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Unimodular Jackiw-Teitelboim gravity and de Sitter quantum cosmology

Bruno Alexandre1,*, Altay Etkin2,†, and Farbod-Sayyed Rassouli3,‡

  • 1Abdus Salam Centre for Theoretical Physics, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
  • 2School of Mathematical Sciences and STAG Research Centre, University of Southampton, Highfield Campus, Southampton SO17 1BJ, United Kingdom
  • 3School of Physics and Astronomy and Nottingham Centre of Gravity, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

  • *Contact author: bruno.alexandre20@imperial.ac.uk
  • †Contact author: a.etkin@soton.ac.uk
  • ‡Contact author: sayyed.rassouli@nottingham.ac.uk
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Phys. Rev. D 111, 124050 – Published 25 June, 2025

DOI: https://doi.org/10.1103/cmbb-cwlj

Abstract

In this work, we show that a gauge-theoretic description of Jackiw-Teitelboim (JT) gravity naturally yields a Henneaux-Teitelboim (HT) unimodular gravity via a central extension of its isometry group, valid for both flat and curved two-dimensional spacetimes. HT gravity introduces a unimodular time canonically conjugate to the cosmological constant, serving as a physical time in quantum cosmology. By studying the minisuperspace reduction of HT2 gravity, the Wheeler-DeWitt equation becomes a Schrödinger-like equation, giving a consistent and unitary quantum theory. Analysis of the wave function’s probability density reveals a quantum distribution for the scale factor a, offering a quantum perspective on the expansion and contraction of the Universe. In this perspective, the possibility of reaching the singular point a=0 signals that topology change could occur. Finally, we give a consistent quantum description of unimodular time that aligns seamlessly with Page-Wootters formulation of quantum mechanics, where quantum correlations between unimodular time and JT gravity are studied in HT2 quantum cosmology.

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References (81)

  1. K. V. Kuchar, Phys. Rev. D 43, 3332 (1991).
  2. L. Bombelli, W. E. Couch, and R. J. Torrence, Phys. Rev. D 44, 2589 (1991).
  3. A. Daughton, J. Louko, and R. D. Sorkin, in Proceedings of the 5th Canadian Conference on General Relativity and Relativistic Astrophysics (5CCGRRA) (1993).
  4. R. D. Sorkin, Int. J. Theor. Phys. 33, 523 (1994).
  5. A. Daughton, J. Louko, and R. D. Sorkin, Phys. Rev. D 58, 084008 (1998).
  6. A. Einstein, Do gravitational fields play an essential part in the structure of the elementary particles of matter? in The Principle of Relativity, edited by A. Einstein (Dover Books on Physics, New York, 1952), pp. 189–198.
  7. S. Weinberg, Rev. Mod. Phys. 61, 1 (1989).
  8. M. Henneaux and C. Teitelboim, Phys. Lett. B 222, 195 (1989).
  9. W. G. Unruh, Phys. Rev. D 40, 1048 (1989).
  10. L. Smolin, Phys. Rev. D 80, 084003 (2009).
  11. L. Smolin, Phys. Rev. D 84, 044047 (2011).
  12. N. Kaloper and A. Padilla, Phys. Rev. Lett. 112, 091304 (2014).
  13. J. M. Fernández Cristóbal, Ann. Phys. (N.Y.) 350, 441 (2014).
  14. A. Padilla and I. D. Saltas, Eur. Phys. J. C 75, 561 (2015).
  15. R. Bufalo, M. Oksanen, and A. Tureanu, Eur. Phys. J. C 75, 477 (2015).
  16. N. Kaloper, A. Padilla, D. Stefanyszyn, and G. Zahariade, Phys. Rev. Lett. 116, 051302 (2016).
  17. R. Percacci, Found. Phys. 48, 1364 (2018).
  18. L. Lombriser, Phys. Lett. B 797, 134804 (2019).
  19. R. Carballo-Rubio, L. J. Garay, and G. García-Moreno, Classical Quantum Gravity 39, 243001 (2022).
  20. S. Alexander, J. Magueijo, and L. Smolin, Symmetry 11, 1130 (2019).
  21. J. Magueijo, T. Zlosnik, and S. Speziale, Phys. Rev. D 102, 064006 (2020).
  22. J. Magueijo, Phys. Lett. B 820, 136487 (2021).
  23. J. Magueijo, Phys. Rev. D 106, 084021 (2022).
  24. P. Jiroušek and A. Vikman, J. Cosmol. Astropart. Phys. 04 (2019) 004.
  25. P. Jiroušek, K. Shimada, A. Vikman, and M. Yamaguchi, J. Cosmol. Astropart. Phys. 04 (2021) 028.
  26. A. Vikman, in Proceedings of the 55th Rencontres de Moriond on Gravitation (2021).
  27. B. Alexandre and J. a. Magueijo, Phys. Rev. D 107, 063501 (2023).
  28. B. Alexandre, R. Isichei, and J. a. Magueijo, Phys. Rev. D 108, 023526 (2023).
  29. J. Magueijo and R. Isichei, Phys. Rev. D 107, 023526 (2023).
  30. V. Chandrasekaran, R. Longo, G. Penington, and E. Witten, J. High Energy Phys. 02 (2023) 082.
  31. E. Witten, Proc. Symp. Pure Math. 107, 247 (2024).
  32. C. Gomez, arXiv:2302.14747.
  33. C. Gomez, arXiv:2304.11845.
  34. E. Witten, J. High Energy Phys. 03 (2024) 077.
  35. D. N. Page and W. K. Wootters, Phys. Rev. D 27, 2885 (1983).
  36. W. K. Wootters, Int. J. Theor. Phys. 23, 701 (1984).
  37. V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. D 92, 045033 (2015).
  38. A. R. H. Smith and M. Ahmadi, Quantum 3, 160 (2019).
  39. P. A. Hohn, A. R. H. Smith, and M. P. E. Lock, Phys. Rev. D 104, 066001 (2021).
  40. J. De Vuyst, S. Eccles, P. A. Hohn, and J. Kirklin, arXiv:2405.00114.
  41. J. De Vuyst, S. Eccles, P. A. Hohn, and J. Kirklin, arXiv:2412.15502.
  42. D. Cangemi and R. Jackiw, Phys. Rev. Lett. 69, 233 (1992).
  43. R. Jackiw, in Proceedings of the 19th International Colloquium on Group Theoretical Methods in Physics (1992).
  44. D. Cangemi, Phys. Lett. B 297, 261 (1992).
  45. G. Grignani and G. Nardelli, Nucl. Phys. B412, 320 (1994).
  46. D. Cangemi and R. Jackiw, Phys. Lett. B 299, 24 (1993).
  47. S. K. Kim, K. S. Soh, and J.-H. Yee, Phys. Rev. D 47, 4433 (1993).
  48. S. K. Kim, K. S. Soh, and J.-H. Yee, Phys. Lett. B 300, 223 (1993).
  49. D. Cangemi and R. Jackiw, Ann. Phys. (N.Y.) 225, 229 (1993).
  50. D. Cangemi and G. V. Dunne, Phys. Rev. D 48, 5721 (1993).
  51. R. Jackiw, in International Conference on Interface Between Physics and Mathematics (IPM 93) (Part 1: Plenary Session, 6-10 Sep 1993: Part 2: Tutorial Lectures, 13-17 Sep 1993) (1993), pp. 116–129.
  52. K. Hammer, P. Jirousek, and A. Vikman, arXiv:2001.03169.
  53. A. Etkin, J. Magueijo, and F.-S. Rassouli, Phys. Lett. B 855, 138810 (2024).
  54. H. A. González, D. Grumiller, and J. Salzer, J. High Energy Phys. 05 (2018) 083.
  55. H. R. Afshar, J. High Energy Phys. 02 (2020) 126.
  56. H. Afshar, H. A. González, D. Grumiller, and D. Vassilevich, Phys. Rev. D 101, 086024 (2020).
  57. V. Godet and C. Marteau, J. High Energy Phys. 07 (2021) 138.
  58. H. Afshar and B. Oblak, J. High Energy Phys. 11 (2022) 172.
  59. A. Kar, L. Lamprou, C. Marteau, and F. Rosso, J. High Energy Phys. 03 (2023) 249.
  60. F. Rosso, J. High Energy Phys. 02 (2023) 037.
  61. H. Afshar and N. Aghamir, J. High Energy Phys. 03 (2023) 009.
  62. C. G. Callan, Jr., S. B. Giddings, J. A. Harvey, and A. Strominger, Phys. Rev. D 45, R1005 (1992).
  63. V. Godet and C. Marteau, J. High Energy Phys. 12 (2020) 020.
  64. C. Teitelboim, Phys. Lett. B 126, 41 (1983).
  65. R. Jackiw, Nucl. Phys. B252, 343 (1985).
  66. K. Isler and C. A. Trugenberger, Phys. Rev. Lett. 63, 834 (1989).
  67. A. H. Chamseddine and D. Wyler, Phys. Lett. B 228, 75 (1989).
  68. A. Kar, L. Lamprou, C. Marteau, and F. Rosso, Phys. Rev. Lett. 129, 201601 (2022).
  69. J. Maldacena, G. J. Turiaci, and Z. Yang, J. High Energy Phys. 01 (2021) 139.
  70. J. Cotler and K. Jensen, J. High Energy Phys. 12 (2021) 089.
  71. J. Cotler, K. Jensen, and A. Maloney, J. High Energy Phys. 06 (2020) 048.
  72. U. Moitra, S. K. Sake, and S. P. Trivedi, J. High Energy Phys. 06 (2022) 138.
  73. J. Cotler and K. Jensen, Phys. Rev. Lett. 131, 211601 (2023).
  74. K. K. Nanda, S. K. Sake, and S. P. Trivedi, J. High Energy Phys. 02 (2024) 145.
  75. J. Cotler and K. Jensen, J. High Energy Phys. 12 (2024) 016.
  76. D. Anninos, C. Baracco, and B. Mühlmann, J. Cosmol. Astropart. Phys. 10 (2024) 031.
  77. J. Held and H. Maxfield, arXiv:2410.14824.
  78. W. Buchmuller, A. Hebecker, and A. Westphal, arXiv:2412.09211.
  79. M. Honda, H. Matsui, K. Numajiri, and K. Okabayashi, arXiv:2412.20398.
  80. N. Iizuka and S. K. Sake, arXiv:2501.02614.
  81. I. Dey, K. K. Nanda, A. Roy, S. K. Sake, and S. P. Trivedi, arXiv:2501.03148.

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Phys. Rev. D 111, 124050– Published 25 June, 2025
  • Received 13 March 2025
  • Accepted 10 June 2025
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