- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Matter-antimatter asymmetry in a rotating universe: Dirac spinors in axisymmetric Bianchi IX cosmology

Tatevik Vardanyan*

  • *Contact author: tatevik@thp.uni-koeln.de
PDF

Phys. Rev. D 113, 023536 – Published 22 January, 2026

DOI: https://doi.org/10.1103/djsl-k718

Abstract

The standard ΛCDM model, based on a highly symmetric Friedmann-Lemaître-Robertson-Walker (FLRW) geometry, successfully explains many observations but faces unresolved issues, motivating the exploration of alternative cosmological frameworks. We investigate the influence of spacetime geometry on the matter-antimatter asymmetry of the Universe within the Bianchi IX cosmological model. Motivated by early-Universe dynamics, potential contributions to cosmological angular momentum, and the axisymmetric Bianchi IX model’s relevance to certain cosmic microwave background anomalies, we formulate the Dirac field in this background. Starting with a Lagrangian formalism, we derive the Dirac equation and develop the harmonic analysis of spinor fields, extending previous treatments in the mixmaster universe. We solve the Dirac equations for nonrotating and rotating axisymmetric Bianchi IX spacetimes using a fixed-background approximation. We find that spatial anisotropy induces spin-dependent energy splittings, while global rotation produces particle-antiparticle asymmetries in the energy spectra, effects absent in FLRW models. These results demonstrate that spacetime geometry alone can imprint nontrivial structure on particle spectra, suggesting that geometric effects may contribute to the matter-antimatter asymmetry.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (91)

  1. C. Bennett et al., Astrophys. J. 583, 1 (2003).
  2. Planck Collaboration, Astron. Astrophys. 641, A6 (2020); Planck Collaboration652, C4(E) (2021).
  3. J. K. Adelman-McCarthy et al., Astrophys. J. Suppl. Ser. 162, 38 (2006).
  4. L. Perivolaropoulos and F. Skara, New Astron. Rev. 95, 101659 (2022).
  5. A. D. Popolo and M. L. Delliou, Galaxies 5, 17 (2017).
  6. P. K. Aluri et al., Classical Quantum Gravity 40, 094001 (2023).
  7. V. A. Belinskii, I. M. Khalatnikov, and E. M. Lifshitz, Adv. Phys. 19, 525 (1970).
  8. V. A. Belinskii, I. M. Khalatnikov, and E. M. Lifshitz, Adv. Phys. 31, 639 (1982).
  9. L.-X. Li, Gen. Relativ. Gravit. 30, 497 (1998).
  10. I. Ciufolini and J. A. Wheeler, Gravitation and Inertia (Princeton University Press, Princeton, NJ, 1995).
  11. G. W. Gibbons, Phys. Lett. 84B, 431 (1979).
  12. G. W. Gibbons, Ann. Phys. (N.Y.) 125, 98 (1980).
  13. O. Obregon and M. Ryan, J. Math. Phys. (N.Y.) 22, 623 (1981).
  14. T. Damour and P. Spindel, Phys. Rev. D 83, 123520 (2011).
  15. P. Sundell and T. Koivisto, Phys. Rev. D 92, 123529 (2015).
  16. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1982).
  17. T. Vardanyan, Exploring matter-antimatter asymmetry in a rotating universe, Ph.D. thesis, University of Cologne, 2025, https://kups.ub.uni-koeln.de/78502/.
  18. J. S. Dowker and D. F. Pettengill, J. Phys. A 7, 1527 (1974).
  19. B. L. Hu, Phys. Rev. D 8, 1048 (1973).
  20. J. C. Mather et al., Astrophys. J. Lett. 354, L37 (1990).
  21. C. J. Copi, D. Huterer, D. J. Schwarz, and G. D. Starkman, Adv. Astron. 2010, 847541 (2010).
  22. D. J. Schwarz, C. J. Copi, D. Huterer, and G. D. Starkman, Classical Quantum Gravity 33, 184001 (2016).
  23. C. L. Bennett, R. S. Hill, G. Hinshaw, D. Larson, K. M. Smith, J. Dunkley et al., Astrophys. J. Suppl. Ser. 192, 17 (2011).
  24. E. Abdalla et al., J. High Energy Astrophys. 34, 49 (2022).
  25. B. Famaey and S. McGaugh, Living Rev. Relativity 15, 10 (2012).

  26. D. Blas, Introduction to dark matter, Durham University (2019), available at https://conference.ippp.dur.ac.uk/event/1291/attachments/6076/8176/DM_Blas1.pdf.

  27. K. Freese, EAS Publ. Ser. 36, 113 (2009).
  28. L. Bergström, Rep. Prog. Phys. 63, 793 (2000).
  29. G. Bertone, D. Hooper, and J. Silk, Phys. Rep. 405, 279 (2005).
  30. F. C. van den Bosch, A. Burkert, and R. A. Swaters, Mon. Not. R. Astron. Soc. 326, 1205 (2001).
  31. M. Viel, G. D. Becker, J. S. Bolton, and M. G. Haehnelt, Phys. Rev. D 88, 043502 (2013).
  32. J. S. Bullock and M. Boylan-Kolchin, Annu. Rev. Astron. Astrophys. 55, 343 (2017).
  33. W. Hu, R. Barkana, and A. Gruzinov, Phys. Rev. Lett. 85, 1158 (2000).
  34. G. Steigman, Annu. Rev. Astron. Astrophys. 14, 339 (1976).
  35. G. Steigman, J. Cosmol. Astropart. Phys. 10 (2008) 001.
  36. V. A. Rubakov and D. S. Gorbunov, Introduction to the Theory of the Early Universe: Hot Big Bang Theory, 2nd ed. (World Scientific, Singapore, 2017).
  37. L. Canetti, M. Drewes, and M. Shaposhnikov, New J. Phys. 14, 095012 (2012).
  38. G. Steigman, Proc. Sci., NICXI2010 (2010) 001 [arXiv:1008.4765].
  39. E. Komatsu et al. (WMAP Collaboration), Astrophys. J. Suppl. Ser. 192, 18 (2011).
  40. A. D. Sakharov, JETP Lett. 6, 24 (1967).
  41. V. A. Kuzmin, V. A. Rubakov, and M. E. Shaposhnikov, Phys. Lett. B 155B, 36 (1985).
  42. H. Davoudiasl, R. Kitano, G. D. Kribs, H. Murayama, and P. J. Steinhardt, Phys. Rev. Lett. 93, 201301 (2004).
  43. M. Dine and A. Kusenko, Rev. Mod. Phys. 76, 1 (2003).
  44. V. A. Rubakov and M. E. Shaposhnikov, Usp. Fiz. Nauk 166, 493 (1996).
  45. A. Riotto and M. Trodden, Annu. Rev. Nucl. Part. Sci. 49, 35 (1999).
  46. V. A. Rubakov and D. S. Gorbunov, Introduction to the Theory of the Early Universe: Cosmological Perturbations and Inflationary Theory (World Scientific, Singapore, 2011).
  47. G. F. R. Ellis, R. Maartens, and M. A. H. MacCallum, Relativistic Cosmology (Cambridge University Press, Cambridge, England, 2012).
  48. A. A. Grib, S. G. Mamaev, and V. M. Mostepanenko, Vacuum Quantum Effects in Strong Fields (Friedmann Laboratory Publishing, St. Petersburg, 1994).
  49. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 4th ed. (Pergamon Press, Oxford, 1975).
  50. E. Lifshitz, J. Phys. (USSR) 10, 116 (1946).
  51. C. W. Misner, Phys. Rev. Lett. 22, 1071 (1969).
  52. M. P. Ryan, Ann. Phys. (N.Y.) 65, 506 (1971).
  53. M. P. Ryan, Ann. Phys. (N.Y.) 68, 541 (1971).
  54. B. L. Hu and L. Parker, Phys. Rev. D 17, 933 (1978).
  55. R. van den Hoogen and I. Olasagasti, Phys. Rev. D 59, 107302 (1999).
  56. G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2738 (1977).
  57. S. W. Hawking and I. G. Moss, Phys. Lett. 110B, 35 (1982).
  58. R. M. Wald, Phys. Rev. D 28, 2118 (1983).
  59. P. J. E. Peebles, The Large-Scale Structure of the Universe (Princeton University Press, Princeton, NJ, 1980).
  60. G. Gamow, Nature (London) 158, 549 (1946).
  61. K. Gödel, Kurt Gödel: Collected Works (Oxford University Press, Oxford, 1990).
  62. C. B. Collins and S. W. Hawking, Mon. Not. R. Astron. Soc. 162, 307 (1973).
  63. Y. N. Obukhov, in Colloquium on Cosmic Rotation, edited by M. Scherfner et al. (Wissenschaft und Technik Verlag, Berlin, 2000), pp. 23–96.
  64. W. Godłowski, M. Szydłowski, P. Flin, and M. Biernacka, Gen. Relativ. Gravit. 35, 907 (2003).
  65. W. Godłowski, Int. J. Mod. Phys. D 20, 1643 (2011).
  66. P. Wang, N. I. Libeskind, E. Tempel, X. Kang, and Q. Guo, Nat. Astron. 5, 839 (2021).
  67. H. S. Hwang and M. G. Lee, Astrophys. J. 662, 236 (2007).
  68. C. Kiefer, Quantum Gravity, 4th ed. (Oxford University Press, Oxford, 2025).
  69. R. T. Jantzen, Proceedings of the International School Enrico Fermi, Course LXXXVI (1982) on Gamov Cosmology (1987), arXiv:gr-qc/0102035.
  70. C. W. Misner, Astrophys. J. 151, 431 (1968).
  71. M. P. Ryan, Hamiltonian Cosmology (Springer, Berlin, 1972).
  72. M. P. Ryan and L. C. Shepley, Homogeneous Relativistic Cosmologies (Princeton University Press, Princeton, NJ, 1975).
  73. R. T. Jantzen, Commun. Math. Phys. 64, 211 (1979).
  74. R. T. Jantzen and C. Uggla, J. Math. Phys. (N.Y.) 40, 353 (1999).
  75. L. E. Parker and D. J. Toms, Quantum Field Theory in Curved Spacetime (Cambridge University Press, Cambridge, England, 2009).
  76. C. Kiefer, N. Kwidzinski, and W. Piechocki, Eur. Phys. J. C 78, 691 (2018).
  77. L. Parker, Phys. Rev. D 3, 346 (1971).
  78. M. Srednicki, Quantum Field Theory, 1st ed. (Cambridge University Press, Cambridge, England, 2007).
  79. J. J. Sakurai, Modern Quantum Mechanics, revised ed. ed. (Addison-Wesley, Boston, 1993).
  80. E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, Reading, MA, 1990).
  81. I. M. Gel’fand, R. A. Minlos, and Z. Y. Shapiro, Representations of the Rotation and Lorentz Groups and Their Applications (Pergamon Press, New York, 1963), translated from Predstavleniya gruppy vrashchenii i gruppy Lorentsa, originally published by Fizmatgiz, Moscow, 1958.
  82. E. C. Kemble, The Fundamental Principles of Quantum Mechanics (McGraw-Hill, New York and London, 1937).
  83. E. P. Wigner, Group Theory and its Application to the Quantum Mechanics of Atomic Spectra (Academic Press, New York, 1959).
  84. J. N. Goldberg, A. J. Macfarlane, E. T. Newman, F. Rohrlich, and E. C. G. Sudarshan, J. Math. Phys. (N.Y.) 8, 2155 (1967).
  85. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, NJ, 1957).
  86. A. S. Davydov, Quantum Mechanics (Pergamon Press, Oxford, 1965).
  87. C. V. Winter, Physica (Amsterdam) 20, 274 (1954).
  88. G. W. King, R. M. Hainer, and P. C. Crossl, J. Chem. Phys. 11, 27 (1943).
  89. R. S. Mulliken, Phys. Rev. 59, 873 (1941).
  90. L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, 3rd ed., Course of Theoretical Physics Vol. 3 (Butterworth-Heinemann, Oxford, 1981).
  91. J. H. V. Vleck, Phys. Rev. 33, 467 (1929).

Outline

Information

Phys. Rev. D 113, 023536– Published 22 January, 2026
  • Received 18 July 2025
  • Accepted 2 January 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation