- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Wave-envelope dark matter beyond the monochromatic paradigm

Yechan Kim* and Hye-Sung Lee†

  • *Contact author: cj7801@kaist.ac.kr
  • †Contact author: hyesung.lee@kaist.ac.kr
PDF

Phys. Rev. D 114, 055045 – Published 23 September, 2026

DOI: https://doi.org/10.1103/5wft-r6dl

Abstract

Ultralight dark matter searches widely assume that signals are monochromatic, with a single frequency set by the mass. This assumption is generally violated in the presence of field mixing, even when the constituent fields have similar frequencies. Instead, dark matter signals can exhibit a two-timescale structure with intrinsic slow modulation. We demonstrate that mixing between ultralight wave dark matter fields induces a parametric structure, leading to a scenario we refer to as wave-envelope dark matter, in which a slow-beating envelope emerges alongside the primary oscillation. This results in distinctive features such as slow modulation and characteristic sideband structures in the frequency spectrum, beyond the conventional monochromatic expectation. As a representative example, we briefly discuss implications for neutrino observables.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (62)

  1. W. Hu, R. Barkana, and A. Gruzinov, Phys. Rev. Lett. 85, 1158 (2000).
  2. L. Hui, Annu. Rev. Astron. Astrophys. 59, 247 (2021).
  3. A. Arvanitaki, P. W. Graham, J. M. Hogan, S. Rajendran, and K. Van Tilburg, Phys. Rev. D 97, 075020 (2018).
  4. C. J. Kennedy, E. Oelker, J. M. Robinson, T. Bothwell, D. Kedar, W. R. Milner, G. E. Marti, A. Derevianko, and J. Ye, Phys. Rev. Lett. 125, 201302 (2020).
  5. T. Kobayashi et al., Phys. Rev. Lett. 129, 241301 (2022).
  6. M. Filzinger, A. R. Caddell, D. Jani, M. Steinel, L. Giani, N. Huntemann, and B. M. Roberts, Phys. Rev. Lett. 134, 031001 (2025).
  7. Y. Kim, H.-S. Lee, J. Lee, and J. Yi, arXiv:2509.22892.
  8. K. Van Tilburg, N. Leefer, L. Bougas, and D. Budker, Phys. Rev. Lett. 115, 011802 (2015).
  9. J. Guo, Y. He, J. Liu, X.-P. Wang, and K.-P. Xie, Commun. Phys. 6, 225 (2023).
  10. V. V. Flambaum and I. B. Samsonov, Phys. Rev. D 110, 075044 (2024).
  11. A. Berlin, Phys. Rev. Lett. 117, 231801 (2016).
  12. G. Krnjaic, P. A. N. Machado, and L. Necib, Phys. Rev. D 97, 075017 (2018).
  13. M. Losada, Y. Nir, G. Perez, I. Savoray, and Y. Shpilman, J. High Energy Phys. 03 (2023) 032.
  14. A. Dev, G. Krnjaic, P. Machado, and H. Ramani, Phys. Rev. D 107, 035006 (2023).
  15. G.-y. Huang and N. Nath, J. Cosmol. Astropart. Phys. 05 (2022) 034.
  16. Y. ChoeJo, Y. Kim, and H.-S. Lee, Phys. Rev. D 108, 095028 (2023).
  17. P. Martínez-Miravé, Y. F. Perez-Gonzalez, and M. Sen, Phys. Rev. D 110, 055005 (2024).
  18. Y. Kim and H.-S. Lee, J. High Energy Phys. 07 (2025) 269.
  19. L. Kofman, A. D. Linde, and A. A. Starobinsky, Phys. Rev. Lett. 73, 3195 (1994).
  20. L. Kofman, A. D. Linde, and A. A. Starobinsky, Phys. Rev. D 56, 3258 (1997).
  21. P. B. Greene, L. Kofman, A. D. Linde, and A. A. Starobinsky, Phys. Rev. D 56, 6175 (1997).
  22. P. B. Greene, L. Kofman, and A. A. Starobinsky, Nucl. Phys. B543, 423 (1999).
  23. J. Soda and Y. Urakawa, Eur. Phys. J. C 78, 779 (2018).
  24. H. Fukunaga, N. Kitajima, and Y. Urakawa, J. Cosmol. Astropart. Phys. 06 (2019) 055.
  25. R. T. Co, L. J. Hall, K. Harigaya, K. A. Olive, and S. Verner, J. Cosmol. Astropart. Phys. 08 (2020) 036.
  26. K. Nakayama and W. Yin, J. High Energy Phys. 10 (2021) 026.
  27. J. A. Dror, K. Harigaya, and V. Narayan, Phys. Rev. D 99, 035036 (2019).
  28. E. Masaki, A. Aoki, and J. Soda, Phys. Rev. D 101, 043505 (2020).
  29. P. Carenza, A. Mirizzi, and G. Sigl, Phys. Rev. D 101, 103016 (2020).
  30. A. Arza, T. Schwetz, and E. Todarello, J. Cosmol. Astropart. Phys. 10 (2020) 013.
  31. N. Kitajima, J. Soda, and Y. Urakawa, J. Cosmol. Astropart. Phys. 10 (2018) 008.
  32. P. C. M. Delgado, Phys. Rev. D 108, 123539 (2023).
  33. B. Underwood and Y. Zhai, J. Cosmol. Astropart. Phys. 04 (2014) 002.
  34. C. T. Hill and G. G. Ross, Nucl. Phys. B311, 253 (1988).
  35. J. E. Kim, H. P. Nilles, and M. Peloso, J. Cosmol. Astropart. Phys. 01 (2005) 005.
  36. R. Daido, N. Kitajima, and F. Takahashi, Phys. Rev. D 93, 075027 (2016).
  37. H.-K. Guo, K. Sinha, C. Sun, J. Swaim, and D. Vagie, J. Cosmol. Astropart. Phys. 10 (2021) 028.
  38. N. Glennon, N. Musoke, and C. Prescod-Weinstein, Phys. Rev. D 107, 063520 (2023).
  39. A. E. Mirasola, N. Musoke, M. C. Neyrinck, C. Prescod-Weinstein, and J. L. Zagorac, J. Cosmol. Astropart. Phys. 06 (2026) 007.
  40. H. Fukuda and K. Nakayama, J. High Energy Phys. 01 (2020) 128.
  41. Z.-H. Lyu, R.-G. Cai, Z.-K. Guo, J.-F. He, and J. Liu, Phys. Rev. D 112, 104066 (2025).
  42. Z.-Q. Zhu, Y.-S. Piao, and J. Zhang, Phys. Rev. D 113, 063048 (2026).
  43. M. S. Turner, Phys. Rev. D 28, 1243 (1983).
  44. S. Das and E. O. Nadler, Phys. Rev. D 103, 043517 (2021).
  45. J. A. R. Cembranos, A. L. Maroto, S. J. Núñez Jareño, and H. Villarrubia-Rojo, J. High Energy Phys. 08 (2018) 073.
  46. R. G. García, P. Brax, and P. Valageas, Phys. Rev. D 109, 043516 (2024).
  47. H. Koo and J.-W. Lee, J. Cosmol. Astropart. Phys. 01 (2026) 020.
  48. H. Früchting, J. Res. Natl. Bureau Stand. Sect. B 73B, 21 (1969).
  49. I. Kovacic, R. H. Rand, and S. M. Sah, Appl. Mech. Rev. 70, 020802 (2018).
  50. F. Verhulst, in Perturbation Theory: Mathematics, Methods and Applications (Springer, New York, 2022), pp. 167–183.
  51. M. Doi, T. Kotani, H. Nishiura, and E. Takasugi, Prog. Theor. Phys. 69, 602 (1983).
  52. J. Schechter and J. W. F. Valle, Phys. Rev. D 25, 2951 (1982).
  53. P. D. Bolton, F. F. Deppisch, and P. S. Bhupal Dev, J. High Energy Phys. 03 (2020) 170.
  54. P. Sikivie, Phys. Rev. Lett. 51, 1415 (1983); 52, 695(E) (1984).
  55. D. Budker, P. W. Graham, M. Ledbetter, S. Rajendran, and A. Sushkov, Phys. Rev. X 4, 021030 (2014).
  56. J. L. Ouellet et al., Phys. Rev. Lett. 122, 121802 (2019).
  57. R. Khatiwada et al. (ADMX Collaboration), Rev. Sci. Instrum. 92, 124502 (2021).
  58. S. Ahn et al. (CAPP Collaboration), Phys. Rev. X 14, 031023 (2024).
  59. J. F. Navarro, C. S. Frenk, and S. D. M. White, Astrophys. J. 462, 563 (1996).
  60. J. F. Navarro, C. S. Frenk, and S. D. M. White, Astrophys. J. 490, 493 (1997).
  61. P. J. McMillan, Mon. Not. R. Astron. Soc. 465, 76 (2016).
  62. D. Hooper, Phys. Dark Universe 15, 53 (2017).

Outline

Information

Phys. Rev. D 114, 055045– Published 23 September, 2026
  • Received 28 April 2026
  • Accepted 18 August 2026
Crossmark - Check for updates button
Creative Commons Logo

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. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation