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Cosmology of gravitational axions

Stephon Alexander1,*, Gregory Gabadadze2,†, Leah Jenks3,4,‡, and Nicolás Yunes5,§

  • 1Brown Theoretical Physics Center and Department of Physics, Brown University, Providence, Rhode Island 02903, USA
  • 2Center for Cosmology and Particle Physics, Department of Physics, New York University, New York City, New York 10003, USA
  • 3Kavli Institute for Cosmological Physics, University of Chicago, Chicago, Illinois 60637, USA
  • 4William H. Miller III Department of Physics & Astronomy, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218, USA
  • 5Illinois Center for Advanced Studies of the Universe, Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

  • *Contact author: stephon_alexander@brown.edu
  • †Contact author: gg32@nyu.edu
  • ‡Contact author: ljenks3@jh.edu
  • §Contact author: nyunes@illinois.edu
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Phys. Rev. D 114, 023529 – Published 13 July, 2026

DOI: https://doi.org/10.1103/yst4-cr4c

Abstract

We show how a mass term for gravitational axions (“gravi-axions”) with a Chern-Simons coupling to gravity can naturally arise due to nonperturbative contributions from Euclidean wormholes, breaking the continuous shift symmetry of the standard theory. The induced mass can be generated in a cosmologically relevant range to be the dark matter or dark energy of the universe for a reasonable and well-motivated range of the symmetry breaking scale. Upon generating the gravi-axion mass term, we discuss the cosmology of the theory. We find that the gravi-axion can be produced to be the dominant dark matter component via misalignment or gravitational particle production, and that in a different regime, the gravi-axion can act as dynamical dark energy. We discuss gravi-axion decay into gravitons as a potential observational window for this theory. Finally, we find that, for late-time, astrophysical compact objects, cosmologically relevant gravi-axions behave as minimally coupled, massive scalar fields.

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References (122)

  1. R. D. Peccei and Helen R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38, 1440 (1977).
  2. R. D. Peccei and Helen R. Quinn, Constraints imposed by CP conservation in the presence of instantons, Phys. Rev. D 16, 1791 (1977).
  3. Steven Weinberg, A new light boson?, Phys. Rev. Lett. 40, 223 (1978).
  4. Frank Wilczek, Problem of strong P and T invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978).
  5. Jihn E. Kim, Weak interaction singlet and strong CP invariance, Phys. Rev. Lett. 43, 103 (1979).
  6. Mikhail A. Shifman, A. I. Vainshtein, and Valentin I. Zakharov, Can confinement ensure natural CP invariance of strong interactions?, Nucl. Phys. B166, 493 (1980).
  7. A. R. Zhitnitsky, On possible suppression of the axion hadron interactions. (In Russian), Sov. J. Nucl. Phys. 31, 260 (1980).
  8. Michael Dine, Willy Fischler, and Mark Srednicki, A simple solution to the strong CP problem with a harmless axion, Phys. Lett. 104B, 199 (1981).
  9. Peter Svrcek and Edward Witten, Axions in string theory, J. High Energy Phys. 06 (2006) 051.
  10. Eduard Masso and Ramon Toldra, On a light spinless particle coupled to photons, Phys. Rev. D 52, 1755 (1995).
  11. Eduard Masso, Axions and axion like particles, Nucl. Phys. B, Proc. Suppl. 114, 67 (2003).
  12. Joseph P. Conlon, The QCD axion and moduli stabilisation, J. High Energy Phys. 05 (2006) 078.
  13. Asimina Arvanitaki, Savas Dimopoulos, Sergei Dubovsky, Nemanja Kaloper, and John March-Russell, String axiverse, Phys. Rev. D 81, 123530 (2010).
  14. Pierre Sikivie, Axion cosmology, Lect. Notes Phys. 741, 19 (2008).
  15. David J. E. Marsh, Axion cosmology, Phys. Rep. 643, 1 (2016).
  16. John Preskill, Mark B. Wise, and Frank Wilczek, Cosmology of the invisible axion, Phys. Lett. 120B, 127 (1983).
  17. L. F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. 120B, 133 (1983).
  18. Michael Dine and Willy Fischler, The not so harmless axion, Phys. Lett. 120B, 137 (1983).
  19. P. Sikivie, Experimental tests of the invisible axion, Phys. Rev. Lett. 51, 1415 (1983); 52, 695(E) (1984).
  20. J. Ipser and P. Sikivie, Are galactic halos made of axions?, Phys. Rev. Lett. 50, 925 (1983).
  21. Wayne Hu, Rennan Barkana, and Andrei Gruzinov, Cold and fuzzy dark matter, Phys. Rev. Lett. 85, 1158 (2000).
  22. Lam Hui, Wave dark matter, Annu. Rev. Astron. Astrophys. 59, 247 (2021).
  23. Joshua A. Frieman, Christopher T. Hill, Albert Stebbins, and Ioav Waga, Cosmology with ultralight pseudo Nambu-Goldstone bosons, Phys. Rev. Lett. 75, 2077 (1995).
  24. Sean M. Carroll, Quintessence and the rest of the world, Phys. Rev. Lett. 81, 3067 (1998).
  25. Arthur Lue, Li-Min Wang, and Marc Kamionkowski, Cosmological signature of new parity violating interactions, Phys. Rev. Lett. 83, 1506 (1999).
  26. R. Jackiw and S. Y. Pi, Chern-Simons modification of general relativity, Phys. Rev. D 68, 104012 (2003).
  27. S. Alexander and N. Yunes, Chern-Simons modified general relativity, Phys. Rep. 480, 1 (2009).
  28. Luis Alvarez-Gaume and Edward Witten, Gravitational anomalies, Nucl. Phys. B234, 269 (1984).
  29. J. Polchinski, String Theory. Vol. 2: Superstring Theory and Beyond, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2007).
  30. Stephon H. S. Alexander, Michael E. Peskin, and M. M. Sheikh-Jabbari, Leptogenesis from gravity waves in models of inflation, Phys. Rev. Lett. 96, 081301 (2006).
  31. Michael B. Green, J. H. Schwarz, and Edward Witten, Superstring Theory. Vol. 2: Loop Amplitides, Anomalies and Phenomenology (Cambridge University Press, Cambridge, England, 1987).
  32. Stephon H. S. Alexander and Gates, S. James, Jr., Can the string scale be related to the cosmic baryon asymmetry?, J. Cosmol. Astropart. Phys. 06 (2006) 018.
  33. Stephon Alexander, Gregory Gabadadze, Leah Jenks, and Nicolás Yunes, Chern-Simons caps for rotating black holes, Phys. Rev. D 104, 064033 (2021).
  34. Stephon Alexander and Cyril Creque-Sarbinowski, UV completions of Chern-Simons gravity, Phys. Rev. D 108, 104046 (2023).
  35. Daniel Grumiller and Nicolas Yunes, How do black holes spin in Chern-Simons modified gravity?, Phys. Rev. D 77, 044015 (2008).
  36. Tetsuya Shiromizu and Kentaro Tanabe, Static spacetimes with/without black holes in dynamical Chern-Simons gravity, Phys. Rev. D 87, 081504 (2013).
  37. Nicolas Yunes and Frans Pretorius, Dynamical Chern-Simons modified gravity. I. Spinning black holes in the slow-rotation approximation, Phys. Rev. D 79, 084043 (2009).
  38. Vitor Cardoso and Leonardo Gualtieri, Perturbations of Schwarzschild black holes in dynamical Chern-Simons modified gravity, Phys. Rev. D 80, 064008 (2009); 81, 089903(E) (2010).
  39. Kent Yagi, Nicolas Yunes, and Takahiro Tanaka, Slowly rotating black holes in dynamical Chern-Simons gravity: Deformation quadratic in the spin, Phys. Rev. D 86, 044037 (2012); 89, 049902(E) (2014).
  40. Stephon Alexander, Gregory Gabadadze, Leah Jenks, and Nicolás Yunes, Black hole superradiance in dynamical Chern-Simons gravity, Phys. Rev. D 107, 084016 (2023).
  41. Carlos F. Sopuerta and Nicolas Yunes, New kludge scheme for the construction of approximate waveforms for extreme-mass-ratio inspirals, Phys. Rev. D 84, 124060 (2011).
  42. Stephon Alexander, Lee Samuel Finn, and Nicolas Yunes, A gravitational-wave probe of effective quantum gravity, Phys. Rev. D 78, 066005 (2008).
  43. Nicolas Yunes, Richard O’Shaughnessy, Benjamin J. Owen, and Stephon Alexander, Testing gravitational parity violation with coincident gravitational waves and short gamma-ray bursts, Phys. Rev. D 82, 064017 (2010).
  44. Stephon H. Alexander and Nicolas Yunes, Gravitational wave probes of parity violation in compact binary coalescences, Phys. Rev. D 97, 064033 (2018).
  45. Leah Jenks, Lyla Choi, Macarena Lagos, and Nicolás Yunes, Parametrized parity violation in gravitational wave propagation, Phys. Rev. D 108, 044023 (2023).
  46. Macarena Lagos, Leah Jenks, Maximiliano Isi, Kenta Hotokezaka, Brian D. Metzger, Eric Burns, Will M. Farr, Scott Perkins, Kaze W. K. Wong, and Nicolas Yunes, Birefringence tests of gravity with multimessenger binaries, Phys. Rev. D 109, 124003 (2024).
  47. Tatsuya Daniel, Leah Jenks, and Stephon Alexander, Gravitational waves in Chern-Simons-Gauss-Bonnet gravity, Phys. Rev. D 109, 124012 (2024).
  48. Thomas Callister, Leah Jenks, Daniel E. Holz, and Nicolás Yunes, New probe of gravitational parity violation through nonobservation of the stochastic gravitational-wave background, Phys. Rev. D 111, 044041 (2025).
  49. Stephon Haigh-Solom Alexander, Michael E. Peskin, and Mohammad M. Sheikh-Jabbari, Leptogenesis from gravity waves in models of inflation, Phys. Rev. Lett. 96, 081301 (2006).
  50. Stephon Alexander, Antonino Marciano, and David Spergel, Chern-Simons inflation and baryogenesis, J. Cosmol. Astropart. Phys. 04 (2013) 046.
  51. Keisuke Inomata, Leah Jenks, and Marc Kamionkowski, Parity-breaking galaxy 4-point function from lensing by chiral gravitational waves, Phys. Rev. D 111, 043504 (2025).
  52. Tristan L. Smith, Adrienne L. Erickcek, Robert R. Caldwell, and Marc Kamionkowski, The effects of Chern-Simons gravity on bodies orbiting the Earth, Phys. Rev. D 77, 024015 (2008).
  53. G. G. L. Nashed and Shin’ichi Nojiri, Slow-rotating black holes with potential in dynamical Chern-Simons modified gravitational theory, J. Cosmol. Astropart. Phys. 02 (2023) 033.
  54. Chloe Richards, Alexandru Dima, and Helvi Witek, Black holes in massive dynamical Chern-Simons gravity: Scalar hair and quasibound states at decoupling, Phys. Rev. D 108, 044078 (2023).
  55. Ki-Myeong Lee, Wormholes and Goldstone bosons, Phys. Rev. Lett. 61, 263 (1988).
  56. L. F. Abbott and Mark B. Wise, Wormholes and global symmetries, Nucl. Phys. B325, 687 (1989).
  57. Soo-Jong Rey, The axion dynamics in wormhole background, Phys. Rev. D 39, 3185 (1989).
  58. Benjamin Grinstein and Mark B. Wise, Light scalars in quantum gravity, Phys. Lett. B 212, 407 (1988).
  59. J. David Brown, C. P. Burgess, A. Kshirsagar, Bernard F. Whiting, and James W. York, Jr., Scalar field wormholes, Nucl. Phys. B328, 213 (1989).
  60. Renata Kallosh, Andrei D. Linde, Dmitri A. Linde, and Leonard Susskind, Gravity and global symmetries, Phys. Rev. D 52, 912 (1995).
  61. Steven B. Giddings and Andrew Strominger, Axion induced topology change in quantum gravity and string theory, Nucl. Phys. B306, 890 (1988).
  62. Sidney R. Coleman, Why there is nothing rather than something: A theory of the cosmological constant, Nucl. Phys. B310, 643 (1988).
  63. John Preskill, Wormholes in space-time and the constants of nature, Nucl. Phys. B323, 141 (1989).
  64. Igor R. Klebanov, Leonard Susskind, and Tom Banks, Wormholes and the cosmological constant, Nucl. Phys. B317, 665 (1989).
  65. Kiwoon Choi and R. Holman, A wormhole solution to the strong CP problem, Phys. Rev. Lett. 62, 2575 (1989).
  66. John Preskill, Sandip P. Trivedi, and Mark B. Wise, Wormholes in space-time and θ (QCD), Phys. Lett. B 223, 26 (1989).
  67. Rodrigo Alonso and Alfredo Urbano, Wormholes and masses for Goldstone bosons, J. High Energy Phys. 02 (2019) 136.
  68. Arthur Hebecker, Thomas Mikhail, and Pablo Soler, Euclidean wormholes, baby universes, and their impact on particle physics and cosmology, Front. Astron. Space Sci. 5, 35 (2018).
  69. Dhong Yeon Cheong, Koichi Hamaguchi, Yoshiki Kanazawa, Sung Mook Lee, Natsumi Nagata, and Seong Chan Park, Wormhole-induced ALP dark matter, J. High Energy Phys. 02 (2025) 183.
  70. Dhong Yeon Cheong, Seong Chan Park, and Chang Sub Shin, Effective theory approach for axion wormholes, J. High Energy Phys. 07 (2024) 039.
  71. A. G. Adame et al., DESI 2024 VI: Cosmological constraints from the measurements of baryon acoustic oscillations, J. Cosmol. Astropart. Phys. 02 (2025) 021.
  72. M. Abdul Karim et al., DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints, Phys. Rev. D 112, 083515 (2025).
  73. Robert Delbourgo and Abdus Salam, The gravitational correction to PCAC, Phys. Lett. B 40, 381 (1972).
  74. Thomas Schäfer and Edward V. Shuryak, Instantons in QCD, Rev. Mod. Phys. 70, 323 (1998).
  75. Hector O. Silva, A. Miguel Holgado, Alejandro Cárdenas-Avendaño, and Nicolás Yunes, Astrophysical and theoretical physics implications from multimessenger neutron star observations, Phys. Rev. Lett. 126, 181101 (2021).
  76. J. Chung and G. M. Hulbert, A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized-α method, J. Appl. Mech., Trans. A.S.M.E. 60, 371 (1993).
  77. Edward W. Kolb and Michael S. Turner, The Early Universe (Taylor and Francis, London, 2019), Vol. 69.
  78. Ciaran A. J. O’Hare, Cosmology of axion dark matter, Proc. Sci., COSMICWISPers (2024) 040.
  79. N. Aghanim et al., Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  80. Alexander Vilenkin, Cosmic strings and domain walls, Phys. Rep. 121, 263 (1985).
  81. Leonard Parker, Quantized fields and particle creation in expanding universes. 1., Phys. Rev. 183, 1057 (1969).
  82. L. Parker, Quantized fields and particle creation in expanding universes. 2., Phys. Rev. D 3, 346 (1971); 3, 2546(E) (1971).
  83. L. H. Ford, Cosmological particle production: A review, Rep. Prog. Phys. 84, 116901 (2021).
  84. Daniel J. H. Chung, Edward W. Kolb, and Antonio Riotto, Superheavy dark matter, Phys. Rev. D 59, 023501 (1998).
  85. Daniel J. H. Chung, Edward W. Kolb, and Antonio Riotto, Nonthermal supermassive dark matter, Phys. Rev. Lett. 81, 4048 (1998).
  86. Edward W. Kolb and Andrew J. Long, Cosmological gravitational particle production and its implications for cosmological relics, Rev. Mod. Phys. 96, 045005 (2024).
  87. Erwin Schrödinger, The proper vibrations of the expanding universe, Physica 6, 899 (1939).
  88. Peter W. Graham, Jeremy Mardon, and Surjeet Rajendran, Vector dark matter from inflationary fluctuations, Phys. Rev. D 93, 103520 (2016).
  89. Yohei Ema, Ryusuke Jinno, Kyohei Mukaida, and Kazunori Nakayama, Gravitational effects on inflaton decay, J. Cosmol. Astropart. Phys. 05 (2015) 038.
  90. Yohei Ema, Ryusuke Jinno, Kyohei Mukaida, and Kazunori Nakayama, Gravitational particle production in oscillating backgrounds and its cosmological implications, Phys. Rev. D 94, 063517 (2016).
  91. Yohei Ema, Kazunori Nakayama, and Yong Tang, Production of purely gravitational dark matter: The case of fermion and vector boson, J. High Energy Phys. 07 (2019) 060.
  92. Edward W. Kolb and Andrew J. Long, Completely dark photons from gravitational particle production during the inflationary era, J. High Energy Phys. 03 (2021) 283.
  93. Aqeel Ahmed, Bohdan Grzadkowski, and Anna Socha, Gravitational production of vector dark matter, J. High Energy Phys. 08 (2020) 059.
  94. Stephon Alexander, Leah Jenks, and Evan McDonough, Higher spin dark matter, Phys. Lett. B 819, 136436 (2021).
  95. Edward W. Kolb, Andrew J. Long, and Evan McDonough, Catastrophic production of slow gravitinos, Phys. Rev. D 104, 075015 (2021).
  96. Edward W. Kolb, Andrew J. Long, and Evan McDonough, Gravitino swampland conjecture, Phys. Rev. Lett. 127, 131603 (2021).
  97. Edward W. Kolb, Siyang Ling, Andrew J. Long, and Rachel A. Rosen, Cosmological gravitational particle production of massive spin-2 particles, J. High Energy Phys. 05 (2023) 181.
  98. Christian Capanelli, Leah Jenks, Edward W. Kolb, and Evan McDonough, Cosmological implications of Kalb-Ramond-like particles, J. High Energy Phys. 06 (2024) 075.
  99. Kunio Kaneta, Wenqi Ke, Yann Mambrini, Keith A. Olive, and Sarunas Verner, Gravitational production of spin-3/2 particles during reheating, Phys. Rev. D 108, 115027 (2023).
  100. Azadeh Maleknejad and Evan McDonough, Ultralight pion and superheavy baryon dark matter, Phys. Rev. D 106, 095011 (2022).
  101. Christian Capanelli, Leah Jenks, Edward W. Kolb, and Evan McDonough, Gravitational production of completely dark photons with nonminimal couplings to gravity, J. High Energy Phys. 09 (2024) 071.
  102. Christian Capanelli, Leah Jenks, Edward W. Kolb, and Evan McDonough, Runaway gravitational production of dark photons, Phys. Rev. Lett. 133, 061602 (2024).
  103. Leah Jenks, Edward W. Kolb, and Keyer Thyme, Gravitational particle production of scalars: Analytic and numerical approaches including early reheating, J. High Energy Phys. 05 (2025) 077.
  104. Davide Racco, Sarunas Verner, and Wei Xue, Gravitational production of heavy particles during and after inflation, J. High Energy Phys. 09 (2024) 129.
  105. Tammi Chowdhury, Leah Jenks, Edward W. Kolb, and Evan McDonough, Higgs inflation: Particle factory, J. High Energy Phys. 06 (2025) 170..
  106. Marco Figliolia, Francesco Grippa, Gaetano Lambiase, and Luca Visinelli, Gravitational Signatures of Axion Dark Matter via Parity-Violating Interactions, 2025.
  107. Yohei Ema, Kyohei Mukaida, and Kazunori Nakayama, Scalar field couplings to quadratic curvature and decay into gravitons, J. High Energy Phys. 05 (2022) 087.
  108. Asher Berlin, Diego Blas, Raffaele Tito D’Agnolo, Sebastian A. R. Ellis, Roni Harnik, Yonatan Kahn, and Jan Schütte-Engel, Detecting high-frequency gravitational waves with microwave cavities, Phys. Rev. D 105, 116011 (2022).
  109. Nancy Aggarwal et al., Challenges and opportunities of gravitational-wave searches above 10 kHz, Living Rev. Relativity 28, 10 (2025).
  110. Dmitri E. Kharzeev, Azadeh Maleknejad, and Saba Shalamberidze, QuGrav: Bringing gravitational waves to light with qumodes, Phys. Rev. Res. 8, 013140 (2026).
  111. Takeshi Chiba, Slow-roll thawing quintessence, Phys. Rev. D 79, 083517 (2009); 80, 109902(E) (2009).
  112. Sourish Dutta and Robert J. Scherrer, Hilltop quintessence, Phys. Rev. D 78, 123525 (2008).
  113. Eric V. Linder, The dynamics of quintessence, the quintessence of dynamics, Gen. Relativ. Gravit. 40, 329 (2008).
  114. Shinji Tsujikawa, Quintessence: A review, Classical Quantum Gravity 30, 214003 (2013).
  115. Yasunori Nomura, T. Watari, and T. Yanagida, Quintessence axion potential induced by electroweak instanton effects, Phys. Lett. B 484, 103 (2000).
  116. Tomi Koivisto and David F. Mota, Gauss-Bonnet quintessence: Background evolution, large scale structure and cosmological constraints, Phys. Rev. D 75, 023518 (2007).
  117. Jose María Ezquiaga and Miguel Zumalacárregui, Dark energy after GW170817: Dead ends and the road ahead, Phys. Rev. Lett. 119, 251304 (2017).
  118. K. Lodha et al., Extended dark energy analysis using DESI DR2 BAO measurements, Phys. Rev. D 112, 083511 (2025).
  119. Anowar J. Shajib and Joshua A. Frieman, Scalar-field dark energy models: Current and forecast constraints, Phys. Rev. D 112, 063508 (2025).
  120. Stephon Alexander, Sam Cormack, Antonino Marcianò, and Nicolás Yunes, Gravitational-wave mediated preheating, Phys. Lett. B 743, 82 (2015).
  121. Keisuke Inomata and Marc Kamionkowski, Chiral photons from chiral gravitational waves, Phys. Rev. Lett. 123, 031305 (2019).
  122. Keisuke Inomata and Marc Kamionkowski, Circular polarization of the cosmic microwave background from vector and tensor perturbations, Phys. Rev. D 99, 043501 (2019).

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Phys. Rev. D 114, 023529– Published 13 July, 2026
  • Received 9 December 2025
  • Accepted 9 June 2026
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