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Impact of cavities on the detection of quadratically coupled ultralight dark matter

Clare Burrage1,*, Angus Macdonald1,†, Michael P. Ross2,‡, Gray Rybka2,§, and Elisa Todarello1,∥

  • *Contact author: clare.burrage@nottingham.ac.uk
  • †Contact author: angus.macdonald@nottingham.ac.uk
  • ‡Contact author: mpross2@uw.edu
  • §Contact author: grybka@uw.edu
  • ∥Contact author: elisa.todarello@berkeley.edu
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Phys. Rev. D 113, 063505 – Published 3 March, 2026

DOI: https://doi.org/10.1103/bml1-j932

Abstract

Ultralight scalar fields may explain the nature of the dark matter in our Universe. If such scalars couple quadratically to particles of the Standard Model the scalar acquires an effective mass that depends on the local matter energy density. The changing mass causes the field to deviate from its cosmological value in experimental environments. In this work we show that the presence of a local overdensity enclosing the experiment, for example a cavity, vacuum chamber, or satellite can strongly suppress the value of the scalar and its gradient in the interior. This makes detection of such scalar dark matter challenging, and significantly relaxes constraints on strongly coupled models. We also discuss the possibility that quadratically coupled ultralight scalar dark matter could be detected by the differential measurement of the force on two cavities of the same mass but different internal structure.

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References (78)

  1. C. M. Will, The confrontation between general relativity and experiment, Living Rev. Relativity 17, 4 (2014).
  2. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  3. J. A. Frieman, C. T. Hill, A. Stebbins, and I. Waga, Cosmology with ultralight pseudo Nambu-Goldstone bosons, Phys. Rev. Lett. 75, 2077 (1995).
  4. L. Hui, Wave dark matter, Annu. Rev. Astron. Astrophys. 59, 247 (2021).
  5. D. Antypas et al., New horizons: Scalar and vector ultralight dark matter, arXiv:2203.14915.
  6. C. Burrage, E. J. Copeland, P. Millington, and M. Spannowsky, Fifth forces, Higgs portals and broken scale invariance, J. Cosmol. Astropart. Phys. 11 (2018) 036.
  7. T. Clifton, P. G. Ferreira, A. Padilla, and C. Skordis, Modified gravity and cosmology, Phys. Rep. 513, 1 (2012).
  8. A. Joyce, B. Jain, J. Khoury, and M. Trodden, Beyond the cosmological standard model, Phys. Rep. 568, 1 (2015).
  9. S. Weinberg, A new light boson?, Phys. Rev. Lett. 40, 223 (1978).
  10. F. Wilczek, Problem of strong P and T invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978).
  11. L. F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. 120B, 133 (1983).
  12. M. Dine and W. Fischler, The not so harmless axion, Phys. Lett. 120B, 137 (1983).
  13. J. Preskill, M. B. Wise, and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. 120B, 127 (1983).
  14. P. Arias, D. Cadamuro, M. Goodsell, J. Jaeckel, J. Redondo, and A. Ringwald, WISPy cold dark matter, J. Cosmol. Astropart. Phys. 06 (2012) 013.
  15. I. Broeckel, M. Cicoli, A. Maharana, K. Singh, and K. Sinha, Moduli stabilisation and the statistics of axion physics in the landscape, J. High Energy Phys. 08 (2021) 059; 01 (2022) 191(A).
  16. R. L. Davis, Cosmic axions from cosmic strings, Phys. Lett. B 180, 225 (1986).
  17. J. W. Foster, N. L. Rodd, and B. R. Safdi, Revealing the dark matter halo with axion direct detection, Phys. Rev. D 97, 123006 (2018).
  18. P. Sikivie and E. M. Todarello, Duration of classicality in highly degenerate interacting Bosonic systems, Phys. Lett. B 770, 331 (2017).
  19. S. S. Chakrabarty, S. Enomoto, Y. Han, P. Sikivie, and E. M. Todarello, Gravitational self-interactions of a degenerate quantum scalar field, Phys. Rev. D 97, 043531 (2018).
  20. G. Dvali and S. Zell, Classicality and quantum break-time for cosmic axions, J. Cosmol. Astropart. Phys. 07 (2018) 064.
  21. A. Eberhardt, M. Kopp, and T. Abel, When quantum corrections alter the predictions of classical field theory for scalar field dark matter, Phys. Rev. D 106, 103002 (2022).
  22. T. Damour and J. F. Donoghue, Equivalence principle violations and couplings of a light dilaton, Phys. Rev. D 82, 084033 (2010).
  23. T. Damour and J. F. Donoghue, Phenomenology of the equivalence principle with light scalars, Classical Quantum Gravity 27, 202001 (2010).
  24. H. Kim and G. Perez, Oscillations of atomic energy levels induced by QCD axion dark matter, Phys. Rev. D 109, 015005 (2024).
  25. C. D. Panda, M. J. Tao, M. Ceja, J. Khoury, G. M. Tino, and H. Müller, Measuring gravitational attraction with a lattice atom interferometer, Nature (London) 631, 515 (2024).
  26. A. Hees, O. Minazzoli, E. Savalle, Y. V. Stadnik, and P. Wolf, Violation of the equivalence principle from light scalar dark matter, Phys. Rev. D 98, 064051 (2018).
  27. M. Filzinger, A. R. Caddell, D. Jani, M. Steinel, L. Giani, N. Huntemann, and B. M. Roberts, Ultralight dark matter search with space-time separated atomic clocks and cavities, Phys. Rev. Lett. 134, 031001 (2025).
  28. A. Arvanitaki, P. W. Graham, J. M. Hogan, S. Rajendran, and K. Van Tilburg, Search for light scalar dark matter with atomic gravitational wave detectors, Phys. Rev. D 97, 075020 (2018).
  29. S. Sponar, R. I. P. Sedmik, M. Pitschmann, H. Abele, and Y. Hasegawa, Tests of fundamental quantum mechanics and dark interactions with low-energy neutrons, Nat. Rev. Phys. 3, 309 (2021).
  30. B. Elder, G. Mentasti, E. Pasatembou, C. F. A. Baynham, O. Buchmueller, C. R. Contaldi, C. de Rham, R. Hobson, and A. J. Tolley, Prospects for detecting new dark physics with the next generation of atomic clocks, Phys. Rev. D 112, 044053 (2025).
  31. S. M. Vermeulen, P. Relton, H. Grote, V. Raymond, C. Affeldt, F. Bergamin, A. Bisht, M. Brinkmann, K. Danzmann, S. Doravari et al., Direct limits for scalar field dark matter from a gravitational-wave detector, Nature (London) 600, 424 (2021).
  32. J. Bergé, P. Brax, G. Métris, M. Pernot-Borràs, P. Touboul, and J.-P. Uzan, MICROSCOPE mission: First constraints on the violation of the weak equivalence principle by a light scalar dilaton, Phys. Rev. Lett. 120, 141101 (2018).
  33. M. Abe et al. (MAGIS-100 Collaboration), Matter-wave atomic gradiometer interferometric sensor (MAGIS-100), Quantum Sci. Technol. 6, 044003 (2021).
  34. A. Bertoldi et al., AEDGE: Atomic experiment for dark matter and gravity exploration in space, Exp. Astron. 51, 1417 (2021).
  35. Y. A. El-Neaj et al. (AEDGE Collaboration), AEDGE: Atomic experiment for dark matter and gravity exploration in space, Eur. Phys. J. Quantum Technol. 7, 6 (2020).
  36. S. Abend et al., Terrestrial very-long-baseline atom interferometry: Workshop summary, AVS Quantum Sci. 6, 024701 (2024).
  37. L. Badurina et al., AION: An atom interferometer observatory and network, J. Cosmol. Astropart. Phys. 05 (2020) 011.
  38. A. Hees, J. Guéna, M. Abgrall, S. Bize, and P. Wolf, Searching for an oscillating massive scalar field as a dark matter candidate using atomic hyperfine frequency comparisons, Phys. Rev. Lett. 117, 061301 (2016).
  39. C. J. Kennedy, E. Oelker, J. M. Robinson, T. Bothwell, D. Kedar, W. R. Milner, G. E. Marti, A. Derevianko, and J. Ye, Precision metrology meets cosmology: Improved constraints on ultralight dark matter from atom-cavity frequency comparisons, Phys. Rev. Lett. 125, 201302 (2020).
  40. R. Oswald et al., Search for dark-matter-induced oscillations of fundamental constants using molecular spectroscopy, Phys. Rev. Lett. 129, 031302 (2022).
  41. H. Banks, E. Fuchs, and M. McCullough, A nuclear interferometer for ultra-light dark matter detection, arXiv:2407.11112.
  42. M. Bauer and G. Rostagni, Fifth forces from QCD axions scale differently, Phys. Rev. Lett. 132, 101802 (2024).
  43. Y. Grossman, B. Yu, and S. Zhou, Axion forces in axion backgrounds, J. High Energy Phys. 01 (2026) 145.
  44. D. O’Connell, M. J. Ramsey-Musolf, and M. B. Wise, Minimal extension of the standard model scalar sector, Phys. Rev. D 75, 037701 (2007).
  45. B. Patt and F. Wilczek, Higgs-field portal into hidden sectors, arXiv:hep-ph/0605188.
  46. C. Delaunay, M. Geller, Z. Heller-Algazi, G. Perez, and K. Springmann, Natural ultralight dark matter: The quadratic twin, Phys. Rev. D 113, 035011 (2026).
  47. M. Bauer, S. Chakraborti, and G. Rostagni, Axion bounds from quantum technology, J. High Energy Phys. 05 (2025) 023.
  48. K. Van Tilburg, Wake forces in a background of quadratically coupled mediators, Phys. Rev. D 109, 096036 (2024).
  49. J. Gué, P. Wolf, and A. Hees, Search for QCD coupled axion dark matter with data from the MICROSCOPE space experiment, Phys. Rev. Lett. 135, 171001 (2025).
  50. X. Gan, D. Liu, D. Liu, X. Luo, and B. Yu, Detecting ultralight dark matter with matter effect, J. High Energy Phys. 02 (2026) 043.
  51. A. Banerjee, G. Perez, M. Safronova, I. Savoray, and A. Shalit, The phenomenology of quadratically coupled ultra light dark matter, J. High Energy Phys. 10 (2023) 042.
  52. A. Banerjee, I. M. Bloch, Q. Bonnefoy, S. A. R. Ellis, G. Perez, I. Savoray, K. Springmann, and Y. V. Stadnik, Momentum and matter matter for axion dark matter matters on earth, arXiv:2502.04455.
  53. Y. G. del Castillo, B. Hammett, and J. Jaeckel, Enhanced axion-wind near earth’s surface, J. Cosmol. Astropart. Phys. 10 (2025) 022.
  54. M. Bauer and S. Chakraborti, Validity of bounds on light axions for f≲1013  GeV, Phys. Rev. D 112, 103019 (2025).
  55. T. Binoth and J. J. van der Bij, Influence of strongly coupled, hidden scalars on Higgs signals, Z. Phys. C 75, 17 (1997).
  56. R. M. Schabinger and J. D. Wells, A Minimal spontaneously broken hidden sector and its impact on Higgs boson physics at the large hadron collider, Phys. Rev. D 72, 093007 (2005).
  57. M. Ahlers, J. Jaeckel, J. Redondo, and A. Ringwald, Probing hidden sector photons through the Higgs window, Phys. Rev. D 78, 075005 (2008).
  58. B. Batell, M. Pospelov, and A. Ritz, Probing a secluded U(1) at B-factories, Phys. Rev. D 79, 115008 (2009).
  59. C. Englert and J. Jaeckel, Probing the symmetric Higgs portal with di-Higgs boson production, Phys. Rev. D 100, 095017 (2019).
  60. C. Englert, J. Jaeckel, M. Spannowsky, and P. Stylianou, Power meets precision to explore the symmetric Higgs portal, Phys. Lett. B 806, 135526 (2020).
  61. P. Brax, C. Burrage, J. A. R. Cembranos, and P. Valageas, Invisible dilaton, Phys. Rev. D 107, 095015 (2023).
  62. A. Hook and J. Huang, Probing axions with neutron star inspirals and other stellar processes, J. High Energy Phys. 06 (2018) 036.
  63. H. Kim, A. Lenoci, G. Perez, and W. Ratzinger, Probing an ultralight QCD axion with electromagnetic quadratic interaction, Phys. Rev. D 109, 015030 (2024).
  64. S. Chattopadhyay, D. S. Chattopadhyay, and R. S. Gupta, Cosmological selection of a small weak scale from large vacuum energy: A minimal approach, Phys. Rev. Lett. 134, 241803 (2025).
  65. R. Balkin, J. Serra, K. Springmann, and A. Weiler, The QCD axion at finite density, J. High Energy Phys. 07 (2020) 221.
  66. R. Balkin, J. Serra, K. Springmann, S. Stelzl, and A. Weiler, White dwarfs as a probe of exceptionally light QCD axions, Phys. Rev. D 109, 095032 (2024).
  67. R. Balkin, J. Serra, K. Springmann, S. Stelzl, and A. Weiler, Heavy neutron stars from light scalars, J. High Energy Phys. 02 (2025) 141.
  68. A. Gómez-Bañón, K. Bartnick, K. Springmann, and J. A. Pons, Constraining light QCD axions with isolated neutron star cooling, Phys. Rev. Lett. 133, 251002 (2024).
  69. P. F. de Salas and A. Widmark, Dark matter local density determination: Recent observations and future prospects, Rep. Prog. Phys. 84, 104901 (2021).
  70. T. Gustafsson and G. D. McBain, scikit-fem: A Python package for finite element assembly, J. Open Source Softwaare 5, 2369 (2020).
  71. S. Schlamminger, K. Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, Test of the equivalence principle using a rotating torsion balance, Phys. Rev. Lett. 100, 041101 (2008).
  72. T. A. Wagner, S. Schlamminger, J. H. Gundlach, and E. G. Adelberger, Torsion-balance tests of the weak equivalence principle, Classical Quantum Gravity 29, 184002 (2012).
  73. P. Touboul et al., MICROSCOPE mission: First results of a space test of the equivalence principle, Phys. Rev. Lett. 119, 231101 (2017).
  74. P. Touboul et al. (MICROSCOPE Collaboration), Space test of the equivalence principle: First results of the MICROSCOPE mission, Classical Quantum Gravity 36, 225006 (2019).
  75. E. Calloni, M. De Laurentis, R. De Rosa, F. Garufi, L. Rosa, L. Di Fiore, G. Esposito, C. Rovelli, P. Ruggi, and F. Tafuri (Archimedes Collaboration), Towards weighing the condensation energy to ascertain the Archimedes force of vacuum, Phys. Rev. D 90, 022002 (2014).
  76. K. Zhou, Ponderomotive effects of ultralight dark matter, J. High Energy Phys. 05 (2025) 134.
  77. C. Burrage, B. Elder, Y. G. del Castillo, and J. Jaeckel, On the time-dependent density of quadratically coupled dark matter around ordinary matter objects, Phys. Rev. D 111, 103526 (2025).
  78. A. Macdonald, E. Todarello, C. Burrage, M. Ross, and G. Rybka, Code for: Impact of cavities on the detection of quadratically coupled ultra-light dark matter, https://github.com/ajmphysics/Impact-of-Cavities-on-Quadratic-ULDM-Detection (2026).

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Phys. Rev. D 113, 063505– Published 3 March, 2026
  • Received 8 August 2025
  • Accepted 11 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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