- 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

Phase transitions and gravitational waves in a non-Abelian vector dark matter scenario

Nico Benincasa1,*, Luigi Delle Rose2,3,†, Luca Panizzi2,3,‡, Maimoona Razzaq2,3,§, and Savio Urzetta2,∥

  • *Contact author: nico.benincasa@kbfi.ee
  • †Contact author: luigi.dellerose@unical.it
  • ‡Contact author: luca.panizzi@unical.it
  • §Contact author: maimoona.razzaq@unical.it
  • ∥Contact author: sav.urze98@gmail.com
PDF

Phys. Rev. D 112, 095004 – Published 7 November, 2025

DOI: https://doi.org/10.1103/xd9f-bq4p

Abstract

We study a scenario where the Standard Model is extended by a SU(2) gauge group in the dark sector. The three associated dark gauge bosons are stabilized via a custodial symmetry triggered by an additional dark SU(2) scalar doublet, thus making them viable dark-matter candidates. After considering the most recent constraints for this model, we analyze the phase transition dynamics and compute the power spectrum of the resulting stochastic gravitational-wave background. Finally, we find regions of the parameter space yielding the observed dark-matter relic density while also leading to a strong enough phase transition with an associated gravitational-wave signal reaching the sensitivity of a future space-based gravitational-wave detector, such as LISA, DECIGO, BBO, TianQin, or Taiji.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (77)

  1. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, 061102 (2016).
  2. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), GW170817: Observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119, 161101 (2017).
  3. E. Witten, Cosmic separation of phases, Phys. Rev. D 30, 272 (1984).
  4. C. J. Hogan, Gravitational radiation from cosmological phase transitions, Mon. Not. R. Astron. Soc. 218, 629 (1986).
  5. P. Amaro-Seoane et al., Laser interferometer space antenna, arXiv:1702.00786.
  6. S. Kawamura et al., The Japanese space gravitational wave antenna: DECIGO, Classical Quantum Gravity 28, 094011 (2011).
  7. V. Corbin and N. J. Cornish, Detecting the cosmic gravitational wave background with the big bang observer, Classical Quantum Gravity 23, 2435 (2006).
  8. J. Luo et al. (TianQin Collaborations), TianQin: A space-borne gravitational wave detector, Classical Quantum Gravity 33, 035010 (2016).
  9. W.-R. Hu and Y.-L. Wu, The Taiji program in space for gravitational wave physics and the nature of gravity, Natl. Sci. Rev. 4, 685 (2017).
  10. K. Kajantie, M. Laine, K. Rummukainen, and M. E. Shaposhnikov, Is there a hot electroweak phase transition at mH≳mW?, Phys. Rev. Lett. 77, 2887 (1996).
  11. T. Hambye, Hidden vector dark matter, J. High Energy Phys. 01 (2009) 028.
  12. T. Hambye and M. H. G. Tytgat, Confined hidden vector dark matter, Phys. Lett. B 683, 39 (2010).
  13. F. Chen, J. M. Cline, and A. R. Frey, Nonabelian dark matter: Models and constraints, Phys. Rev. D 80, 083516 (2009).
  14. J. L. Diaz-Cruz and E. Ma, Neutral SU(2) gauge extension of the standard model and a vector-boson dark-matter candidate, Phys. Lett. B 695, 264 (2011).
  15. S. Bhattacharya, J. L. Diaz-Cruz, E. Ma, and D. Wegman, Dark vector-gauge-boson model, Phys. Rev. D 85, 055008 (2012).
  16. T. Hambye and A. Strumia, Dynamical generation of the weak and dark matter scale, Phys. Rev. D 88, 055022 (2013).
  17. S. Fraser, E. Ma, and M. Zakeri, SU(2)N model of vector dark matter with a leptonic connection, Int. J. Mod. Phys. A 30, 1550018 (2015).
  18. C. Gross, O. Lebedev, and Y. Mambrini, Non-Abelian gauge fields as dark matter, J. High Energy Phys. 08 (2015) 158.
  19. N. Bernal, X. Chu, C. Garcia-Cely, T. Hambye, and B. Zaldivar, Production regimes for self-interacting dark matter, J. Cosmol. Astropart. Phys. 03 (2016) 018.
  20. S. Di Chiara and K. Tuominen, A minimal model for SU(N) vector dark matter, J. High Energy Phys. 11 (2015) 188.
  21. B. Barman, S. Bhattacharya, S. K. Patra, and J. Chakrabortty, Non-Abelian vector boson dark matter, its unified route and signatures at the LHC, J. Cosmol. Astropart. Phys. 12 (2017) 021.
  22. I. Baldes and C. Garcia-Cely, Strong gravitational radiation from a simple dark matter model, J. High Energy Phys. 05 (2019) 190.
  23. B. Barman, S. Bhattacharya, and M. Zakeri, Non-Abelian vector boson as FIMP dark matter, J. Cosmol. Astropart. Phys. 02 (2020) 029.
  24. E. Hall, T. Konstandin, R. McGehee, H. Murayama, and G. Servant, Baryogenesis from a dark first-order phase transition, J. High Energy Phys. 04 (2020) 042.
  25. D. Marfatia and P.-Y. Tseng, Gravitational wave signals of dark matter freeze-out, J. High Energy Phys. 02 (2021) 022.
  26. J. Hisano, A. Ibarra, and R. Nagai, Direct detection of vector dark matter through electromagnetic multipoles, J. Cosmol. Astropart. Phys. 10 (2020) 015.
  27. N. Baouche, A. Ahriche, G. Faisel, and S. Nasri, Phenomenology of the hidden SU(2) vector dark matter model, Phys. Rev. D 104, 075022 (2021).
  28. A. Belyaev, A. Deandrea, S. Moretti, L. Panizzi, D. A. Ross, and N. Thongyoi, A fermionic portal to vector dark matter from a new gauge sector, arXiv:2204.03510.
  29. T. Abe, K. S. Babu, and A. Kaladharan, Gravitational wave signatures of a chiral fermion dark matter model, J. Cosmol. Astropart. Phys. 07 (2024) 048.
  30. M. Arteaga, A. Ghoshal, and A. Strumia, Gravitational waves and black holes from the phase transition in models of dynamical symmetry breaking, J. Cosmol. Astropart. Phys. 05 (2025) 029.
  31. M. Arteaga Tupia, A. Ghoshal, and A. Strumia, Primordial magnetogenesis from a supercooled dynamical electroweak phase transition, arXiv:2506.16387.
  32. P. Athron, C. Balázs, A. Fowlie, L. Morris, and L. Wu, Cosmological phase transitions: From perturbative particle physics to gravitational waves, Prog. Part. Nucl. Phys. 135, 104094 (2024).
  33. A. Belyaev, A. Deandrea, S. Moretti, L. Panizzi, and N. Thongyoi, A fermionic portal to a non-Abelian dark sector, arXiv:2203.04681.
  34. N. Aghanim et al. (Planck Collaborations), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  35. G. Alguero, G. Belanger, F. Boudjema, S. Chakraborti, A. Goudelis, S. Kraml, A. Mjallal, and A. Pukhov, micromegas6.0: N-component dark matter, Comput. Phys. Commun. 299, 109133 (2024).
  36. J. Aalbers et al. (LZ Collaborations), First dark matter search results from the LUX-ZEPLIN (LZ) experiment, arXiv:2207.03764.
  37. C. Amole et al. (PICO Collaborations), Dark matter search results from the PICO-60 C3F8 bubble chamber, Phys. Rev. Lett. 118, 251301 (2017).
  38. E. Aprile et al. (XENON Collaborations), Dark matter search results from a one ton-year exposure of XENON1T, Phys. Rev. Lett. 121, 111302 (2018).
  39. Y. Meng et al. (PandaX-4T Collaborations), Dark matter search results from the PandaX-4T commissioning run, Phys. Rev. Lett. 127, 261802 (2021).
  40. P. Agnes et al. (DarkSide Collaborations), Low-mass dark matter search with the DarkSide-50 experiment, Phys. Rev. Lett. 121, 081307 (2018).
  41. A. H. Abdelhameed et al. (CRESST Collaborations), First results from the CRESST-III low-mass dark matter program, Phys. Rev. D 100, 102002 (2019).
  42. G. Bélanger, J. Da Silva, T. Perrillat-Bottonet, and A. Pukhov, Limits on dark matter proton scattering from neutrino telescopes using micrOMEGAs, J. Cosmol. Astropart. Phys. 12 (2015) 036.
  43. F. Ambrogi, C. Arina, M. Backovic, J. Heisig, F. Maltoni, L. Mantani, O. Mattelaer, and G. Mohlabeng, MadDM v.3.0: A comprehensive tool for dark matter studies, Phys. Dark Universe 24, 100249 (2019).
  44. A. Albert et al. (Fermi-LAT and DES Collaborations), Searching for dark matter annihilation in recently discovered Milky Way satellites with Fermi-LAT, Astrophys. J. 834, 110 (2017).
  45. G. Arcadi, C. Gross, O. Lebedev, S. Pokorski, and T. Toma, Evading direct dark matter detection in Higgs portal models, Phys. Lett. B 769, 129 (2017).
  46. G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo, M. Sher, and J. P. Silva, Theory and phenomenology of two-Higgs-doublet models, Phys. Rep. 516, 1 (2012).
  47. M. E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections, Phys. Rev. D 46, 381 (1992).
  48. M. E. Peskin and T. Takeuchi, A new constraint on a strongly interacting Higgs sector, Phys. Rev. Lett. 65, 964 (1990).
  49. A. Beniwal, M. Lewicki, M. White, and A. G. Williams, Gravitational waves and electroweak baryogenesis in a global study of the extended scalar singlet model, J. High Energy Phys. 02 (2019) 183.
  50. W. Grimus, L. Lavoura, O. M. Ogreid, and P. Osland, The oblique parameters in multi-Higgs-doublet models, Nucl. Phys. B801, 81 (2008).
  51. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  52. H. Bahl, T. Biekötter, S. Heinemeyer, C. Li, S. Paasch, G. Weiglein, and J. Wittbrodt, higgstools: BSM scalar phenomenology with new versions of higgsbounds and higgssignals, Comput. Phys. Commun. 291, 108803 (2023).
  53. M. Aaboud et al. (ATLAS Collaborations), Search for invisible Higgs boson decays in vector boson fusion at s=13  TeV with the ATLAS detector, Phys. Lett. B 793, 499 (2019).
  54. G. Aad et al. (ATLAS Collaborations), Combination of searches for invisible decays of the Higgs boson using 139  fb−1 of proton-proton collision data at s=13  TeV collected with the ATLAS experiment, Phys. Lett. B 842, 137963 (2023).
  55. S. Coleman and E. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking, Phys. Rev. D 7, 1888 (1973).
  56. J. M. Cline, K. Kainulainen, and M. Trott, Electroweak baryogenesis in two Higgs doublet models and B meson anomalies, J. High Energy Phys. 11 (2011) 089.
  57. L. Dolan and R. Jackiw, Symmetry behavior at finite temperature, Phys. Rev. D 9, 3320 (1974).
  58. D. J. Gross, R. D. Pisarski, and L. G. Yaffe, QCD and instantons at finite temperature, Rev. Mod. Phys. 53, 43 (1981).
  59. R. R. Parwani, Resummation in a hot scalar field theory, Phys. Rev. D 45, 4695 (1992); 48, 5965(E) (1993).
  60. M. E. Carrington, Effective potential at finite temperature in the standard model, Phys. Rev. D 45, 2933 (1992).
  61. J. R. Espinosa, T. Konstandin, J. M. No, and G. Servant, Energy budget of cosmological first-order phase transitions, J. Cosmol. Astropart. Phys. 06 (2010) 028.
  62. C. Grojean and G. Servant, Gravitational waves from phase transitions at the electroweak scale and beyond, Phys. Rev. D 75, 043507 (2007).
  63. M. Kamionkowski, A. Kosowsky, and M. S. Turner, Gravitational radiation from first order phase transitions, Phys. Rev. D 49, 2837 (1994).
  64. C. J. Hogan, Gravitational radiation from cosmological phase transitions, Mon. Not. R. Astron. Soc. 218, 629 (1986).
  65. M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Gravitational waves from the sound of a first order phase transition, Phys. Rev. Lett. 112, 041301 (2014).
  66. C. Caprini, R. Durrer, and G. Servant, The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition, J. Cosmol. Astropart. Phys. 12 (2009) 024.
  67. C. Caprini et al., Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions, J. Cosmol. Astropart. Phys. 04 (2016) 001.
  68. M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Shape of the acoustic gravitational wave power spectrum from a first order phase transition, Phys. Rev. D 96, 103520 (2017); 101, 089902(E) (2020).
  69. C. Caprini et al., Detecting gravitational waves from cosmological phase transitions with LISA: An update, J. Cosmol. Astropart. Phys. 03 (2020) 024.
  70. K. Schmitz, LISA sensitivity to gravitational waves from sound waves, Symmetry 12, 1477 (2020).
  71. D. Croon, O. Gould, P. Schicho, T. V. I. Tenkanen, and G. White, Theoretical uncertainties for cosmological first-order phase transitions, J. High Energy Phys. 04 (2021) 055.
  72. P. Athron, C. Balazs, A. Fowlie, L. Morris, G. White, and Y. Zhang, How arbitrary are perturbative calculations of the electroweak phase transition?, J. High Energy Phys. 01 (2023) 050.
  73. H.-K. Guo, K. Sinha, D. Vagie, and G. White, Phase transitions in an expanding universe: Stochastic gravitational waves in standard and non-standard histories, J. Cosmol. Astropart. Phys. 01 (2021) 001.
  74. J. Ellis, M. Lewicki, J. M. No, and V. Vaskonen, Gravitational wave energy budget in strongly supercooled phase transitions, J. Cosmol. Astropart. Phys. 06 (2019) 024.
  75. C. L. Wainwright, CosmoTransitions: Computing cosmological phase transition temperatures and bubble profiles with multiple fields, Comput. Phys. Commun. 183, 2006 (2012).
  76. N. Benincasa, L. Delle Rose, K. Kannike, and L. Marzola, Multi-step phase transitions and gravitational waves in the inert doublet model, J. Cosmol. Astropart. Phys. 12 (2022) 025.
  77. E. Thrane and J. D. Romano, Sensitivity curves for searches for gravitational-wave backgrounds, Phys. Rev. D 88, 124032 (2013).

Outline

Information

Phys. Rev. D 112, 095004– Published 7 November, 2025
  • Received 7 July 2025
  • Accepted 4 October 2025
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