tomberg, Planck scale black hole dark matter from Higgs inflation, J. Cosmol. Astropart. Phys. 01 (2019) 038.
  62. J. Beltrán Jiménez and F. J. Maldonado Torralba, Revisiting the stability of quadratic Poincaré gauge gravity, Eur. Phys. J. C 80, 611 (2020).
  63. J. Rubio and E. S. Tomberg, Preheating in Palatini Higgs inflation, J. Cosmol. Astropart. Phys. 04 (2019) 021.
  64. M. Shaposhnikov, A. Shkerin, and S. Zell, Standard model meets gravity: Electroweak symmetry breaking and inflation, Phys. Rev. D 103, 033006 (2021).
  65. G. K. Karananas, M. Michel, and J. Rubio, One residue to rule them all: Electroweak symmetry breaking, inflation and field-space geometry, Phys. Lett. B 811, 135876 (2020).
  66. M. Långvik, J.-M. Ojanperä, S. Raatikainen, and S. Rasanen, Higgs inflation with the Holst and the Nieh–Yan term, Phys. Rev. D 103, 083514 (2021).
  67. M. Shaposhnikov, A. Shkerin, I. Timiryasov, and S. Zell, Higgs inflation in Einstein-Cartan gravity, J. Cosmol. Astropart. Phys. 02 (2021) 008; 10 (2021) E01.
  68. Y. Mikura, Y. Tada, and S. Yokoyama, Conformal inflation in the metric-affine geometry, Europhys. Lett. 132, 39001 (2020).
  69. M. Shaposhnikov, A. Shkerin, I. Timiryasov, and S. Zell, Einstein-Cartan portal to dark matter, Phys. Rev. Lett. 126, 161301 (2021); 127, 169901(E) (2021).
  70. M. Kubota, K.-Y. Oda, K. Shimada, and M. Yamaguchi, Cosmological perturbations in Palatini formalism, J. Cosmol. Astropart. Phys. 03 (2021) 006.
  71. V.-M. Enckell, S. Nurmi, S. Räsänen, and E. Tomberg, Critical point Higgs inflation in the palatini formulation, J. High Energy Phys. 04 (2021) 059.
  72. D. Iosifidis and L. Ravera, The cosmology of quadratic torsionful gravity, Eur. Phys. J. C 81, 736 (2021).
  73. F. Bombacigno, S. Boudet, G. J. Olmo, and G. Montani, Big bounce and future time singularity resolution in Bianchi I cosmologies: The projective invariant Nieh-Yan case, Phys. Rev. D 103, 124031 (2021).
  74. A. Racioppi, J. Rajasalu, and K. Selke, Multiple point criticality principle and Coleman-Weinberg inflation, J. High Energy Phys. 06 (2022) 107.
  75. D. Y. Cheong, S. M. Lee, and S. C. Park, Reheating in models with non-minimal coupling in metric and Palatini formalisms, J. Cosmol. Astropart. Phys. 02 (2022) 029.
  76. C. Dioguardi, A. Racioppi, and E. Tomberg, Slow-roll inflation in Palatini F(R) gravity, J. High Energy Phys. 06 (2022) 106.
  77. M. Piani and J. Rubio, Higgs-dilaton inflation in Einstein-Cartan gravity, J. Cosmol. Astropart. Phys. 05 (2022) 009.
  78. F. Dux, A. Florio, J. Klarić, A. Shkerin, and I. Timiryasov, Preheating in palatini Higgs inflation on the lattice, J. Cosmol. Astropart. Phys. 09 (2022) 015.
  79. C. Rigouzzo and S. Zell, Coupling metric-affine gravity to a Higgs-like scalar field, Phys. Rev. D 106, 024015 (2022).
  80. G. Pradisi and A. Salvio, (In)equivalence of metric-affine and metric effective field theories, Eur. Phys. J. C 82, 840 (2022).
  81. A. Salvio, Inflating and reheating the universe with an independent affine connection, Phys. Rev. D 106, 103510 (2022).
  82. S. Rasanen and Y. Verbin, Palatini formulation for gauge theory: Implications for slow-roll inflation, Open J. Astophysics 6 (2023).
  83. I. D. Gialamas and K. Tamvakis, Inflation in metric-affine quadratic gravity, J. Cosmol. Astropart. Phys. 03 (2023) 042.
  84. I. D. Gialamas and H. Veermäe, Electroweak vacuum decay in metric-affine gravity, Phys. Lett. B 844, 138109 (2023).
  85. I. D. Gialamas, A. Karam, T. D. Pappas, and E. Tomberg, Implications of Palatini gravity for inflation and beyond, Int. J. Geom. Methods Mod. Phys. 20, 2330007 (2023).
  86. M. Piani and J. Rubio, Preheating in Einstein-Cartan Higgs inflation: Oscillon formation, J. Cosmol. Astropart. Phys. 12 (2023) 002.
  87. A. Poisson, I. Timiryasov, and S. Zell, Critical points in Palatini Higgs inflation with small non-minimal coupling, J. High Energy Phys. 03 (2024) 130.
  88. W. Barker and S. Zell, Einstein-Proca theory from the Einstein-Cartan formulation, Phys. Rev. D 109, 024007 (2024).
  89. G. K. Karananas, M. Shaposhnikov, and S. Zell, Scale invariant Einstein-Cartan gravity and flat space conformal symmetry, J. High Energy Phys. 11 (2023) 171.
  90. R. Martini, G. Paci, and D. Sauro, Radiative corrections to the R and R2 invariants from torsion fluctuations on maximally symmetric spaces, J. High Energy Phys. 12 (2024) 138.
  91. M. He, M. Hong, and K. Mukaida, Starobinsky inflation and beyond in Einstein-Cartan gravity, J. Cosmol. Astropart. Phys. 05 (2024) 107.
  92. F. Bauer and D. A. Demir, Higgs-Palatini inflation and unitarity, Phys. Lett. B 698, 425 (2011).
  93. M. Shaposhnikov, A. Shkerin, and S. Zell, Quantum effects in Palatini Higgs inflation, J. Cosmol. Astropart. Phys. 07 (2020) 064.
  94. K. Hayashi and T. Nakano, Extended translation invariance and associated gauge fields, Prog. Theor. Phys. 38, 491 (1967).
  95. K. Hayashi and T. Shirafuji, Gravity from poincare gauge theory of the fundamental particles. 4. Mass and energy of particle spectrum, Prog. Theor. Phys. 64, 2222 (1980).
  96. H.-j. Yo and J. M. Nester, Hamiltonian analysis of poincare gauge theory scalar modes, Int. J. Mod. Phys. D 08, 459 (1999).
  97. H.-J. Yo and J. M. Nester, Hamiltonian analysis of poincare gauge theory: Higher spin modes, Int. J. Mod. Phys. D 11, 747 (2002).
  98. D. Puetzfeld, Status of non-Riemannian cosmology, New Astron. Rev. 49, 59 (2005).
  99. E. Sezgin and P. van Nieuwenhuizen, New ghost free gravity Lagrangians with propagating torsion, Phys. Rev. D 21, 3269 (1980).
  100. E. Sezgin, Class of ghost free gravity Lagrangians with massive or massless propagating torsion, Phys. Rev. D 24, 1677 (1981).
  101. M. Blagojevic and I. A. Nikolic, Hamiltonian dynamics of poincare gauge theory: General structure in the time gauge, Phys. Rev. D 28, 2455 (1983).
  102. M. Blagojevic and M. Vasilic, Extra gauge symmetries in a weak field approximation of an R+T**2+R**2 theory of gravity, Phys. Rev. D 35, 3748 (1987).
  103. R. Kuhfuss and J. Nitsch, Propagating modes in gauge field theories of gravity, Gen. Relativ. Gravit. 18, 1207 (1986).
  104. M. Blagojevic, Gravitation and Gauge Symmetries (CRC Press, Bristol and Philadelphia, 2002).
  105. H.-J. Yo and J. M. Nester, Dynamic scalar torsion and an oscillating universe, Mod. Phys. Lett. A 22, 2057 (2007).
  106. K.-F. Shie, J. M. Nester, and H.-J. Yo, Torsion cosmology and the accelerating universe, Phys. Rev. D 78, 023522 (2008).
  107. V. P. Nair, S. Randjbar-Daemi, and V. Rubakov, Massive spin-2 fields of geometric origin in curved spacetimes, Phys. Rev. D 80, 104031 (2009).
  108. V. Nikiforova, S. Randjbar-Daemi, and V. Rubakov, Infrared modified gravity with dynamical torsion, Phys. Rev. D 80, 124050 (2009).
  109. H. Chen, F.-H. Ho, J. M. Nester, C.-H. Wang, and H.-J. Yo, Cosmological dynamics with propagating Lorentz connection modes of spin zero, J. Cosmol. Astropart. Phys. 10 (2009) 027.
  110. W.-T. Ni, Searches for the role of spin and polarization in gravity, Rep. Prog. Phys. 73, 056901 (2010).
  111. P. Baekler, F. W. Hehl, and J. M. Nester, Poincare gauge theory of gravity: Friedman cosmology with even and odd parity modes. Analytic part, Phys. Rev. D 83, 024001 (2011).
  112. F.-H. Ho and J. M. Nester, Poincaré gauge theory with even and odd parity dynamic connection modes: Isotropic Bianchi cosmological models, J. Phys. Conf. Ser. 330, 012005 (2011).
  113. F.-H. Ho and J. M. Nester, Poincaré gauge theory with coupled even and odd parity dynamic spin-0 modes: Dynamic equations for isotropic Bianchi cosmologies, Ann. Phys. (Berlin) 524, 97 (2012).
  114. Y. C. Ong, K. Izumi, J. M. Nester, and P. Chen, Problems with propagation and time evolution in f(T) gravity, Phys. Rev. D 88, 024019 (2013).
  115. D. Puetzfeld and Y. N. Obukhov, Prospects of detecting spacetime torsion, Int. J. Mod. Phys. D 23, 1442004 (2014).
  116. G. K. Karananas, The particle spectrum of parity-violating Poincaré gravitational theory, Classical Quantum Gravity 32, 055012 (2015).
  117. W.-T. Ni, Searches for the role of spin and polarization in gravity: A five-year update, Int. J. Mod. Phys. Conf. Ser. 40, 1660010 (2016).
  118. F.-H. Ho, H. Chen, J. M. Nester, and H.-J. Yo, General Poincaré gauge theory cosmology, Chin. J. Phys. (Taipei) 53, 110109 (2015).
  119. G. K. Karananas, Poincaré, scale and conformal symmetries gauge perspective and cosmological ramifications, Ph.D. thesis, Ecole Polytechnique, Lausanne, 2016, arXiv:1608.08451.
  120. Y. N. Obukhov, Gravitational waves in Poincaré gauge gravity theory, Phys. Rev. D 95, 084028 (2017).
  121. M. Blagojević, B. Cvetković, and Y. N. Obukhov, Generalized plane waves in Poincaré gauge theory of gravity, Phys. Rev. D 96, 064031 (2017).
  122. M. Blagojević and B. Cvetković, General Poincaré gauge theory: Hamiltonian structure and particle spectrum, Phys. Rev. D 98, 024014 (2018).
  123. H.-H. Tseng, Gravitational theories with torsion, Ph.D. thesis, Taiwan, Natl. Tsing Hua U., 2018, arXiv:1812.00314.
  124. J. Beltrán Jiménez and A. Delhom, Ghosts in metric-affine higher order curvature gravity, Eur. Phys. J. C 79, 656 (2019).
  125. H. Zhang and L. Xu, Late-time acceleration and inflation in a Poincaré gauge cosmological model, J. Cosmol. Astropart. Phys. 09 (2019) 050.
  126. K. Aoki and K. Shimada, Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?, Phys. Rev. D 100, 044037 (2019).
  127. H. Zhang and L. Xu, Inflation in the parity-conserving Poincaré gauge cosmology, J. Cosmol. Astropart. Phys. 10 (2020) 003.
  128. J. Beltrán Jiménez and F. J. Maldonado Torralba, Revisiting the stability of quadratic Poincaré gauge gravity, Eur. Phys. J. C 80, 611 (2020).
  129. R. Percacci and E. Sezgin, New class of ghost- and tachyon-free metric affine gravities, Phys. Rev. D 101, 084040 (2020).
  130. W. E. V. Barker, A. N. Lasenby, M. P. Hobson, and W. J. Handley, Systematic study of background cosmology in unitary Poincaré gauge theories with application to emergent dark radiation and H0 tension, Phys. Rev. D 102, 024048 (2020).
  131. J. Beltrán Jiménez and A. Delhom, Instabilities in metric-affine theories of gravity with higher order curvature terms, Eur. Phys. J. C 80, 585 (2020).
  132. F. J. Maldonado Torralba, New effective theories of gravitation and their phenomenological consequences, Ph.D. thesis, Cape Town U., Dept. Math., 2020, arXiv:2101.11523.
  133. W. E. V. Barker, A. N. Lasenby, M. P. Hobson, and W. J. Handley, Nonlinear Hamiltonian analysis of new quadratic torsion theories: Cases with curvature-free constraints, Phys. Rev. D 104, 084036 (2021).
  134. C. Marzo, Ghost and tachyon free propagation up to spin 3 in Lorentz invariant field theories, Phys. Rev. D 105, 065017 (2022).
  135. C. Marzo, Radiatively stable ghost and tachyon freedom in metric affine gravity, Phys. Rev. D 106, 024045 (2022).
  136. A. de la Cruz Dombriz, F. J. Maldonado Torralba, and D. F. Mota, Dark matter candidate from torsion, Phys. Lett. B 834, 137488 (2022).
  137. A. Baldazzi, O. Melichev, and R. Percacci, Metric-affine gravity as an effective field theory, Ann. Phys. (Amsterdam) 438, 168757 (2022).
  138. J. Annala and S. Rasanen, Stability of non-degenerate Ricci-type Palatini theories, J. Cosmol. Astropart. Phys. 04 (2023) 014; 08 (2023) E02; 05 (2025) E01.
  139. Y. Mikura, V. Naso, and R. Percacci, Some simple theories of gravity with propagating torsion, Phys. Rev. D 109, 104071 (2024).
  140. Y. Mikura and R. Percacci, Some simple theories of gravity with propagating nonmetricity, Eur. Phys. J. C 85, 377 (2025).
  141. W. Barker and C. Marzo, Particle spectra of general Ricci-type Palatini or metric-affine theories, Phys. Rev. D 109, 104017 (2024).
  142. G. K. Karananas, M. Shaposhnikov, and S. Zell, Weyl-invariant Einstein-Cartan gravity: Unifying the strong CP and hierarchy puzzles, J. High Energy Phys. 11 (2024) 146.
  143. C. Møller, Conservation law and absolute parallelism in general relativity, K. Dan. Vidensk. Selsk. Mat. Fys. Skr. 1, 1 (1961).
  144. C. Pellegrini and J. Plebanski, Tetrad fields and gravitational fields, K. Dan. Vidensk. Selsk. Mat. Fys. Skr. 2, 1 (1963).
  145. Y. M. Cho, Einstein Lagrangian as the translational Yang-Mills Lagrangian, Phys. Rev. D 14, 2521 (1976).
  146. K. Hayashi and T. Shirafuji, New general relativity, Phys. Rev. D 19, 3524 (1979); 24, 3312(A) (1982).
  147. A. Dimakis, The initial value problem of the poincare gauge theory in vacuum. 1: Second order formalism, Ann. Inst. Henri Poincare Phys. Theor. 51, 371 (1989).
  148. A. Dimakis, The initial value problem of the poincare gauge theory in vacuum. 1: First order formalism, Ann. Inst. Henri Poincare Phys. Theor. 51, 389 (1989).
  149. J. Lemke, Shock waves in the poincare gauge theory of gravitation, Phys. Lett. A 143, 13 (1990).
  150. R. D. Hecht, J. Lemke, and R. P. Wallner, Tachyonic torsion shock waves in poincare gauge theory, Phys. Lett. A 151, 12 (1990).
  151. R. D. Hecht, J. Lemke, and R. P. Wallner, Can Poincare gauge theory be saved?, Phys. Rev. D 44, 2442 (1991).
  152. N. Afshordi, D. J. H. Chung, and G. Geshnizjani, Cuscuton: A causal field theory with an infinite speed of sound, Phys. Rev. D 75, 083513 (2007).
  153. J. Magueijo, Bimetric varying speed of light theories and primordial fluctuations, Phys. Rev. D 79, 043525 (2009).
  154. C. Charmousis and A. Padilla, The instability of vacua in Gauss-Bonnet gravity, J. High Energy Phys. 12 (2008) 038.
  155. C. Charmousis, G. Niz, A. Padilla, and P. M. Saffin, Strong coupling in Horava gravity, J. High Energy Phys. 08 (2009) 070.
  156. A. Papazoglou and T. P. Sotiriou, Strong coupling in extended Horava-Lifshitz gravity, Phys. Lett. B 685, 197 (2010).
  157. D. Baumann, L. Senatore, and M. Zaldarriaga, Scale-invariance and the strong coupling problem, J. Cosmol. Astropart. Phys. 05 (2011) 004.
  158. G. D’Amico, C. de Rham, S. Dubovsky, G. Gabadadze, D. Pirtskhalava, and A. J. Tolley, Massive cosmologies, Phys. Rev. D 84, 124046 (2011).
  159. A. E. Gumrukcuoglu, C. Lin, and S. Mukohyama, Anisotropic Friedmann-Robertson-Walker universe from nonlinear massive gravity, Phys. Lett. B 717, 295 (2012).
  160. A. Wang, Hořava gravity at a Lifshitz point: A progress report, Int. J. Mod. Phys. D 26, 1730014 (2017).
  161. C. Mazuet, S. Mukohyama, and M. S. Volkov, Anisotropic deformations of spatially open cosmology in massive gravity theory, J. Cosmol. Astropart. Phys. 04 (2017) 039.
  162. J. Beltrán Jiménez and A. Jiménez-Cano, On the strong coupling of Einsteinian cubic gravity and its generalisations, J. Cosmol. Astropart. Phys. 01 (2021) 069.
  163. A. Jiménez Cano, Metric-affine gauge theories of gravity. Foundations and new insights, Ph.D. thesis, Granada U., Theor. Phys. Astrophys., 2021, arXiv:2201.12847.
  164. W. E. V. Barker, Supercomputers against strong coupling in gravity with curvature and torsion, Eur. Phys. J. C 83, 228 (2023).
  165. A. Delhom, A. Jiménez-Cano, and F. J. Maldonado Torralba, Instabilities in Field Theory: A Primer with Applications in Modified Gravity (Springer, New York, 2022).
  166. G. K. Karananas, Particle content of (scalar curvature)2 gravities revisited, Phys. Rev. D 111, 044068 (2025).
  167. A. I. Vainshtein, To the problem of nonvanishing gravitation mass, Phys. Lett. 39B, 393 (1972).
  168. C. Deffayet, G. R. Dvali, G. Gabadadze, and A. I. Vainshtein, Nonperturbative continuity in graviton mass versus perturbative discontinuity, Phys. Rev. D 65, 044026 (2002).
  169. C. Deffayet and J.-W. Rombouts, Ghosts, strong coupling and accidental symmetries in massive gravity, Phys. Rev. D 72, 044003 (2005).
  170. C. de Rham, Massive gravity, Living Rev. Relativity 17, 7 (2014).
  171. S. Deser, M. Sandora, A. Waldron, and G. Zahariade, Covariant constraints for generic massive gravity and analysis of its characteristics, Phys. Rev. D 90, 104043 (2014).
  172. G. Velo and D. Zwanziger, Noncausality and other defects of interaction Lagrangians for particles with spin one and higher, Phys. Rev. 188, 2218 (1969).
  173. C. Aragone and S. Deser, Constraints on gravitationally coupled tensor fields, Nuovo Cimento A 3, 709 (1971).
  174. W.-H. Cheng, D.-C. Chern, and J. M. Nester, Canonical analysis of the one parameter teleparallel theory, Phys. Rev. D 38, 2656 (1988).
  175. R. D. Hecht, J. M. Nester, and V. V. Zhytnikov, Some poincare gauge theory Lagrangians with well posed initial value problems, Phys. Lett. A 222, 37 (1996).
  176. H. Chen, J. M. Nester, and H.-J. Yo, Acausal PGT modes and the nonlinear constraint effect, Acta Phys. Pol. B 29, 961 (1998).
  177. D. Blixt, M. Hohmann, and C. Pfeifer, Hamiltonian and primary constraints of new general relativity, Phys. Rev. D 99, 084025 (2019).
  178. D. Blixt, M. Hohmann, M. Krššák, and C. Pfeifer, Hamiltonian analysis in new general relativity, in 15th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories (2019), arXiv:1905.11919.
  179. D. Blixt, M.-J. Guzmán, M. Hohmann, and C. Pfeifer, Review of the Hamiltonian analysis in teleparallel gravity, Int. J. Geom. Methods Mod. Phys. 18, 2130005 (2021).
  180. K. Krasnov and E. Mitsou, Pure Lorentz spin connection theories and uniqueness of general relativity, Classical Quantum Gravity 38, 205009 (2021).
  181. S. Bahamonde, K. F. Dialektopoulos, C. Escamilla-Rivera, G. Farrugia, V. Gakis, M. Hendry, M. Hohmann, J. Levi Said, J. Mifsud, and E. Di Valentino, Teleparallel gravity: From theory to cosmology, Rep. Prog. Phys. 86, 026901 (2023).
  182. M. Blagojević and B. Cvetković, Three-dimensional gravity with propagating torsion: Hamiltonian structure of the scalar sector, Phys. Rev. D 88, 104032 (2013).
  183. M. Blagojević and B. Cvetković, Poincaré gauge theory in 3D: canonical stability of the scalar sector, arXiv:1310.8309.
  184. K. Aoki, Nonlinearly ghost-free higher curvature gravity, Phys. Rev. D 102, 124049 (2020).
  185. G. K. Karananas, Geometrical origin of inflation in Weyl-invariant Einstein-Cartan gravity, Phys. Lett. B 862, 139343 (2025).
  186. M. Shaposhnikov, Progress in Einstein-Cartan gravity, arXiv:2506.11847.
  187. I. D. Gialamas and K. Tamvakis, Inflation in Weyl-invariant Einstein-Cartan gravity, Phys. Rev. D 111, 044007 (2025).
  188. I. D. Gialamas and K. Tamvakis, Dynamically induced spin-2 mass in a Weyl-invariant framework, Phys. Rev. D 112, 084051 (2025).
  189. J. Beltrán Jiménez, L. Heisenberg, and T. S. Koivisto, The geometrical trinity of gravity, Universe 5, 173 (2019).
  190. M. Piva, Massive higher-spin multiplets and asymptotic freedom in quantum gravity, Phys. Rev. D 105, 045006 (2022).
  191. D. Iosifidis, R. Myrzakulov, L. Ravera, G. Yergaliyeva, and K. Yerzhanov, Metric-Affine vector–tensor correspondence and implications in F(R,T,Q,T,D) gravity, Phys. Dark Universe 37, 101094 (2022).
  192. A. Jiménez-Cano and F. J. Maldonado Torralba, Vector stability in quadratic metric-affine theories, J. Cosmol. Astropart. Phys. 09 (2022) 044.
  193. D. Iosifidis and K. Pallikaris, Describing metric-affine theories anew: Alternative frameworks, examples and solutions, J. Cosmol. Astropart. Phys. 05 (2023) 037.
  194. W. Barker, M. Hobson, A. Lasenby, Y.-C. Lin, and Z. Wei, Every Poincaré gauge theory is conformal: A compelling case for dynamical vector torsion, Phys. Lett. B 863, 139316 (2025).
  195. O. Melichev and R. Percacci, On the renormalization of Poincaré gauge theories, J. High Energy Phys. 03 (2024) 133.
  196. O. Melichev, Quadratic gravity with propagating torsion and asymptotic freedom, J. High Energy Phys. 08 (2025) 130.
  197. D. Francia, S. L. Lyakhovich, and A. A. Sharapov, On the gauge symmetries of Maxwell-like higher-spin Lagrangians, Nucl. Phys. B881, 248 (2014).
  198. G. K. Karananas, M. Shaposhnikov, and S. Zell, On the gravitational origin of the QCD axion, Phys. Rev. Lett. 135, 241001 (2025).
  199. Cambridge service for data driven discovery (CSD3), https://www.csd3.cam.ac.uk.
  200. Distributed research utilising advanced computing (DiRAC), https://www.dirac.ac.uk.
  201. W. Barker, C. Marzo, and A. Santoni, Corroborating code and data at https://github.com/ wevbarker/SupplementalMaterials-2507.

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Phys. Rev. D 114, 084099– Published 30 October, 2026
  • Received 17 July 2025
  • Accepted 21 August 2026
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