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Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions

Published 22 Jun 2023 in gr-qc, hep-ph, and hep-th | (2306.13134v2)

Abstract: General Relativity (GR) exists in different formulations, which are equivalent in pure gravity. Once matter is included, however, observable predictions generically depend on the version of GR. In order to quantify the resulting ambiguity, we employ metric-affine gravity, which encompasses as special cases the metric, Palatini, Einstein-Cartan and Weyl formulations. We first discuss the interaction of fermions with torsion and non-metricity, also commenting on projective symmetry. With a view towards the Standard Model, we then construct a generic model of (complex) scalar, fermionic and gauge fields coupled to GR and derive an equivalent metric theory, which features numerous new interaction terms. As a first observable consequence, we point out that a gravitational mechanism for producing dark matter in the form of singlet fermions can be used to distinguish between metric gravity and other formulations of GR.

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References (279)
  1. LIGO and Virgo Collaboration, B. P. Abbott et al., “Observation of Gravitational Waves from a Binary Black Hole Merger,” Phys. Rev. Lett. 116 no. 6, (2016) 061102, arXiv:1602.03837 [gr-qc].
  2. A. Einstein, “Die Feldgleichungen der Gravitation,” Sitzungsber. Preuss. Akad. Wiss 18 (1915) 844.
  3. H. Weyl, “Gravitation and electricity,” Sitzungsber. Preuss. Akad. Wiss. 26 (1918) 465.
  4. A. Palatini, “Deduzione invariantiva delle equazioni gravitazionali dal principio di Hamilton,” Rendiconti del Circolo Matematico di Palermo 43 no. 1, (Dec, 1919) 203–212.
  5. H. Weyl, Space-Time-Matter. Dover Publications, 1922.
  6. A. S. Eddington, The Mathematical Theory of Relativity. Cambridge University Press, 1923.
  7. É. Cartan, “Sur une généralisation de la notion de courbure de Riemann et les espaces à torsion,” Comptes Rendus, Ac. Sc. Paris 174 (1922) 593–595.
  8. 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, vol. 40, pp. 325–412. Gauthier-Villars, 1923.
  9. 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, vol. 41, pp. 1–25. Gauthier-Villars, 1924.
  10. 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, vol. 42, pp. 17–88. Gauthier-Villars, 1925.
  11. A. Einstein, “Einheitliche Feldtheorie von Gravitation und Elektrizität,” Sitzungsber. Preuss. Akad. Wiss 22 (1925) 414.
  12. A. Einstein, “Riemanngeometrie mit Aufrechterhaltung des Begriffes des Fern-Parallelismus,” Sitzungsber. Preuss. Akad. Wiss 17 (1928) 217.
  13. A. Einstein, “Neue Möglichkeit für eine einheitliche Feldtheorie von Gravitation und Elektrizität,” Sitzungsber. Preuss. Akad. Wiss 18 (1928) 224.
  14. R. Hojman and C. Mukku, “Invariant deduction of the gravitational equations from the principle of hamilton (translation),” in Cosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity, P. G. Bergmann and V. De Sabbata, eds., pp. 477–488. Springer US, Boston, MA, 1980.
  15. G. D. Kerlick, “On a generalization of the notion of riemann curvature and spaces with torsion (translation),” in Cosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity, P. G. Bergmann and V. De Sabbata, eds., pp. 489–491. Springer US, Boston, MA, 1980.
  16. A. Unzicker and T. Case, “Translation of Einstein’s Attempt of a Unified Field Theory with Teleparallelism,” arXiv:physics/0503046 [physics.hist-ph].
  17. M. Ferraris, M. Francaviglia, and C. Reina, “Variational formulation of general relativity from 1915 to 1925 “Palatini’s method”discovered by Einstein in 1925,” General Relativity and Gravitation 14 no. 3, (1982) 243–254.
  18. R. Kallosh and A. Linde, “Universality Class in Conformal Inflation,” JCAP 07 (2013) 002, arXiv:1306.5220 [hep-th].
  19. R. Kallosh and A. Linde, “Multi-field Conformal Cosmological Attractors,” JCAP 12 (2013) 006, arXiv:1309.2015 [hep-th].
  20. G. K. Karananas and A. Monin, “Weyl vs. Conformal,” Phys. Lett. B 757 (2016) 257–260, arXiv:1510.08042 [hep-th].
  21. I. Oda, “Planck and Electroweak Scales Emerging from Conformal Gravity,” Eur. Phys. J. C 78 no. 10, (2018) 798, arXiv:1806.03420 [hep-th].
  22. A. Barnaveli, S. Lucat, and T. Prokopec, “Inflation as a spontaneous symmetry breaking of Weyl symmetry,” JCAP 01 (2019) 022, arXiv:1809.10586 [gr-qc].
  23. D. M. Ghilencea and H. M. Lee, “Weyl gauge symmetry and its spontaneous breaking in the standard model and inflation,” Phys. Rev. D 99 no. 11, (2019) 115007, arXiv:1809.09174 [hep-th].
  24. A. Edery and Y. Nakayama, “Palatini formulation of pure R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT gravity yields Einstein gravity with no massless scalar,” Phys. Rev. D 99 no. 12, (2019) 124018, arXiv:1902.07876 [hep-th].
  25. P. G. Ferreira, C. T. Hill, J. Noller, and G. G. Ross, “Scale-independent R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT inflation,” Phys. Rev. D 100 no. 12, (2019) 123516, arXiv:1906.03415 [gr-qc].
  26. Y.-C. Lin, M. P. Hobson, and A. N. Lasenby, “Ghost- and tachyon-free Weyl gauge theories: A systematic approach,” Phys. Rev. D 104 no. 2, (2021) 024034, arXiv:2005.02228 [gr-qc].
  27. M. P. Hobson and A. N. Lasenby, “Weyl gauge theories of gravity do not predict a second clock effect,” Phys. Rev. D 102 no. 8, (2020) 084040, arXiv:2009.06407 [gr-qc].
  28. Y. Tang and Y.-L. Wu, “Weyl scaling invariant R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT gravity for inflation and dark matter,” Phys. Lett. B 809 (2020) 135716, arXiv:2006.02811 [hep-ph].
  29. G. K. Karananas, M. Shaposhnikov, A. Shkerin, and S. Zell, “Scale and Weyl invariance in Einstein-Cartan gravity,” Phys. Rev. D 104 no. 12, (2021) 124014, arXiv:2108.05897 [hep-th].
  30. G. J. Olmo, E. Orazi, and G. Pradisi, “Conformal metric-affine gravities,” JCAP 10 (2022) 057, arXiv:2207.12597 [hep-th].
  31. D. Sauro and O. Zanusso, “The origin of Weyl gauging in metric-affine theories,” Class. Quant. Grav. 39 no. 18, (2022) 185001, arXiv:2203.08692 [hep-th].
  32. S. Aoki and H. M. Lee, “Weyl gravity extension of Higgs inflation,” Phys. Rev. D 108 no. 3, (2023) 035045, arXiv:2207.05484 [hep-ph].
  33. D. Sauro, R. Martini, and O. Zanusso, “Projective transformations in metric-affine and Weylian geometries,” arXiv:2208.10872 [hep-th].
  34. Y. Nakayama, “Geometrical trinity of unimodular gravity,” Class. Quant. Grav. 40 no. 12, (2023) 125005, arXiv:2209.09462 [gr-qc].
  35. Z. Lalak and P. Michalak, “Spontaneous scale symmetry breaking at high temperature,” JHEP 05 (2023) 206, arXiv:2211.09045 [hep-ph].
  36. G. Paci, D. Sauro, and O. Zanusso, “Conformally covariant operators of mixed-symmetry tensors and MAGs,” arXiv:2302.14093 [hep-th].
  37. F. W. Hehl, G. D. Kerlick, and P. Von Der Heyde, “On Hypermomentum in General Relativity. 2. The Geometry of Space-Time,” Z. Naturforsch. A 31 (1976) 524–527.
  38. F. W. Hehl, G. D. Kerlick, and P. Von Der Heyde, “On Hypermomentum in General Relativity. 3. Coupling Hypermomentum to Geometry,” Z. Naturforsch. A 31 (1976) 823–827.
  39. F. W. Hehl, G. D. Kerlick, and P. Von Der Heyde, “On a New Metric Affine Theory of Gravitation,” Phys. Lett. B 63 (1976) 446–448.
  40. F. W. Hehl, G. D. Kerlick, E. A. Lord, and L. L. Smalley, “Hypermomentum and the Microscopic Violation of the Riemannian Constraint in General Relativity,” Phys. Lett. B 70 (1977) 70–72.
  41. F. W. Hehl, “Four lectures on poincaré gauge field theory,” in Cosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity, P. G. Bergmann and V. De Sabbata, eds., pp. 5–61. Springer US, Boston, MA, 1980.
  42. F. W. Hehl, J. D. McCrea, E. W. Mielke, and Y. Ne’eman, “Metric affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance,” Phys. Rept. 258 (1995) 1–171, arXiv:gr-qc/9402012.
  43. CRC Press, Bristol and Philadelphia, 2002.
  44. M. Blagojevic, “Three lectures on Poincare gauge theory,” SFIN A 1 (2003) 147–172, arXiv:gr-qc/0302040.
  45. Y. N. Obukhov, “Poincaré gauge gravity: An overview,” Int. J. Geom. Meth. Mod. Phys. 15 no. supp01, (2018) 1840005, arXiv:1805.07385 [gr-qc].
  46. L. Heisenberg, “A systematic approach to generalisations of General Relativity and their cosmological implications,” Phys. Rept. 796 (2019) 1–113, arXiv:1807.01725 [gr-qc].
  47. J. Beltrán Jiménez, L. Heisenberg, and T. S. Koivisto, “The Geometrical Trinity of Gravity,” Universe 5 no. 7, (2019) 173, arXiv:1903.06830 [hep-th].
  48. C. Rigouzzo and S. Zell, “Coupling metric-affine gravity to a Higgs-like scalar field,” Phys. Rev. D 106 no. 2, (2022) 024015, arXiv:2204.03003 [hep-th].
  49. C. Møller, “Conservation Law and Absolute Parallelism in General Relativity,” K. Dan. Vidensk. Selsk. Mat. Fys. Skr. 1 (1961) 1.
  50. C. Pellegrini and J. Plebanski, “Tetrad Fields and Gravitational Fields,” K. Dan. Vidensk. Selsk. Mat. Fys. Skr. 2 (1963) 1.
  51. K. Hayashi and T. Nakano, “Extended translation invariance and associated gauge fields,” Prog. Theor. Phys. 38 (1967) 491–507.
  52. Y. M. Cho, “Einstein Lagrangian as the Translational Yang-Mills Lagrangian,” Phys. Rev. D 14 (1976) 2521.
  53. K. Hayashi and T. Shirafuji, “New general relativity.,” Phys. Rev. D 19 (1979) 3524–3553. [Addendum: Phys.Rev.D 24, 3312–3314 (1982)].
  54. J. M. Nester and H.-J. Yo, “Symmetric teleparallel general relativity,” Chin. J. Phys. 37 (1999) 113, arXiv:gr-qc/9809049.
  55. J. Beltrán Jiménez, L. Heisenberg, D. Iosifidis, A. Jiménez-Cano, and T. S. Koivisto, “General teleparallel quadratic gravity,” Phys. Lett. B 805 (2020) 135422, arXiv:1909.09045 [gr-qc].
  56. E. Schrödinger, Space-Time Structure. Cambridge University Press, 1950.
  57. J. Kijowski, “On a new variational principle in general relativity and the energy of the gravitational field,” General Relativity and Gravitation 9 (1978) 857–877.
  58. N. Dadhich and J. M. Pons, “On the equivalence of the Einstein-Hilbert and the Einstein-Palatini formulations of general relativity for an arbitrary connection,” Gen. Rel. Grav. 44 (2012) 2337–2352, arXiv:1010.0869 [gr-qc].
  59. A. N. Bernal, B. Janssen, A. Jimenez-Cano, J. A. Orejuela, M. Sanchez, and P. Sanchez-Moreno, “On the (non-)uniqueness of the Levi-Civita solution in the Einstein–Hilbert–Palatini formalism,” Phys. Lett. B 768 (2017) 280–287, arXiv:1606.08756 [gr-qc].
  60. R. Utiyama, “Invariant theoretical interpretation of interaction,” Phys. Rev. 101 (1956) 1597–1607.
  61. T. W. B. Kibble, “Lorentz invariance and the gravitational field,” J. Math. Phys. 2 (1961) 212–221.
  62. D. W. Sciama, “On the analogy between charge and spin in general relativity,” in Recent developments in general relativity, p. 415. Pergamon Press, Oxford, 1962.
  63. K. S. Stelle, “Classical Gravity with Higher Derivatives,” Gen. Rel. Grav. 9 (1978) 353–371.
  64. D. E. Neville, “A Gravity Lagrangian With Ghost Free Curvature**2 Terms,” Phys. Rev. D 18 (1978) 3535.
  65. D. E. Neville, “Gravity Theories With Propagating Torsion,” Phys. Rev. D 21 (1980) 867.
  66. E. Sezgin and P. van Nieuwenhuizen, “New Ghost Free Gravity Lagrangians with Propagating Torsion,” Phys. Rev. D 21 (1980) 3269.
  67. K. Hayashi and T. Shirafuji, “Gravity from Poincare Gauge Theory of the Fundamental Particles. 1. Linear and Quadratic Lagrangians,” Prog. Theor. Phys. 64 (1980) 866. [Erratum: Prog.Theor.Phys. 65, 2079 (1981)].
  68. 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 (1980) 2222.
  69. E. Sezgin, “Class of Ghost Free Gravity Lagrangians With Massive or Massless Propagating Torsion,” Phys. Rev. D 24 (1981) 1677–1680.
  70. R. Kuhfuss and J. Nitsch, “Propagating Modes in Gauge Field Theories of Gravity,” Gen. Rel. Grav. 18 (1986) 1207.
  71. V. P. Nair, S. Randjbar-Daemi, and V. Rubakov, “Massive Spin-2 fields of Geometric Origin in Curved Spacetimes,” Phys. Rev. D 80 (2009) 104031, arXiv:0811.3781 [hep-th].
  72. V. Nikiforova, S. Randjbar-Daemi, and V. Rubakov, “Infrared Modified Gravity with Dynamical Torsion,” Phys. Rev. D 80 (2009) 124050, arXiv:0905.3732 [hep-th].
  73. G. K. Karananas, “The particle spectrum of parity-violating Poincaré gravitational theory,” Class. Quant. Grav. 32 no. 5, (2015) 055012, arXiv:1411.5613 [gr-qc].
  74. PhD thesis, Ecole Polytechnique, Lausanne, 2016. arXiv:1608.08451 [hep-th].
  75. Y. N. Obukhov, “Gravitational waves in Poincaré gauge gravity theory,” Phys. Rev. D 95 no. 8, (2017) 084028, arXiv:1702.05185 [gr-qc].
  76. M. Blagojević, B. Cvetković, and Y. N. Obukhov, “Generalized plane waves in Poincaré gauge theory of gravity,” Phys. Rev. D 96 no. 6, (2017) 064031, arXiv:1708.08766 [gr-qc].
  77. M. Blagojević and B. Cvetković, “General Poincaré gauge theory: Hamiltonian structure and particle spectrum,” Phys. Rev. D 98 (2018) 024014, arXiv:1804.05556 [gr-qc].
  78. Y.-C. Lin, M. P. Hobson, and A. N. Lasenby, “Ghost and tachyon free Poincaré gauge theories: A systematic approach,” Phys. Rev. D 99 no. 6, (2019) 064001, arXiv:1812.02675 [gr-qc].
  79. J. Beltrán Jiménez and A. Delhom, “Ghosts in metric-affine higher order curvature gravity,” Eur. Phys. J. C 79 no. 8, (2019) 656, arXiv:1901.08988 [gr-qc].
  80. K. Aoki and K. Shimada, “Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?,” Phys. Rev. D 100 no. 4, (2019) 044037, arXiv:1904.10175 [hep-th].
  81. J. Beltrán Jiménez and F. J. Maldonado Torralba, “Revisiting the stability of quadratic Poincaré gauge gravity,” Eur. Phys. J. C 80 no. 7, (2020) 611, arXiv:1910.07506 [gr-qc].
  82. Y.-C. Lin, M. P. Hobson, and A. N. Lasenby, “Power-counting renormalizable, ghost-and-tachyon-free Poincaré gauge theories,” Phys. Rev. D 101 no. 6, (2020) 064038, arXiv:1910.14197 [gr-qc].
  83. R. Percacci and E. Sezgin, “New class of ghost- and tachyon-free metric affine gravities,” Phys. Rev. D 101 no. 8, (2020) 084040, arXiv:1912.01023 [hep-th].
  84. J. Beltrán Jiménez and A. Delhom, “Instabilities in metric-affine theories of gravity with higher order curvature terms,” Eur. Phys. J. C 80 no. 6, (2020) 585, arXiv:2004.11357 [gr-qc].
  85. C. Marzo, “Ghost and tachyon free propagation up to spin 3 in Lorentz invariant field theories,” Phys. Rev. D 105 no. 6, (2022) 065017, arXiv:2108.11982 [hep-ph].
  86. C. Marzo, “Radiatively stable ghost and tachyon freedom in metric affine gravity,” Phys. Rev. D 106 no. 2, (2022) 024045, arXiv:2110.14788 [hep-th].
  87. A. Baldazzi, O. Melichev, and R. Percacci, “Metric-Affine Gravity as an effective field theory,” Annals Phys. 438 (2022) 168757, arXiv:2112.10193 [gr-qc].
  88. G. Pradisi and A. Salvio, “(In)equivalence of metric-affine and metric effective field theories,” Eur. Phys. J. C 82 no. 9, (2022) 840, arXiv:2206.15041 [hep-th].
  89. J. Annala and S. Rasanen, “Stability of non-degenerate Ricci-type Palatini theories,” JCAP 04 (2023) 014, arXiv:2212.09820 [gr-qc]. [Erratum: JCAP 08, E02 (2023)].
  90. H.-j. Yo and J. M. Nester, “Hamiltonian analysis of Poincare gauge theory scalar modes,” Int. J. Mod. Phys. D 08 (1999) 459–479, arXiv:gr-qc/9902032.
  91. H.-J. Yo and J. M. Nester, “Hamiltonian analysis of Poincare gauge theory: Higher spin modes,” Int. J. Mod. Phys. D 11 (2002) 747–780, arXiv:gr-qc/0112030.
  92. J. Beltran Jimenez and T. S. Koivisto, “Extended Gauss-Bonnet gravities in Weyl geometry,” Class. Quant. Grav. 31 (2014) 135002, arXiv:1402.1846 [gr-qc].
  93. D. Iosifidis, C. G. Tsagas, and A. C. Petkou, “Raychaudhuri equation in spacetimes with torsion and nonmetricity,” Phys. Rev. D 98 no. 10, (2018) 104037, arXiv:1809.04992 [gr-qc].
  94. D. Iosifidis and T. Koivisto, “Scale transformations in metric-affine geometry,” Universe 5 (2019) 82, arXiv:1810.12276 [gr-qc].
  95. T. Helpin and M. S. Volkov, “A metric-affine version of the Horndeski theory,” Int. J. Mod. Phys. A 35 no. 02n03, (2020) 2040010, arXiv:1911.12768 [hep-th].
  96. J. A. Orejuela García, Lovelock Theories as extensions to General Relativity. PhD thesis, U. Granada (main), 2020.
  97. D. M. Ghilencea, “Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation,” Eur. Phys. J. C 80 no. 12, (4, 2020) 1147, arXiv:2003.08516 [hep-th].
  98. J. Beltrán Jiménez, L. Heisenberg, and T. Koivisto, “The coupling of matter and spacetime geometry,” Class. Quant. Grav. 37 no. 19, (2020) 195013, arXiv:2004.04606 [hep-th].
  99. Y. Xu, T. Harko, S. Shahidi, and S.-D. Liang, “Weyl type f⁢(Q,T)𝑓𝑄𝑇f(Q,T)italic_f ( italic_Q , italic_T ) gravity, and its cosmological implications,” Eur. Phys. J. C 80 no. 5, (2020) 449, arXiv:2005.04025 [gr-qc].
  100. J.-Z. Yang, S. Shahidi, T. Harko, and S.-D. Liang, “Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type f⁢(Q,T)𝑓𝑄𝑇f(Q,T)italic_f ( italic_Q , italic_T ) gravity,” Eur. Phys. J. C 81 no. 2, (2021) 111, arXiv:2101.09956 [gr-qc].
  101. I. Quiros, “Nonmetricity theories and aspects of gauge symmetry,” Phys. Rev. D 105 no. 10, (2022) 104060, arXiv:2111.05490 [gr-qc].
  102. I. Quiros, “Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity,” Phys. Rev. D 107 no. 10, (2023) 104028, arXiv:2208.10048 [gr-qc].
  103. J.-Z. Yang, S. Shahidi, and T. Harko, “Black hole solutions in the quadratic Weyl conformal geometric theory of gravity,” Eur. Phys. J. C 82 no. 12, (2022) 1171, arXiv:2212.05542 [gr-qc].
  104. P. Burikham, T. Harko, K. Pimsamarn, and S. Shahidi, “Dark matter as a Weyl geometric effect,” Phys. Rev. D 107 no. 6, (2023) 064008, arXiv:2302.08289 [gr-qc].
  105. Z. Haghani and T. Harko, “Compact stellar structures in Weyl geometric gravity,” Phys. Rev. D 107 no. 6, (2023) 064068, arXiv:2303.10339 [gr-qc].
  106. W. Barker and S. Zell, “A Purely Gravitational Origin for Einstein-Proca Theory,” arXiv:2306.14953 [hep-th].
  107. V. I. Rodichev, “Twisted Space and Nonlinear Field Equations,” Zhur. Eksptl’. i Teoret. Fiz. 40 (5, 1961) 1029.
  108. R. Hojman, C. Mukku, and W. A. Sayed, “Parity violation in metric torsion theories of gravitation,” Phys. Rev. D 22 (1980) 1915–1921.
  109. P. C. Nelson, “Gravity With Propagating Pseudoscalar Torsion,” Phys. Lett. A 79 (1980) 285.
  110. H. T. Nieh and M. L. Yan, “An Identity in Riemann-cartan Geometry,” J. Math. Phys. 23 (1982) 373.
  111. R. Percacci, “The Higgs phenomenon in quantum gravity,” Nucl. Phys. B 353 (1991) 271–290, arXiv:0712.3545 [hep-th].
  112. World Scientific Publishing Co Pte Ltd, 1991.
  113. S. Holst, “Barbero’s Hamiltonian derived from a generalized Hilbert-Palatini action,” Phys. Rev. D 53 (1996) 5966–5969, arXiv:gr-qc/9511026.
  114. Y. N. Obukhov, E. J. Vlachynsky, W. Esser, R. Tresguerres, and F. W. Hehl, “An Exact solution of the metric affine gauge theory with dilation, shear, and spin charges,” Phys. Lett. A 220 (1996) 1, arXiv:gr-qc/9604027.
  115. Y. N. Obukhov, E. J. Vlachynsky, W. Esser, and F. W. Hehl, “Irreducible decompositions in metric affine gravity models,” arXiv:gr-qc/9705039.
  116. I. L. Shapiro, “Physical aspects of the space-time torsion,” Phys. Rept. 357 (2002) 113, arXiv:hep-th/0103093.
  117. L. Freidel, D. Minic, and T. Takeuchi, “Quantum gravity, torsion, parity violation and all that,” Phys. Rev. D 72 (2005) 104002, arXiv:hep-th/0507253.
  118. S. Alexandrov, “Immirzi parameter and fermions with non-minimal coupling,” Class. Quant. Grav. 25 (2008) 145012, arXiv:0802.1221 [gr-qc].
  119. D. Diakonov, A. G. Tumanov, and A. A. Vladimirov, “Low-energy General Relativity with torsion: A Systematic derivative expansion,” Phys. Rev. D 84 (2011) 124042, arXiv:1104.2432 [hep-th].
  120. J. a. Magueijo, T. G. Zlosnik, and T. W. B. Kibble, “Cosmology with a spin,” Phys. Rev. D 87 no. 6, (2013) 063504, arXiv:1212.0585 [astro-ph.CO].
  121. C. Pagani and R. Percacci, “Quantum gravity with torsion and non-metricity,” Class. Quant. Grav. 32 no. 19, (2015) 195019, arXiv:1506.02882 [gr-qc].
  122. S. Rasanen, “Higgs inflation in the Palatini formulation with kinetic terms for the metric,” Open J. Astrophys. 2 no. 1, (2019) 1, arXiv:1811.09514 [gr-qc].
  123. K. Shimada, K. Aoki, and K.-i. Maeda, “Metric-affine Gravity and Inflation,” Phys. Rev. D 99 no. 10, (2019) 104020, arXiv:1812.03420 [gr-qc].
  124. A. Perez and C. Rovelli, “Physical effects of the Immirzi parameter,” Phys. Rev. D 73 (2006) 044013, arXiv:gr-qc/0505081.
  125. V. Taveras and N. Yunes, “The Barbero-Immirzi Parameter as a Scalar Field: K-Inflation from Loop Quantum Gravity?,” Phys. Rev. D 78 (2008) 064070, arXiv:0807.2652 [gr-qc].
  126. A. Torres-Gomez and K. Krasnov, “Remarks on Barbero-Immirzi parameter as a field,” Phys. Rev. D 79 (2009) 104014, arXiv:0811.1998 [gr-qc].
  127. G. Calcagni and S. Mercuri, “The Barbero-Immirzi field in canonical formalism of pure gravity,” Phys. Rev. D 79 (2009) 084004, arXiv:0902.0957 [gr-qc].
  128. S. Mercuri, “Peccei-Quinn mechanism in gravity and the nature of the Barbero-Immirzi parameter,” Phys. Rev. Lett. 103 (2009) 081302, arXiv:0902.2764 [gr-qc].
  129. M. Långvik, J.-M. Ojanperä, S. Raatikainen, and S. Rasanen, “Higgs inflation with the Holst and the Nieh–Yan term,” Phys. Rev. D 103 no. 8, (2021) 083514, arXiv:2007.12595 [astro-ph.CO].
  130. M. Shaposhnikov, A. Shkerin, I. Timiryasov, and S. Zell, “Einstein-Cartan gravity, matter, and scale-invariant generalization ,” JHEP 10 (2020) 177, arXiv:2007.16158 [hep-th].
  131. G. K. Karananas, M. Shaposhnikov, A. Shkerin, and S. Zell, “Matter matters in Einstein-Cartan gravity,” Phys. Rev. D 104 no. 6, (2021) 064036, arXiv:2106.13811 [hep-th].
  132. D. Iosifidis, “The full quadratic metric-affine gravity (including parity odd terms): exact solutions for the affine-connection,” Class. Quant. Grav. 39 no. 9, (2022) 095002, arXiv:2112.09154 [gr-qc].
  133. S. Rasanen and Y. Verbin, “Palatini formulation for gauge theory: implications for slow-roll inflation,” arXiv:2211.15584 [astro-ph.CO].
  134. W. R. Stoeger and P. B. Yasskin, “Can a macroscopic gyroscope feel torsion,” Gen. Relativ. Gravit. 11 (1979) 427.
  135. C. Lammerzahl, “Constraints on space-time torsion from Hughes-Drever experiments,” Phys. Lett. A 228 (1997) 223, arXiv:gr-qc/9704047.
  136. F. Bauer and D. A. Demir, “Inflation with Non-Minimal Coupling: Metric versus Palatini Formulations,” Phys. Lett. B 665 (2008) 222–226, arXiv:0803.2664 [hep-ph].
  137. K.-F. Shie, J. M. Nester, and H.-J. Yo, “Torsion Cosmology and the Accelerating Universe,” Phys. Rev. D 78 (2008) 023522, arXiv:0805.3834 [gr-qc].
  138. 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,” JCAP 10 (2009) 027, arXiv:0908.3323 [gr-qc].
  139. 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 (2011) 024001, arXiv:1009.5112 [gr-qc].
  140. N. J. Poplawski, “Matter-antimatter asymmetry and dark matter from torsion,” Phys. Rev. D 83 (2011) 084033, arXiv:1101.4012 [gr-qc].
  141. I. B. Khriplovich, “Gravitational four-fermion interaction on the Planck scale,” Phys. Lett. B 709 (2012) 111–113, arXiv:1201.4226 [gr-qc].
  142. I. B. Khriplovich and A. S. Rudenko, “Gravitational four-fermion interaction and dynamics of the early Universe,” JHEP 11 (2013) 174, arXiv:1303.1348 [astro-ph.CO].
  143. T. Markkanen, T. Tenkanen, V. Vaskonen, and H. Veermäe, “Quantum corrections to quartic inflation with a non-minimal coupling: metric vs. Palatini,” JCAP 03 (2018) 029, arXiv:1712.04874 [gr-qc].
  144. P. Carrilho, D. Mulryne, J. Ronayne, and T. Tenkanen, “Attractor Behaviour in Multifield Inflation,” JCAP 06 (2018) 032, arXiv:1804.10489 [astro-ph.CO].
  145. D. Kranas, C. G. Tsagas, J. D. Barrow, and D. Iosifidis, “Friedmann-like universes with torsion,” Eur. Phys. J. C 79 no. 4, (2019) 341, arXiv:1809.10064 [gr-qc].
  146. S. Rasanen and E. Tomberg, “Planck scale black hole dark matter from Higgs inflation,” JCAP 01 (2019) 038, arXiv:1810.12608 [astro-ph.CO].
  147. J. Rubio and E. S. Tomberg, “Preheating in Palatini Higgs inflation,” JCAP 04 (2019) 021, arXiv:1902.10148 [hep-ph].
  148. H. Zhang and L. Xu, “Late-time acceleration and inflation in a Poincaré gauge cosmological model,” JCAP 09 (2019) 050, arXiv:1904.03545 [gr-qc].
  149. H. Zhang and L. Xu, “Inflation in the parity-conserving Poincaré gauge cosmology,” JCAP 10 (2020) 003, arXiv:1906.04340 [gr-qc].
  150. E. N. Saridakis, S. Myrzakul, K. Myrzakulov, and K. Yerzhanov, “Cosmological applications of F⁢(R,T)𝐹𝑅𝑇F(R,T)italic_F ( italic_R , italic_T ) gravity with dynamical curvature and torsion,” Phys. Rev. D 102 no. 2, (2020) 023525, arXiv:1912.03882 [gr-qc].
  151. B. Barman, T. Bhanja, D. Das, and D. Maity, “Minimal model of torsion mediated dark matter,” Phys. Rev. D 101 no. 7, (2020) 075017, arXiv:1912.09249 [hep-ph].
  152. M. Shaposhnikov, A. Shkerin, and S. Zell, “Standard Model Meets Gravity: Electroweak Symmetry Breaking and Inflation,” Phys. Rev. D 103 no. 3, (2021) 033006, arXiv:2001.09088 [hep-th].
  153. K. Aoki and S. Mukohyama, “Consistent inflationary cosmology from quadratic gravity with dynamical torsion,” JCAP 06 (2020) 004, arXiv:2003.00664 [hep-th].
  154. 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 (2020) 135876, arXiv:2006.11290 [hep-th].
  155. M. Shaposhnikov, A. Shkerin, I. Timiryasov, and S. Zell, “Higgs inflation in Einstein-Cartan gravity,” JCAP 02 (2021) 008, arXiv:2007.14978 [hep-ph]. [Erratum: JCAP 10, E01 (2021)].
  156. M. Shaposhnikov, A. Shkerin, I. Timiryasov, and S. Zell, “Einstein-Cartan Portal to Dark Matter,” Phys. Rev. Lett. 126 no. 16, (2021) 161301, arXiv:2008.11686 [hep-ph]. [Erratum: Phys.Rev.Lett. 127, 169901 (2021)].
  157. M. Kubota, K.-Y. Oda, K. Shimada, and M. Yamaguchi, “Cosmological Perturbations in Palatini Formalism,” JCAP 03 (2021) 006, arXiv:2010.07867 [hep-th].
  158. V.-M. Enckell, S. Nurmi, S. Räsänen, and E. Tomberg, “Critical point Higgs inflation in the Palatini formulation,” JHEP 04 (2021) 059, arXiv:2012.03660 [astro-ph.CO].
  159. D. Iosifidis and L. Ravera, “The cosmology of quadratic torsionful gravity,” Eur. Phys. J. C 81 no. 8, (2021) 736, arXiv:2101.10339 [gr-qc].
  160. A. Racioppi, J. Rajasalu, and K. Selke, “Multiple point criticality principle and Coleman-Weinberg inflation,” JHEP 06 (2022) 107, arXiv:2109.03238 [astro-ph.CO].
  161. D. Y. Cheong, S. M. Lee, and S. C. Park, “Reheating in models with non-minimal coupling in metric and Palatini formalisms,” JCAP 02 no. 02, (2022) 029, arXiv:2111.00825 [hep-ph].
  162. D. Benisty, E. I. Guendelman, A. van de Venn, D. Vasak, J. Struckmeier, and H. Stoecker, “The dark side of the torsion: dark energy from propagating torsion,” Eur. Phys. J. C 82 no. 3, (2022) 264, arXiv:2109.01052 [astro-ph.CO].
  163. M. Piani and J. Rubio, “Higgs-Dilaton inflation in Einstein-Cartan gravity,” JCAP 05 no. 05, (2022) 009, arXiv:2202.04665 [gr-qc].
  164. F. Dux, A. Florio, J. Klarić, A. Shkerin, and I. Timiryasov, “Preheating in Palatini Higgs inflation on the lattice,” JCAP 09 (2022) 015, arXiv:2203.13286 [hep-ph].
  165. J. Klaric, A. Shkerin, and G. Vacalis, “Non-perturbative production of fermionic dark matter from fast preheating,” JCAP 02 (2023) 034, arXiv:2209.02668 [gr-qc].
  166. W. Yin, “Weak-Scale Higgs Inflation,” arXiv:2210.15680 [hep-ph].
  167. I. D. Gialamas, A. Karam, and T. D. Pappas, “Gravitational corrections to electroweak vacuum decay: metric vs. Palatini,” Phys. Lett. B 840 (2023) 137885, arXiv:2212.03052 [hep-ph].
  168. M. Piani and J. Rubio, “Preheating in Einstein-Cartan Higgs Inflation: Oscillon formation,” arXiv:2304.13056 [hep-ph].
  169. I. D. Gialamas, A. Karam, T. D. Pappas, and E. Tomberg, “Implications of Palatini gravity for inflation and beyond,” arXiv:2303.14148 [gr-qc].
  170. A. V. Minkevich and A. S. Garkun, “Isotropic cosmology in metric - affine gauge theory of gravity,” arXiv:gr-qc/9805007.
  171. D. Puetzfeld and R. Tresguerres, “A Cosmological model in Weyl-Cartan space-time,” Class. Quant. Grav. 18 (2001) 677–694, arXiv:gr-qc/0101050.
  172. O. V. Babourova and B. N. Frolov, “Matter with dilaton charge in Weyl-Cartan space-time and evolution of the universe,” Class. Quant. Grav. 20 (2003) 1423–1442, arXiv:gr-qc/0209077.
  173. D. Puetzfeld, “Status of non-Riemannian cosmology,” New Astron. Rev. 49 (2005) 59–64, arXiv:gr-qc/0404119.
  174. A. D. I. Latorre, G. J. Olmo, and M. Ronco, “Observable traces of non-metricity: new constraints on metric-affine gravity,” Phys. Lett. B 780 (2018) 294–299, arXiv:1709.04249 [hep-th].
  175. D. Iosifidis, “Cosmic Acceleration with Torsion and Non-metricity in Friedmann-like Universes,” Class. Quant. Grav. 38 no. 1, (2021) 015015, arXiv:2007.12537 [gr-qc].
  176. Y. Mikura, Y. Tada, and S. Yokoyama, “Conformal inflation in the metric-affine geometry,” EPL 132 no. 3, (2020) 39001, arXiv:2008.00628 [hep-th].
  177. D. Iosifidis, “Non-Riemannian cosmology: The role of shear hypermomentum,” Int. J. Geom. Meth. Mod. Phys. 18 no. supp01, (2021) 2150129, arXiv:2010.00875 [gr-qc].
  178. Y. Mikura, Y. Tada, and S. Yokoyama, “Minimal k𝑘kitalic_k-inflation in light of the conformal metric-affine geometry,” Phys. Rev. D 103 no. 10, (2021) L101303, arXiv:2103.13045 [hep-th].
  179. D. Iosifidis, N. Myrzakulov, and R. Myrzakulov, “Metric-Affine Version of Myrzakulov F(R,T,Q,T) Gravity and Cosmological Applications,” Universe 7 no. 8, (2021) 262, arXiv:2106.05083 [gr-qc].
  180. D. Iosifidis and L. Ravera, “Cosmology of quadratic metric-affine gravity,” Phys. Rev. D 105 no. 2, (2022) 024007, arXiv:2109.06167 [gr-qc].
  181. I. D. Gialamas and K. Tamvakis, “Inflation in metric-affine quadratic gravity,” JCAP 03 (2023) 042, arXiv:2212.09896 [gr-qc].
  182. D. Iosifidis, R. Myrzakulov, and L. Ravera, “Cosmology of Metric-Affine R+β⁢R2𝑅𝛽superscript𝑅2R+\beta R^{2}italic_R + italic_β italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT Gravity with Pure Shear Hypermomentum,” arXiv:2301.00669 [gr-qc].
  183. S. Arai et al., “Cosmological gravity probes: Connecting recent theoretical developments to forthcoming observations,” PTEP 2023 no. 7, (2023) 072E01, arXiv:2212.09094 [astro-ph.CO].
  184. D. Iosifidis, “Metric-Affine Cosmologies: kinematics of Perfect (Ideal) Cosmological Hyperfluids and first integrals,” JCAP 09 (2023) 045, arXiv:2301.09868 [gr-qc].
  185. D. Iosifidis and K. Pallikaris, “Describing metric-affine theories anew: alternative frameworks, examples and solutions,” JCAP 05 (2023) 037, arXiv:2301.11364 [gr-qc].
  186. C. G. Boehmer and E. Jensko, “Modified gravity: A unified approach to metric-affine models,” J. Math. Phys. 64 no. 8, (2023) 082505, arXiv:2301.11051 [gr-qc].
  187. I. D. Gialamas and H. Veermäe, “Electroweak vacuum decay in metric-affine gravity,” Phys. Lett. B 844 (2023) 138109, arXiv:2305.07693 [hep-th].
  188. S. Dodelson and L. M. Widrow, “Sterile-neutrinos as dark matter,” Phys. Rev. Lett. 72 (1994) 17–20, arXiv:hep-ph/9303287.
  189. X.-D. Shi and G. M. Fuller, “A New dark matter candidate: Nonthermal sterile neutrinos,” Phys. Rev. Lett. 82 (1999) 2832–2835, arXiv:astro-ph/9810076.
  190. M. Shaposhnikov, “The nuMSM, leptonic asymmetries, and properties of singlet fermions,” JHEP 08 (2008) 008, arXiv:0804.4542 [hep-ph].
  191. L. Canetti, M. Drewes, and M. Shaposhnikov, “Sterile Neutrinos as the Origin of Dark and Baryonic Matter,” Phys. Rev. Lett. 110 no. 6, (2013) 061801, arXiv:1204.3902 [hep-ph].
  192. L. Canetti, M. Drewes, T. Frossard, and M. Shaposhnikov, “Dark Matter, Baryogenesis and Neutrino Oscillations from Right Handed Neutrinos,” Phys. Rev. D 87 (2013) 093006, arXiv:1208.4607 [hep-ph].
  193. J. Ghiglieri and M. Laine, “Sterile neutrino dark matter via coinciding resonances,” JCAP 07 (2020) 012, arXiv:2004.10766 [hep-ph].
  194. A. Boyarsky, M. Drewes, T. Lasserre, S. Mertens, and O. Ruchayskiy, “Sterile neutrino Dark Matter,” Prog. Part. Nucl. Phys. 104 (2019) 1–45, arXiv:1807.07938 [hep-ph].
  195. B. F. Schutz, Geometrical Methods of Mathematical Physics. Cambridge University Press, 1980.
  196. Cambridge University Press, 2004.
  197. E. Mielke, Geometrodynamics of Gauge Fields. Mathematical Physics Studies. Springer, 2017.
  198. C. Rigouzzo and S. Zell, “Metric-affine,”. Available at https://github.com/crigouzzo/metric-affine.
  199. A. Trautman, “On the structure of the Einstein-Cartan equations,” in Symposia mathematica. Volume XII, G. R. Curbastro and T. Levi-Civita, eds. Academic Press, 1973.
  200. V. D. Sandberg, “Are torsion theories of gravitation equivalent to metric theories?,” Phys. Rev. D 12 (1975) 3013–3018.
  201. A. Trautman, “A classification of space-time structures,” Reports on Mathematical Physics 10 no. 3, (1976) 297–310.
  202. F. W. Hehl and G. D. Kerlick, “Metric-affine variational principles in general relativity. I. Riemannian space-time ,” General Relativity and Gravitation 9 (1978) 691–710.
  203. F. W. Hehl, E. A. Lord, and L. L. Smalley, “Metric-affine variational principles in general relativity II. Relaxation of the Riemannian constraint,” General Relativity and Gravitation 13 (1981) 1037–1056.
  204. C. Rigouzzo, “Gauge theory of gravity – non-metricity and consequences for inflation,” Master’s thesis, École polytechnique fédérale de Lausanne, 2021.
  205. S. Raatikainen and S. Rasanen, “Higgs inflation and teleparallel gravity,” JCAP 12 (2019) 021, arXiv:1910.03488 [gr-qc].
  206. J. F. Donoghue, “Is the spin connection confined or condensed?,” Phys. Rev. D 96 no. 4, (2017) 044003, arXiv:1609.03523 [hep-th].
  207. D. Demir and B. Pulice, “Geometric Proca with matter in metric-Palatini gravity,” Eur. Phys. J. C 82 no. 11, (2022) 996, arXiv:2211.00991 [gr-qc].
  208. M. Adak, O. Sert, M. Kalay, and M. Sari, “Symmetric Teleparallel Gravity: Some exact solutions and spinor couplings,” Int. J. Mod. Phys. A 28 (2013) 1350167, arXiv:0810.2388 [gr-qc].
  209. J. Beltrán Jiménez, L. Heisenberg, and T. Koivisto, “Coincident General Relativity,” Phys. Rev. D 98 no. 4, (2018) 044048, arXiv:1710.03116 [gr-qc].
  210. J. Beltrán Jiménez, L. Heisenberg, and T. S. Koivisto, “Teleparallel Palatini theories,” JCAP 08 (2018) 039, arXiv:1803.10185 [gr-qc].
  211. T. Koivisto, “An integrable geometrical foundation of gravity,” Int. J. Geom. Meth. Mod. Phys. 15 (2018) 1840006, arXiv:1802.00650 [gr-qc].
  212. A. Delhom, “Minimal coupling in presence of non-metricity and torsion,” Eur. Phys. J. C 80 no. 8, (2020) 728, arXiv:2002.02404 [gr-qc].
  213. V. C. de Andrade and J. G. Pereira, “Torsion and the electromagnetic field,” Int. J. Mod. Phys. D 08 (1999) 141–151, arXiv:gr-qc/9708051.
  214. V. C. de Andrade and J. G. Pereira, “Gravitational Lorentz force and the description of the gravitational interaction,” Phys. Rev. D 56 (1997) 4689–4695, arXiv:gr-qc/9703059.
  215. V. C. de Andrade, L. C. T. Guillen, and J. G. Pereira, “Gravitational energy momentum density in teleparallel gravity,” Phys. Rev. Lett. 84 (2000) 4533–4536, arXiv:gr-qc/0003100.
  216. V. C. de Andrade, L. C. T. Guillen, and J. G. Pereira, “Teleparallel spin connection,” Phys. Rev. D 64 (2001) 027502, arXiv:gr-qc/0104102.
  217. Y. N. Obukhov and J. G. Pereira, “Metric affine approach to teleparallel gravity,” Phys. Rev. D 67 (2003) 044016, arXiv:gr-qc/0212080.
  218. J. W. Maluf, “Dirac spinor fields in the teleparallel gravity: Comment on ‘Metric affine approach to teleparallel gravity’,” Phys. Rev. D 67 (2003) 108501, arXiv:gr-qc/0304005.
  219. E. W. Mielke, “Consistent coupling to Dirac fields in teleparallelism: Comment on ‘Metric-affine approach to teleparallel gravity’,” Phys. Rev. D 69 (2004) 128501.
  220. R. A. Mosna and J. G. Pereira, “Some remarks on the coupling prescription of teleparallel gravity,” Gen. Rel. Grav. 36 (2004) 2525–2538, arXiv:gr-qc/0312093.
  221. Y. N. Obukhov and J. G. Pereira, “Lessons of spin and torsion: Reply to ‘Consistent coupling to Dirac fields in teleparallelism’,” Phys. Rev. D 69 (2004) 128502, arXiv:gr-qc/0406015.
  222. R. Aldrovandi and J. G. Pereira, Teleparallel Gravity: An Introduction. Springer, 2013.
  223. F. W. Hehl, P. Von Der Heyde, G. D. Kerlick, and J. M. Nester, “General Relativity with Spin and Torsion: Foundations and Prospects,” Rev. Mod. Phys. 48 (1976) 393–416.
  224. S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations. Cambridge University Press, 6, 2005.
  225. R. Aros, M. Contreras, and J. Zanelli, “Path integral measure for first order and metric gravities,” Class. Quant. Grav. 20 (2003) 2937–2944, arXiv:gr-qc/0303113.
  226. P. Minkowski, “μ→e⁢γ→𝜇𝑒𝛾\mu\to e\gammaitalic_μ → italic_e italic_γ at a Rate of One Out of 109superscript10910^{9}10 start_POSTSUPERSCRIPT 9 end_POSTSUPERSCRIPT Muon Decays?,” Phys. Lett. B 67 (1977) 421–428.
  227. T. Yanagida, “Horizontal gauge symmetry and masses of neutrinos,” Conf. Proc. C 7902131 (1979) 95–99.
  228. M. Gell-Mann, P. Ramond, and R. Slansky, “Complex Spinors and Unified Theories,” Conf. Proc. C 790927 (1979) 315–321, arXiv:1306.4669 [hep-th].
  229. R. N. Mohapatra and G. Senjanovic, “Neutrino Mass and Spontaneous Parity Nonconservation,” Phys. Rev. Lett. 44 (1980) 912.
  230. J. Schechter and J. W. F. Valle, “Neutrino Masses in SU(2) x U(1) Theories,” Phys. Rev. D 22 (1980) 2227.
  231. J. Schechter and J. W. F. Valle, “Neutrino Decay and Spontaneous Violation of Lepton Number,” Phys. Rev. D 25 (1982) 774.
  232. A. Boyarsky, A. Neronov, O. Ruchayskiy, and M. Shaposhnikov, “The Masses of active neutrinos in the nuMSM from X-ray astronomy,” JETP Lett. 83 (2006) 133–135, arXiv:hep-ph/0601098.
  233. T. Asaka, S. Blanchet, and M. Shaposhnikov, “The nuMSM, dark matter and neutrino masses,” Phys. Lett. B 631 (2005) 151–156, arXiv:hep-ph/0503065.
  234. T. Asaka and M. Shaposhnikov, “The ν𝜈\nuitalic_νMSM, dark matter and baryon asymmetry of the universe,” Phys. Lett. B 620 (2005) 17–26, arXiv:hep-ph/0505013.
  235. A. Boyarsky, O. Ruchayskiy, and M. Shaposhnikov, “The Role of sterile neutrinos in cosmology and astrophysics,” Ann. Rev. Nucl. Part. Sci. 59 (2009) 191–214, arXiv:0901.0011 [hep-ph].
  236. V. A. Kuzmin, V. A. Rubakov, and M. E. Shaposhnikov, “On the Anomalous Electroweak Baryon Number Nonconservation in the Early Universe,” Phys. Lett. B 155 (1985) 36.
  237. M. Fukugita and T. Yanagida, “Baryogenesis Without Grand Unification,” Phys. Lett. B 174 (1986) 45–47.
  238. M. Drewes, “The Phenomenology of Right Handed Neutrinos,” Int. J. Mod. Phys. E 22 (2013) 1330019, arXiv:1303.6912 [hep-ph].
  239. M. Drewes, B. Garbrecht, P. Hernandez, M. Kekic, J. Lopez-Pavon, J. Racker, N. Rius, J. Salvado, and D. Teresi, “ARS Leptogenesis,” Int. J. Mod. Phys. A 33 no. 05n06, (2018) 1842002, arXiv:1711.02862 [hep-ph].
  240. J. Klarić, M. Shaposhnikov, and I. Timiryasov, “Reconciling resonant leptogenesis and baryogenesis via neutrino oscillations,” Phys. Rev. D 104 no. 5, (2021) 055010, arXiv:2103.16545 [hep-ph].
  241. A. M. Abdullahi et al., “The present and future status of heavy neutral leptons,” J. Phys. G 50 no. 2, (2023) 020501, arXiv:2203.08039 [hep-ph].
  242. A. Garzilli, A. Magalich, T. Theuns, C. S. Frenk, C. Weniger, O. Ruchayskiy, and A. Boyarsky, “The Lyman-α𝛼\alphaitalic_α forest as a diagnostic of the nature of the dark matter,” Mon. Not. Roy. Astron. Soc. 489 no. 3, (2019) 3456–3471, arXiv:1809.06585 [astro-ph.CO].
  243. A. Garzilli, A. Magalich, O. Ruchayskiy, and A. Boyarsky, “How to constrain warm dark matter with the Lyman-α𝛼\alphaitalic_α forest,” Mon. Not. Roy. Astron. Soc. 502 no. 2, (2021) 2356–2363, arXiv:1912.09397 [astro-ph.CO].
  244. F. L. Bezrukov and M. Shaposhnikov, “The Standard Model Higgs boson as the inflaton,” Phys. Lett. B 659 (2008) 703–706, arXiv:0710.3755 [hep-th].
  245. F. Bauer and D. A. Demir, “Higgs-Palatini Inflation and Unitarity,” Phys. Lett. B 698 (2011) 425–429, arXiv:1012.2900 [hep-ph].
  246. M. Shaposhnikov, A. Shkerin, and S. Zell, “Quantum Effects in Palatini Higgs Inflation,” JCAP 07 (2020) 064, arXiv:2002.07105 [hep-ph].
  247. G. K. Karananas, M. Shaposhnikov, and S. Zell, “Field redefinitions, perturbative unitarity and Higgs inflation,” JHEP 06 (2022) 132, arXiv:2203.09534 [hep-ph].
  248. A. Poisson, I. Timiryasov, and S. Zell, “Critical Points in Palatini Higgs Inflation with Small Non-Minimal Coupling,” arXiv:2306.03893 [hep-ph].
  249. S. Weinberg, “Infrared photons and gravitons,” Phys. Rev. 140 (1965) B516–B524.
  250. D. Carney, L. Chaurette, D. Neuenfeld, and G. W. Semenoff, “Infrared quantum information,” Phys. Rev. Lett. 119 no. 18, (2017) 180502, arXiv:1706.03782 [hep-th].
  251. C. Gómez, R. Letschka, and S. Zell, “The Scales of the Infrared,” JHEP 09 (2018) 115, arXiv:1807.07079 [hep-th].
  252. S. Weinberg, “ Ultraviolet divergences in quantum theories of gravitation,” in General Relativity: An Einstein Centenary Survey, pp. 790–831. University Press, Cambridge, 1980.
  253. J. Berges, N. Tetradis, and C. Wetterich, “Nonperturbative renormalization flow in quantum field theory and statistical physics,” Phys. Rept. 363 (2002) 223–386, arXiv:hep-ph/0005122.
  254. M. Reuter and H. Weyer, “Running Newton constant, improved gravitational actions, and galaxy rotation curves,” Phys. Rev. D 70 (2004) 124028, arXiv:hep-th/0410117.
  255. G. Dvali and C. Gomez, “Quantum Compositeness of Gravity: Black Holes, AdS and Inflation,” JCAP 01 (2014) 023, arXiv:1312.4795 [hep-th].
  256. G. Dvali, C. Gomez, and S. Zell, “Quantum Break-Time of de Sitter,” JCAP 06 (2017) 028, arXiv:1701.08776 [hep-th].
  257. M. Michel and S. Zell, “The Timescales of Quantum Breaking,” Fortschr. Phys. 71 (2023) 2300163, arXiv:2306.09410 [quant-ph].
  258. M. E. Peskin and D. V. Schroeder, An Introduction to quantum field theory. Addison-Wesley, Reading, USA, 1995.
  259. V. A. Rubakov, Classical theory of gauge fields. Princeton University Press, Princeton, New Jersey, 5, 2002.
  260. V.-M. Enckell, K. Enqvist, S. Rasanen, and L.-P. Wahlman, “Inflation with R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT term in the Palatini formalism,” JCAP 02 (2019) 022, arXiv:1810.05536 [gr-qc].
  261. I. Antoniadis, A. Karam, A. Lykkas, and K. Tamvakis, “Palatini inflation in models with an R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT term,” JCAP 11 (2018) 028, arXiv:1810.10418 [gr-qc].
  262. T. Tenkanen, “Minimal Higgs inflation with an R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT term in Palatini gravity,” Phys. Rev. D 99 no. 6, (2019) 063528, arXiv:1901.01794 [astro-ph.CO].
  263. I. D. Gialamas and A. B. Lahanas, “Reheating in R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT Palatini inflationary models,” Phys. Rev. D 101 no. 8, (2020) 084007, arXiv:1911.11513 [gr-qc].
  264. I. Antoniadis, A. Karam, A. Lykkas, T. Pappas, and K. Tamvakis, “Single-field inflation in models with an R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT term,” PoS CORFU2019 (2020) 073, arXiv:1912.12757 [gr-qc].
  265. A. Lloyd-Stubbs and J. McDonald, “Sub-Planckian ϕ2superscriptitalic-ϕ2\phi^{2}italic_ϕ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT inflation in the Palatini formulation of gravity with an R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT term,” Phys. Rev. D 101 no. 12, (2020) 123515, arXiv:2002.08324 [hep-ph].
  266. I. Antoniadis, A. Lykkas, and K. Tamvakis, “Constant-roll in the Palatini-R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT models,” JCAP 04 no. 04, (2020) 033, arXiv:2002.12681 [gr-qc].
  267. N. Das and S. Panda, “Inflation and Reheating in f(R,h) theory formulated in the Palatini formalism,” JCAP 05 (2021) 019, arXiv:2005.14054 [gr-qc].
  268. I. D. Gialamas, A. Karam, and A. Racioppi, “Dynamically induced Planck scale and inflation in the Palatini formulation,” JCAP 11 (2020) 014, arXiv:2006.09124 [gr-qc].
  269. K. Dimopoulos and S. Sánchez López, “Quintessential inflation in Palatini f⁢(R)𝑓𝑅f(R)italic_f ( italic_R ) gravity,” Phys. Rev. D 103 no. 4, (2021) 043533, arXiv:2012.06831 [gr-qc].
  270. A. Karam, E. Tomberg, and H. Veermäe, “Tachyonic preheating in Palatini R 2 inflation,” JCAP 06 (2021) 023, arXiv:2102.02712 [astro-ph.CO].
  271. A. Lykkas and K. Tamvakis, “Extended interactions in the Palatini-R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT inflation,” JCAP 08 (2021) 043, arXiv:2103.10136 [gr-qc].
  272. I. D. Gialamas, A. Karam, T. D. Pappas, and V. C. Spanos, “Scale-invariant quadratic gravity and inflation in the Palatini formalism,” Phys. Rev. D 104 no. 2, (2021) 023521, arXiv:2104.04550 [astro-ph.CO].
  273. J. Annala and S. Rasanen, “Inflation with R (α𝛼\alphaitalic_αβ𝛽\betaitalic_β) terms in the Palatini formulation,” JCAP 09 (2021) 032, arXiv:2106.12422 [astro-ph.CO].
  274. C. Dioguardi, A. Racioppi, and E. Tomberg, “Slow-roll inflation in Palatini F(R) gravity,” JHEP 06 (2022) 106, arXiv:2112.12149 [gr-qc].
  275. K. Dimopoulos, A. Karam, S. Sánchez López, and E. Tomberg, “Modelling Quintessential Inflation in Palatini-Modified Gravity,” Galaxies 10 no. 2, (2022) 57, arXiv:2203.05424 [gr-qc].
  276. K. Dimopoulos, A. Karam, S. Sánchez López, and E. Tomberg, “Palatini R 22{}^{2}start_FLOATSUPERSCRIPT 2 end_FLOATSUPERSCRIPT quintessential inflation,” JCAP 10 (2022) 076, arXiv:2206.14117 [gr-qc].
  277. A. B. Lahanas, “Issues in Palatini R2 inflation: Bounds on the reheating temperature,” Phys. Rev. D 106 no. 12, (2022) 123530, arXiv:2210.00837 [gr-qc].
  278. S. Panda, A. Rana, and R. Thakur, “Constant-roll inflation in modified f⁢(R,ϕ)𝑓𝑅italic-ϕf(R,\phi)italic_f ( italic_R , italic_ϕ ) gravity model using Palatini formalism,” Eur. Phys. J. C 83 no. 4, (2023) 297, arXiv:2212.00472 [gr-qc].
  279. J. T. Wheeler, “Sources of torsion in Poincarè gauge gravity,” Eur. Phys. J. C 83 no. 7, (2023) 665, arXiv:2303.14921 [hep-th].
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