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Next-to-minimal freeze-in dark matter

Nicolás Bernal1, Sagnik Mukherjee2, and James Unwin2

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Phys. Rev. D 113, 116042 – Published 30 June, 2026

DOI: https://doi.org/10.1103/bw63-h2y4

Abstract

If the dark matter mass exceeds the highest temperature of the thermal bath, then dark matter production is Boltzmann suppressed. This opens new possibilities for dark matter model building. In particular, weakly interacting massive particle models that are experimentally excluded can be revived in this setting; conversely, freeze-in models, which would typically be beyond experimental reach, are potentially discoverable in the Boltzmann suppressed regime. In a recent letter, we highlighted these aspects for the case of electroweak doublet fermion dark matter assuming instantaneous inflationary reheating. Due to its elegance and simplicity, we coin this minimal freeze-in (MFI) dark matter. Here we consider next-to-minimal extensions of MFI dark matter. We present the implications for noninstantaneous reheating, including scenarios beyond the standard picture in which the Universe is initially matter dominated prior to reheating. Furthermore, we explore model variations within the electroweak dark matter scenario. Specifically, we consider fermion dark matter in higher representations of SU(2)L, exploring the current limits and the near-future discovery potential.

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Minimal freeze-in dark matter: Reviving electroweak doublet dark matter with Boltzmann suppressed freeze-in

Nicolás Bernal, Sagnik Mukherjee, and James Unwin
Phys. Rev. D 113, 115065 (2026)

Article Text

References (93)

  1. N. Bernal, S. Mukherjee, and J. Unwin, companion paper, Minimal freeze-in dark matter: Reviving electroweak doublet dark matter with Boltzmann suppressed freeze-in, Phys. Rev. D 113, 115065 (2026)..
  2. LZ Collaboration, Dark matter search results from 4.2 tonne-years of exposure of the LUX-ZEPLIN (LZ) experiment, Phys. Rev. Lett. 135, 011802 (2025).
  3. D. Tucker-Smith and N. Weiner, Inelastic dark matter, Phys. Rev. D 64, 043502 (2001).
  4. G. F. Giudice, E. W. Kolb, and A. Riotto, Largest temperature of the radiation era and its cosmological implications, Phys. Rev. D 64, 023508 (2001).
  5. C. Cosme, F. Costa, and O. Lebedev, Freeze-in at stronger coupling, Phys. Rev. D 109, 075038 (2024).
  6. C. Cosme, F. Costa, and O. Lebedev, Temperature evolution in the early universe and freeze-in at stronger coupling, J. Cosmol. Astropart. Phys. 06 (2024) 031.
  7. N. Okada and O. Seto, Superheavy WIMP dark matter from incomplete thermalization, Phys. Lett. B 820, 136528 (2021).
  8. N. Koivunen, O. Lebedev, and M. Raidal, Probing sterile neutrino freeze-in at stronger coupling, Eur. Phys. J. C 84, 1234 (2024).
  9. G. Arcadi, F. Costa, A. Goudelis, and O. Lebedev, Higgs portal dark matter freeze-in at stronger coupling: Observational benchmarks, J. High Energy Phys. 07 (2024) 044.
  10. K. K. Boddy, K. Freese, G. Montefalcone, and B. Shams Es Haghi, Minimal dark matter freeze-in with low reheating temperatures and implications for direct detection, Phys. Rev. D 111, 063537 (2025).
  11. G. Arcadi, D. Cabo-Almeida, and O. Lebedev, Z’-mediated dark matter freeze-in at stronger coupling, Phys. Lett. B 861, 139268 (2025).
  12. N. Bernal, C. S. Fong, and Ó. Zapata, Probing low-reheating scenarios with minimal freeze-in dark matter, J. High Energy Phys. 02 (2025) 161.
  13. N. Bernal, G. Cottin, B. Díaz Sáez, and M. López, Testing frozen-in pNGB dark matter with a long-lived dark Higgs, J. High Energy Phys. 01 (2026) 081.
  14. D. Feiteira, O. Lebedev, and V. Oliveira, Warm dark matter from freeze-in at stronger coupling, Phys. Lett. B 877, 140486 (2026).
  15. DARWIN Collaboration, DARWIN: Towards the ultimate dark matter detector, J. Cosmol. Astropart. Phys. 11 (2016) 017.
  16. L. J. Hall, K. Jedamzik, J. March-Russell, and S. M. West, Freeze-in production of FIMP dark matter, J. High Energy Phys. 03 (2010) 080.
  17. F. Elahi, C. Kolda, and J. Unwin, UltraViolet freeze-in, J. High Energy Phys. 03 (2015) 048.
  18. M. A. G. García, Y. Mambrini, K. A. Olive, and M. Peloso, Enhancement of the dark matter abundance before reheating: Applications to gravitino dark matter, Phys. Rev. D 96, 103510 (2017).
  19. N. Bernal, F. Elahi, C. Maldonado, and J. Unwin, Ultraviolet freeze-in and non-standard cosmologies, J. Cosmol. Astropart. Phys. 11 (2019) 026.
  20. M. A. G. García, K. Kaneta, Y. Mambrini, and K. A. Olive, Reheating and post-inflationary production of dark matter, Phys. Rev. D 101, 123507 (2020).
  21. N. Bernal, J. Rubio, and H. Veermäe, Boosting ultraviolet freeze-in in NO models, J. Cosmol. Astropart. Phys. 06 (2020) 047.
  22. N. Bernal, J. Rubio, and H. Veermäe, UV freeze-in in Starobinsky inflation, J. Cosmol. Astropart. Phys. 10 (2020) 021.
  23. R. Allahverdi et al., The first three seconds: A review of possible expansion histories of the early Universe, Open J. Astrophys. 4, 5 (2021).
  24. M. A. G. García, K. Kaneta, Y. Mambrini, K. A. Olive, and S. Verner, Freeze-in from preheating, J. Cosmol. Astropart. Phys. 03 (2022) 016.
  25. B. Barman, N. Bernal, Y. Xu, and Ó. Zapata, Ultraviolet freeze-in with a time-dependent inflaton decay, J. Cosmol. Astropart. Phys. 07 (2022) 019.
  26. B. Batell et al., Conversations and deliberations: Non-standard cosmological epochs and expansion histories, Int. J. Mod. Phys. A 40, 2530004 (2025).
  27. N. Bernal, K. Deka, and M. Losada, Dark matter ultraviolet freeze-in in general reheating scenarios, Phys. Rev. D 111, 055034 (2025).
  28. M. Cirelli, N. Fornengo, and A. Strumia, Minimal dark matter, Nucl. Phys. B753, 178 (2006).
  29. B. R. Safdi and W. L. Xu, Wino and real minimal dark matter excluded by Fermi gamma-ray observations, arXiv:2507.15934.
  30. A. Milagre and L. Lavoura, Unitarity constraints on large multiplets of arbitrary gauge groups, Nucl. Phys. B1004, 116542 (2024).
  31. S. Das, K. Murase, and T. Fujii, Revisiting ultrahigh-energy constraints on decaying superheavy dark matter, Phys. Rev. D 107, 103013 (2023).
  32. O. Deligny, Constraints on superheavy dark matter decaying into hν, Zν and Wℓ, Eur. Phys. J. C 85, 985 (2025).
  33. R. D. Peccei and H. R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38, 1440 (1977).
  34. T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131, 95 (1979).
  35. S. Sarkar, Big bang nucleosynthesis and physics beyond the standard model, Rep. Prog. Phys. 59, 1493 (1996).
  36. T. Hasegawa, N. Hiroshima, K. Kohri, R. S. L. Hansen, T. Tram, and S. Hannestad, MeV-scale reheating temperature and thermalization of oscillating neutrinos by radiative and hadronic decays of massive particles, J. Cosmol. Astropart. Phys. 12 (2019) 012.
  37. M. Kawasaki, K. Kohri, and N. Sugiyama, Cosmological constraints on late time entropy production, Phys. Rev. Lett. 82, 4168 (1999).
  38. BICEP and Keck Collaborations, Improved constraints on primordial gravitational waves using Planck, WMAP, and BICEP/Keck observations through the 2018 observing season, Phys. Rev. Lett. 127, 151301 (2021).
  39. D. Baumann, Inflation, in Theoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small (World Scientific, Singapore, 2011), pp. 523–686, 10.1142/9789814327183_0010.
  40. J. Hisano, S. Matsumoto, M. M. Nojiri, and O. Saito, Non-perturbative effect on dark matter annihilation and gamma ray signature from galactic center, Phys. Rev. D 71, 063528 (2005).
  41. J. L. Feng, M. Kaplinghat, and H.-B. Yu, Sommerfeld enhancements for thermal relic dark matter, Phys. Rev. D 82, 083525 (2010).
  42. C. García-Cely, A. Ibarra, A. S. Lamperstorfer, and M. H. G. Tytgat, Gamma-rays from heavy minimal dark matter, J. Cosmol. Astropart. Phys. 10 (2015) 058.
  43. P. Panci, Electroweak multiplets as dark matter candidates: A brief review, Proc. Sci. CORFU2023 (2024) 033 [arXiv:2405.05087].
  44. H.E.S.S. Collaboration, Search for photon-linelike signatures from dark matter annihilations with H.E.S.S., Phys. Rev. Lett. 110, 041301 (2013).
  45. M. Aghaie, A. Dondarini, G. Marino, and P. Panci, Minimal dark matter in the sky: Updated indirect detection probes, arXiv:2507.17607.
  46. J. Einasto, On the construction of a composite model for the galaxy and on the determination of the system of galactic parameters, Tr. Astrofiz. Inst. Alma-Ata 5, 87 (1965).
  47. K. Kohri, P. K. Paul, and N. Sahu, Super heavy dark matter origin of the PeV neutrino event: KM3-230213A, Phys. Rev. D 112, L031703 (2025).
  48. S. Abe et al., Discovering the Higgsino at CTAO-north within the decade, arXiv:2506.08084.
  49. XENON Collaboration, WIMP dark matter search using a 3.1  tonne−year exposure of the XENONnT experiment, Phys. Rev. Lett. 135, 221003 (2025).
  50. PandaX Collaboration, Dark matter search results from 1.54 tonneyear exposure of PandaX-4T, Phys. Rev. Lett. 134, 011805 (2025).
  51. LZ Collaboration, New constraints on ultraheavy dark matter from the LZ experiment, Phys. Rev. D 109, 112010 (2024).
  52. R. Essig, Direct detection of non-chiral dark matter, Phys. Rev. D 78, 015004 (2008).
  53. J. Hisano, S. Matsumoto, M. M. Nojiri, and O. Saito, Direct detection of the Wino and Higgsino-like neutralino dark matters at one-loop level, Phys. Rev. D 71, 015007 (2005).
  54. Q. Chen, G.-J. Ding, and R. J. Hill, General heavy WIMP nucleon elastic scattering, Phys. Rev. D 108, 116023 (2023).
  55. C. A. J. O’Hare, Can we overcome the neutrino floor at high masses?, Phys. Rev. D 102, 063024 (2020).
  56. N. Bernal, K. Deka, and M. Losada, Thermal dark matter with low-temperature reheating, J. Cosmol. Astropart. Phys. 09 (2024) 024.
  57. R. T. Co, E. González, and K. Harigaya, Increasing temperature toward the completion of reheating, J. Cosmol. Astropart. Phys. 11 (2020) 038.
  58. B. Barman and N. Bernal, Gravitational SIMPs, J. Cosmol. Astropart. Phys. 06 (2021) 011.
  59. K. Harigaya and K. Mukaida, Thermalization after/during reheating, J. High Energy Phys. 05 (2014) 006.
  60. K. Mukaida and M. Yamada, Thermalization process after inflation and effective potential of scalar field, J. Cosmol. Astropart. Phys. 02 (2016) 003.
  61. D. Chowdhury and A. Hait, Thermalization in the presence of a time-dependent dissipation and its impact on dark matter production, J. High Energy Phys. 09 (2023) 085.
  62. N. Bernal, M. Dutra, Y. Mambrini, K. Olive, M. Peloso, and M. Pierre, Spin-2 portal dark matter, Phys. Rev. D 97, 115020 (2018).
  63. M. Dutra, Origins for dark matter particles: From the WIMP miracle to the “FIMP wonder”, Ph.D. thesis, Orsay, LPT, 2019.
  64. S. Cléry, Y. Mambrini, K. A. Olive, and S. Verner, Gravitational portals in the early Universe, Phys. Rev. D 105, 075005 (2022).
  65. N. Bernal, E. Cervantes, K. Deka, and A. Hryczuk, Freezing-in cannibals with low-reheating temperature, J. High Energy Phys. 09 (2025) 083.
  66. H. M. Lee, M. Park, and V. Sanz, Gravity-mediated dark matter at a low reheating temperature, J. High Energy Phys. 05 (2025) 126.
  67. G. Bélanger, N. Bernal, and A. Pukhov, Z’-mediated dark matter with low-temperature reheating, J. High Energy Phys. 03 (2025) 079.
  68. S. Khan, J. Kim, and H. M. Lee, Higgs portal vector dark matter at a low reheating temperature, J. Cosmol. Astropart. Phys. 06 (2025) 040.
  69. N. Bernal, J. P. Neto, J. Silva-Malpartida, and F. S. Queiroz, Enabling thermal dark matter within the vanilla Lμ−Lτ model, Phys. Rev. D 112, 075042 (2025).
  70. 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. Rept. 516, 1 (2012).
  71. N. Bernal, S. Mukherjee, and J. Unwin, Boltzmann suppressed ultraviolet freeze-in, J. Cosmol. Astropart. Phys. 02 (2026) 010.
  72. S. P. Martin, A supersymmetry primer, Adv. Ser. Dir. High Energy Phys. 18, 1 (1998).
  73. G. F. Giudice and A. Masiero, A natural solution to the μ problem in supergravity theories, Phys. Lett. B 206, 480 (1988).
  74. P. Fayet, Spontaneously broken supersymmetric theories of weak, electromagnetic and strong interactions, Phys. Lett. 69B, 489 (1977).
  75. G. R. Farrar and S. Weinberg, Supersymmetry at ordinary energies. II. R invariance, Goldstone bosons, and gauge fermion masses, Phys. Rev. D 27, 2732 (1983).
  76. L. J. Hall and L. Randall, U(1)-R symmetric supersymmetry, Nucl. Phys. B352, 289 (1991).
  77. P. J. Fox, A. E. Nelson, and N. Weiner, Dirac gaugino masses and supersoft supersymmetry breaking, J. High Energy Phys. 08 (2002) 035.
  78. G. D. Kribs, E. Poppitz, and N. Weiner, Flavor in supersymmetry with an extended R-symmetry, Phys. Rev. D 78, 055010 (2008).
  79. J. Unwin and T. Yildirim, A QCD R-axion, Phys. Rev. D 111, 015048 (2025).
  80. J. Unwin, R-symmetric high scale supersymmetry, Phys. Rev. D 86, 095002 (2012).
  81. M. Fabbrichesi and A. Urbano, Natural minimal dark matter, Phys. Rev. D 93, 055017 (2016).
  82. T. Toma, Minimal dark matter in SU(5) grand unification, Phys. Rev. D 111, L051701 (2025).
  83. N. Maru, N. Okada, and S. Okada, Fermionic minimal dark matter in 5D gauge-Higgs unification, Phys. Rev. D 96, 115023 (2017).
  84. T. Banks and N. Seiberg, Symmetries and strings in field theory and gravity, Phys. Rev. D 83, 084019 (2011).
  85. S. Das, J. A. Carpio, and K. Murase, Probing superheavy dark matter through lunar radio observations of ultrahigh-energy neutrinos and the impacts of neutrino cascades, Phys. Rev. D 111, 083007 (2025).
  86. K. C. Y. Ng et al., Sensitivities of KM3NeT on decaying dark matter, arXiv:2007.03692.
  87. B. Ostdiek, Constraining the minimal dark matter fiveplet with LHC searches, Phys. Rev. D 92, 055008 (2015).
  88. N. Kumar and V. Sahdev, Alternative signatures of the quintuplet fermions at the LHC and future linear colliders, Phys. Rev. D 105, 115016 (2022).
  89. Y.-P. Zeng, C. Cai, D.-Y. Liu, Z.-H. Yu, and H.-H. Zhang, Probing quadruplet scalar dark matter at current and future pp colliders, Phys. Rev. D 101, 115033 (2020).
  90. S. Bottaro, A. Strumia, and N. Vignaroli, Minimal dark matter bound states at future colliders, J. High Energy Phys. 06 (2021) 143.
  91. S. Gessner et al., Design initiative for a 10 TeV pCM wakefield collider, arXiv:2503.20214.
  92. S. Chigusa et al., Searches for electroweak states at future plasma wakefield colliders, arXiv:2512.09995.
  93. P. Gondolo and G. Gelmini, Cosmic abundances of stable particles: Improved analysis, Nucl. Phys. B360, 145 (1991).

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Phys. Rev. D 113, 116042– Published 30 June, 2026
  • Received 25 April 2026
  • Accepted 28 May 2026
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