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Forbidden dark matter assisted by a first-order phase transition and the associated gravitational waves

Satyabrata Mahapatra1,*, Partha Kumar Paul2,†, and Narendra Sahu2,‡

  • *Contact author: satyabrata@iitgoa.ac.in
  • †Contact author: ph22resch11012@iith.ac.in
  • ‡Contact author: nsahu@phy.iith.ac.in
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Phys. Rev. D 114, 055044 – Published 23 September, 2026

DOI: https://doi.org/10.1103/f9jp-vvft

Abstract

We propose a simple yet testable framework for light fermion dark matter (DM) with mass in the MeV–GeV range, charged under a dark U(1)D gauge symmetry. Before symmetry-breaking, DM annihilates excessively into massless dark gauge bosons, resulting in an underabundant relic and hence creating severe tension with cosmic microwave background (CMB) and indirect detection constraints. This is naturally remedied by a strong first-order phase transition (FOPT) in the dark sector, triggered by a scalar field Φ, which gives rise to masses for the dark gauge boson (XD) and the physical scalar (ϕ). To achieve the correct relic abundance while evading indirect detection constraints, the s-wave annihilation channel χχ¯→XDϕ is strictly maintained in the kinematically forbidden regime. Crucially, due to the U(1)D gauge structure, the usual χχ¯→ϕϕ annihilation is strictly absent at tree level and only arises at the one-loop level. Within this framework, we explore two distinct possibilities. When the loop-induced χχ¯→ϕϕ channel is also kinematically forbidden, it predominantly determines the relic density. Conversely, when the χχ¯→ϕϕ channel is kinematically allowed, a rich interplay emerges between the tree-level forbidden χχ¯→XDϕ process and the loop-level allowed χχ¯→ϕϕ process, with the dominant contribution being dictated sensitively by the DM mass and gauge coupling. The late-time annihilations are highly suppressed in both of these channels, either by the energetic threshold of the forbidden channel or the p-wave velocity suppression of the loop-induced χχ¯→ϕϕ final-state process, rendering the scenario entirely safe from CMB and indirect search bounds. Moreover, the same symmetry-breaking phase transition is strongly first-order, producing a stochastic gravitational-wave background that could be probed by upcoming space-based interferometers and pulsar timing arrays. We demonstrate that achieving the observed DM abundance tightly correlates the DM mass with the nucleation temperature of the phase transition. Thus, this setup links the DM relic abundance, dark-sector dynamics, and gravitational-wave signals, offering complementary paths to discovery in both terrestrial and cosmological observations.

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References (76)

  1. F. Zwicky, Die Rotverschiebung von extragalaktischen Nebeln, Helv. Phys. Acta 6, 110 (1933).
  2. V. C. Rubin and W. K. Ford, Jr., Rotation of the Andromeda Nebula from a spectroscopic survey of emission regions, Astrophys. J. 159, 379 (1970).
  3. D. Clowe, M. Bradac, A. H. Gonzalez, M. Markevitch, S. W. Randall, C. Jones, and D. Zaritsky, A direct empirical proof of the existence of dark matter, Astrophys. J. Lett. 648, L109 (2006).
  4. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  5. P. A. Zyla et al. (Particle Data Group), Review of particle physics, Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
  6. G. Arcadi, D. Cabo-Almeida, M. Dutra, P. Ghosh, M. Lindner, Y. Mambrini, J. P. Neto, M. Pierre, S. Profumo, and F. S. Queiroz, The waning of the WIMP: Endgame?, Eur. Phys. J. C 85, 152 (2025).
  7. G. Arcadi, M. Dutra, P. Ghosh, M. Lindner, Y. Mambrini, M. Pierre, S. Profumo, and F. S. Queiroz, The waning of the WIMP? A review of models, searches, and constraints, Eur. Phys. J. C 78, 203 (2018).
  8. S. Balan et al., Resonant or asymmetric: The status of sub-GeV dark matter, J. Cosmol. Astropart. Phys. 01 (2025) 053.
  9. A. Cheek, P. Figueroa, G. Herrera, and I. M. Shoemaker, Sub-GeV dark matter under pressure from direct detection, arXiv:2507.15956.
  10. G. Krnjaic, Testing thermal-relic dark matter with a dark photon mediator, Phys. Rev. D 113, 115057 (2026).
  11. B. Dutta, S. Ghosh, and J. Kumar, A sub-GeV dark matter model, Phys. Rev. D 100, 075028 (2019).
  12. R. Essig, T. Volansky, and T.-T. Yu, New constraints and prospects for sub-GeV dark matter scattering off electrons in xenon, Phys. Rev. D 96, 043017 (2017).
  13. K. Bondarenko, A. Boyarsky, T. Bringmann, M. Hufnagel, K. Schmidt-Hoberg, and A. Sokolenko, Direct detection and complementary constraints for sub-GeV dark matter, J. High Energy Phys. 03 (2020) 118.
  14. A. Adhikary, D. Borah, S. Mahapatra, I. Saha, N. Sahu, and V. S. Thounaojam, New realisation of light thermal dark matter with enhanced detection prospects, J. Cosmol. Astropart. Phys. 12 (2024) 043.
  15. D. Borah, P. Das, S. Mahapatra, and N. Sahu, Light thermal dark matter via type-I seesaw portal, J. High Energy Phys. 08 (2025) 023.
  16. D. Borah, S. Mahapatra, N. Sahu, and V. S. Thounaojam, Light thermal dark matter models in the light of DAMIC-M 2025 constraints, Phys. Rev. D 113, 015026 (2026).
  17. E. Ma, P. K. Paul, and N. Sahu, Lepton parity dark matter and naturally unstable domain walls, Phys. Rev. D 112, 095020 (2025).
  18. E. Ma, P. K. Paul, and N. Sahu, Cosmological probes of lepton parity freeze-in dark matter: ΔNeff and gravitational waves, Nucl. Phys. B1027, 117478 (2026).
  19. A. Banik, Y. Cui, Y.-D. Tsai, and Y. Tsai, The sound of dark sectors in pulsar timing arrays, Phys. Dark Universe 53, 102398 (2026).
  20. A. Amiri, B. Díaz Sáez, and K. Ghorbani, (Sub)GeV dark matter in the U(1)X Higgs portal model, Phys. Lett. B 844, 138119 (2023).
  21. E. Aprile et al. (XENON Collaboration), Light dark matter search with ionization signals in XENON1T, Phys. Rev. Lett. 123, 251801 (2019).
  22. A. H. Abdelhameed et al. (CRESST Collaboration), First results from the CRESST-III low-mass dark matter program, Phys. Rev. D 100, 102002 (2019).
  23. E. Aprile et al. (XENON Collaboration), Search for light dark matter in low-energy ionization signals from XENONnT, Phys. Rev. Lett. 134, 161004 (2025).
  24. C. Cheng et al. (PandaX-II Collaboration), Search for light dark matter-electron scatterings in the PandaX-II experiment, Phys. Rev. Lett. 126, 211803 (2021).
  25. S. Li et al. (PandaX Collaboration), Search for light dark matter with ionization signals in the PandaX-4T experiment, Phys. Rev. Lett. 130, 261001 (2023).
  26. L. Barak et al. (SENSEI Collaboration), SENSEI: Direct-detection results on sub-GeV dark matter from a new skipper-CCD, Phys. Rev. Lett. 125, 171802 (2020).
  27. M. F. Albakry et al. (SuperCDMS Collaboration), Light dark matter constraints from SuperCDMS HVeV detectors operated underground with an anticoincidence event selection, Phys. Rev. D 111, 012006 (2025).
  28. K. Aggarwal et al. (DAMIC-M Collaboration), Probing benchmark models of hidden-sector dark matter with DAMIC-M, Phys. Rev. Lett. 135, 071002 (2025).
  29. T. R. Slatyer, Indirect dark matter signatures in the cosmic dark ages. I. Generalizing the bound on s-wave dark matter annihilation from Planck results, Phys. Rev. D 93, 023527 (2016).
  30. A. McDaniel, M. Ajello, C. M. Karwin, M. Di Mauro, A. Drlica-Wagner, and M. A. Sánchez-Conde, Legacy analysis of dark matter annihilation from the Milky Way dwarf spheroidal galaxies with 14 years of Fermi-LAT data, Phys. Rev. D 109, 063024 (2024).
  31. A. Cuoco, M. Krämer, and M. Korsmeier, Novel dark matter constraints from antiprotons in light of AMS-02, Phys. Rev. Lett. 118, 191102 (2017).
  32. R. T. D’Agnolo and J. T. Ruderman, Light dark matter from forbidden channels, Phys. Rev. Lett. 115, 061301 (2015).
  33. R. T. D’Agnolo, D. Liu, J. T. Ruderman, and P.-J. Wang, Forbidden dark matter annihilations into Standard Model particles, J. High Energy Phys. 06 (2021) 103.
  34. M. B. Hindmarsh, M. Lüben, J. Lumma, and M. Pauly, Phase transitions in the early universe, SciPost Phys. Lect. Notes 24, 1 (2021).
  35. 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).
  36. S. Mahapatra, P. K. Paul, N. Sahu, and P. Shukla, Verifiable type-III seesaw and dark matter in a gauged U(1)B−L symmetric model, Eur. Phys. J. C 86, 67 (2026).
  37. E. Ma, P. K. Paul, and N. Sahu, Naturally small Dirac neutrino mass and B−L dark matter, arXiv:2601.05926.
  38. W.-Z. Feng, J. Li, and P. Nath, Cosmologically consistent analysis of gravitational waves from hidden sectors, Phys. Rev. D 110, 015020 (2024).
  39. W.-Z. Feng, J. Li, P. Nath, and Z.-H. Ye, Gauge-independent gravitational waves from cogenesis in a B−L conserving universe, Phys. Rev. D 113, 063504 (2026).
  40. K. Yagi and N. Seto, Detector configuration of DECIGO/BBO and identification of cosmological neutron-star binaries, Phys. Rev. D 83, 044011 (2011); 95, 109901(E) (2017).
  41. N. Seto, S. Kawamura, and T. Nakamura, Possibility of direct measurement of the acceleration of the universe using 0.1-Hz band laser interferometer gravitational wave antenna in space, Phys. Rev. Lett. 87, 221103 (2001).
  42. P. Amaro-Seoane et al. (LISA Collaboration), Laser Interferometer Space Antenna, arXiv:1702.00786.
  43. A. Sesana et al., Unveiling the gravitational universe at μ-Hz frequencies, Exp. Astron. 51, 1333 (2021).
  44. P. Agnes et al. (DarkSide Collaboration), Search for dark matter particle interactions with electron final states with DarkSide-50, Phys. Rev. Lett. 130, 101002 (2023).
  45. E. Aprile et al. (XENON Collaboration), First search for light dark matter in the neutrino fog with XENONnT, Phys. Rev. Lett. 134, 111802 (2025).
  46. M. Zhang et al. (PandaX Collaboration), Search for light dark matter with 259 days of data in PandaX-4T, Phys. Rev. Lett. 135, 211001 (2025); 136, 069901(E) (2026).
  47. P. Agnes et al. (Global Argon Dark Matter Collaboration), Sensitivity projections for a dual-phase argon TPC optimized for light dark matter searches through the ionization channel, Phys. Rev. D 107, 112006 (2023).
  48. R. Agnese et al. (SuperCDMS Collaboration), Projected sensitivity of the SuperCDMS SNOLAB experiment, Phys. Rev. D 95, 082002 (2017).
  49. D. Banerjee et al., Dark matter search in missing energy events with NA64, Phys. Rev. Lett. 123, 121801 (2019).
  50. J. P. Lees et al. (BABAR Collaboration), Search for a dark photon in e+e− collisions at BABAR, Phys. Rev. Lett. 113, 201801 (2014).
  51. J. H. Chang, R. Essig, and S. D. McDermott, Revisiting supernova 1987A constraints on dark photons, J. High Energy Phys. 01 (2017) 107.
  52. A. Caputo, J. Park, and S. Yun, The heavy dark photon handbook: Cosmological and astrophysical bounds, Phys. Rev. D 113, 075001 (2026).
  53. A. Caputo, H.-T. Janka, G. Raffelt, and S. Yun, Cooling the shock: New supernova constraints on dark photons, Phys. Rev. Lett. 134, 151002 (2025).
  54. G. Aad et al. (ATLAS Collaboration), Search for invisible Higgs-boson decays in events with vector-boson fusion signatures using 139  fb−1 of proton-proton data recorded by the ATLAS experiment, J. High Energy Phys. 08 (2022) 104.
  55. S. Balaji, P. S. B. Dev, J. Silk, and Y. Zhang, Improved stellar limits on a light CP-even scalar, J. Cosmol. Astropart. Phys. 12 (2022) 024.
  56. P. S. B. Dev, R. N. Mohapatra, and Y. Zhang, Long lived light scalars as probe of low scale seesaw models, Nucl. Phys. B 923, 179 (2017).
  57. D. Egana-Ugrinovic, S. Homiller, and P. Meade, Light scalars and the Koto anomaly, Phys. Rev. Lett. 124, 191801 (2020).
  58. P. S. B. Dev, R. N. Mohapatra, and Y. Zhang, Constraints on long-lived light scalars with flavor-changing couplings and the KOTO anomaly, Phys. Rev. D 101, 075014 (2020).
  59. J. M. Berryman, A. de Gouvea, P. J. Fox, B. J. Kayser, K. J. Kelly, and J. L. Raaf, Searches for decays of new particles in the DUNE multi-purpose near detector, J. High Energy Phys. 02 (2020) 174.
  60. B. Batell, J. Berger, and A. Ismail, Probing the Higgs portal at the Fermilab short-baseline neutrino experiments, Phys. Rev. D 100, 115039 (2019).
  61. L. A. Anchordoqui et al., The forward physics facility: Sites, experiments, and physics potential, Phys. Rep. 968, 1 (2022).
  62. G. Agazie et al. (NANOGrav Collaboration), The NANOGrav 15 yr data set: Evidence for a gravitational-wave background, Astrophys. J. Lett. 951, L8 (2023).
  63. A. Afzal et al. (NANOGrav Collaboration), The NANOGrav 15 yr data set: Search for signals from new physics, Astrophys. J. Lett. 951, L11 (2023); 971, L27(E) (2024).
  64. J. Antoniadis et al. (EPTA and InPTA Collaborations), The second data release from the European Pulsar Timing Array—III. Search for gravitational wave signals, Astron. Astrophys. 678, A50 (2023).
  65. D. J. Reardon et al., Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array, Astrophys. J. Lett. 951, L6 (2023).
  66. G. Hobbs et al., The International Pulsar Timing Array project: Using pulsars as a gravitational wave detector, Classical Quantum Gravity 27, 084013 (2010).
  67. A. Weltman et al., Fundamental physics with the square kilometre array, Publ. Astron. Soc. Aust. 37, e002 (2020).
  68. J. Garcia-Bellido, H. Murayama, and G. White, Exploring the early universe with Gaia and Theia, J. Cosmol. Astropart. Phys. 12 (2021) 023.
  69. K. Schmitz, New sensitivity curves for gravitational-wave signals from cosmological phase transitions, J. High Energy Phys. 01 (2021) 097.
  70. A. Belyaev, N. D. Christensen, and A. Pukhov, calchep 3.4 for collider physics within and beyond the Standard Model, Comput. Phys. Commun. 184, 1729 (2013).
  71. A. Semenov, lanhep—A package for automatic generation of Feynman rules from the Lagrangian. Version 3.2, Comput. Phys. Commun. 201, 167 (2016).
  72. M. Lewicki and V. Vaskonen, Gravitational waves from bubble collisions and fluid motion in strongly supercooled phase transitions, Eur. Phys. J. C 83, 109 (2023).
  73. C. Caprini, R. Jinno, M. Lewicki, E. Madge, M. Merchand, G. Nardini, M. Pieroni, A. Roper Pol, and V. Vaskonen (LISA Cosmology Working Group), Gravitational waves from first-order phase transitions in LISA: Reconstruction pipeline and physics interpretation, J. Cosmol. Astropart. Phys. 10 (2024) 020.
  74. 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.
  75. 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.
  76. 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.

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Phys. Rev. D 114, 055044– Published 23 September, 2026
  • Received 27 April 2026
  • Accepted 1 September 2026
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