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

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
  • Access by Xinjiang University

Majoron cosmological window: Dark matter and thermal leptogenesis

Arturo de Giorgi1,*, Daniel Naredo-Tuero2,3,†, and Xavier Ponce Díaz4,‡

  • *Contact author: arturo.de-giorgi@durham.ac.uk
  • †Contact author: daniel.naredo@kit.edu
  • ‡Contact author: xavier.poncediaz@unibas.ch
PDF

Phys. Rev. D 114, 075034 – Published 27 October, 2026

DOI: https://doi.org/10.1103/htzs-5yht

Abstract

The majoron is the Nambu-Goldstone boson associated with the spontaneous breaking of a global B−L symmetry. Remarkably, the minimal majoron framework can simultaneously address three key empirical indications of physics beyond the Standard Model: neutrino masses, the matter-antimatter asymmetry, and dark matter. In this work, we identify the cosmologically viable region in which majoron dark matter and high-scale thermal leptogenesis can be realized simultaneously. We show that successful leptogenesis plays a central role in making this scenario predictive: by constraining the right-handed-neutrino mass scale, it determines the irreducible freeze-in contribution to the majoron abundance and fixes the size of the couplings relevant for visible dark matter decays. Combining the irreducible dark matter production mechanisms with warm dark matter limits and indirect searches for decaying dark matter, we map the resulting majoron cosmological window and show that future x- and gamma-ray telescopes can probe part of the surviving parameter space.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (174)

  1. P. Minkowski, μ→eγ at a rate of one out of 109 muon decays?, Phys. Lett. 67B, 421 (1977).
  2. T. Yanagida, Horizontal symmetry and masses of neutrinos, Prog. Theor. Phys. 64, 1103 (1980).
  3. M. Gell-Mann, P. Ramond, and R. Slansky, Complex spinors and unified theories, Conf. Proc. C 790927, 315 (1979).
  4. R. N. Mohapatra and G. Senjanovic, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44, 912 (1980).
  5. J. Schechter and J. W. F. Valle, Neutrino masses in SU(2)×U(1) theories, Phys. Rev. D 22, 2227 (1980).
  6. S. Centelles Chuliá, A. Herrero-Brocal, and A. Vicente, The type-I seesaw family, J. High Energy Phys. 07 (2024) 060.
  7. M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174, 45 (1986).
  8. L. Covi, E. Roulet, and F. Vissani, CP violating decays in leptogenesis scenarios, Phys. Lett. B 384, 169 (1996).
  9. L. Covi and E. Roulet, Baryogenesis from mixed particle decays, Phys. Lett. B 399, 113 (1997).
  10. A. Pilaftsis, CP violation and baryogenesis due to heavy Majorana neutrinos, Phys. Rev. D 56, 5431 (1997).
  11. W. Buchmuller and M. Plumacher, CP asymmetry in Majorana neutrino decays, Phys. Lett. B 431, 354 (1998).
  12. C. Albertus et al., WISPedia—the WISPs encyclopedia, arXiv:2602.09089.
  13. A. Arza et al., The COSMIC WISPers white paper: The physics case for weakly interacting slim particles, arXiv:2603.03433.
  14. Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, Are there real Goldstone bosons associated with broken lepton number?, Phys. Lett. 98B, 265 (1981).
  15. Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, Spontaneously broken lepton number and cosmological constraints on the neutrino mass spectrum, Phys. Rev. Lett. 45, 1926 (1980).
  16. J. Schechter and J. W. F. Valle, Neutrino decay and spontaneous violation of lepton number, Phys. Rev. D 25, 774 (1982).
  17. G. B. Gelmini and M. Roncadelli, Left-handed neutrino mass scale and spontaneously broken lepton number, Phys. Lett. 99B, 411 (1981).
  18. I. Z. Rothstein, K. S. Babu, and D. Seckel, Planck scale symmetry breaking and majoron physics, Nucl. Phys. B403, 725 (1993).
  19. Y. Nomura, T. Watari, and T. Yanagida, Quintessence axion potential induced by electroweak instanton effects, Phys. Lett. B 484, 103 (2000).
  20. M. Frigerio, T. Hambye, and E. Masso, Sub-GeV dark matter as pseudo-Goldstone from the seesaw scale, Phys. Rev. X 1, 021026 (2011).
  21. A. de Giorgi, L. Merlo, X. Ponce Díaz, and S. Rigolin, The minimal massive majoron seesaw model, J. High Energy Phys. 03 (2024) 094.
  22. A. Greljo, X. Ponce Díaz, and A. E. Thomsen, Insights on the cosmic origin of matter from proton stability, J. Cosmol. Astropart. Phys. 11 (2025) 043.
  23. M. Berbig, About electroweak domain walls in majoron models, Phys. Rev. D 113, 109902 (2026).
  24. S. Weinberg, A new light boson?, Phys. Rev. Lett. 40, 223 (1978).
  25. F. Wilczek, Problem of strong P and T invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978).
  26. R. D. Peccei and H. R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38, 1440 (1977).
  27. R. D. Peccei and H. R. Quinn, Constraints imposed by CP conservation in the presence of instantons, Phys. Rev. D 16, 1791 (1977).
  28. E. K. Akhmedov, Z. G. Berezhiani, R. N. Mohapatra, and G. Senjanovic, Planck scale effects on the majoron, Phys. Lett. B 299, 90 (1993).
  29. J. M. Cline, K. Kainulainen, and K. A. Olive, Constraints on majoron models, neutrino masses and baryogenesis, Astropart. Phys. 1, 387 (1993).
  30. J. Heeck and H. H. Patel, Majoron at two loops, Phys. Rev. D 100, 095015 (2019).
  31. A. Herrero-Brocal and A. Vicente, The majoron coupling to charged leptons, J. High Energy Phys. 01 (2024) 078.
  32. L. Di Luzio, F. Mescia, E. Nardi, P. Panci, and R. Ziegler, Astrophobic axions, Phys. Rev. Lett. 120, 261803 (2018).
  33. F. Björkeroth, L. Di Luzio, F. Mescia, E. Nardi, P. Panci, and R. Ziegler, Axion-electron decoupling in nucleophobic axion models, Phys. Rev. D 101, 035027 (2020).
  34. L. Di Luzio, F. Mescia, E. Nardi, and S. Okawa, Renormalization group effects in astrophobic axion models, Phys. Rev. D 106, 055016 (2022).
  35. C. Garcia-Cely and J. Heeck, Neutrino lines from majoron dark matter, J. High Energy Phys. 05 (2017) 102.
  36. K. Akita and M. Niibo, Updated constraints and future prospects on majoron dark matter, J. High Energy Phys. 07 (2023) 132.
  37. F. Arias-Aragon, E. Fernandez-Martinez, M. Gonzalez-Lopez, and L. Merlo, Neutrino masses and Hubble tension via a majoron in MFV, Eur. Phys. J. C 81, 28 (2021).
  38. F. Arias-Aragón, E. Fernández-Martínez, M. González-López, and L. Merlo, Dynamical minimal flavour violating inverse seesaw, J. High Energy Phys. 09 (2022) 210.
  39. Q. Liang, X. Ponce Díaz, and T. T. Yanagida, Axion detection experiments can probe majoron models, Phys. Rev. Lett. 134, 151803 (2025).
  40. Y. Lu, Z. S. C. Picker, A. Kusenko, and T. T. Yanagida, Neutrino masses, matter-antimatter asymmetry, dark matter, and supermassive black hole formation explained with majorons, Phys. Rev. D 113, 015037 (2026).
  41. A. G. Cohen and D. B. Kaplan, Thermodynamic generation of the baryon asymmetry, Phys. Lett. B 199, 251 (1987).
  42. A. G. Cohen and D. B. Kaplan, Spontaneous baryogenesis, Nucl. Phys. B308, 913 (1988).
  43. M. Ibe and K. Kaneta, Spontaneous thermal leptogenesis via majoron oscillation, Phys. Rev. D 92, 035019 (2015).
  44. E. J. Chun and T. H. Jung, Leptogenesis driven by a majoron, Phys. Rev. D 109, 095004 (2024).
  45. J. Wada, Majoron-driven leptogenesis in gauged U(1) Lμ−Lτ model, Phys. Rev. D 110, 103510 (2024).
  46. E. J. Chun, H. M. Lee, and J.-H. Song, Spontaneous leptogenesis in type I seesaw models, Phys. Rev. D 113, 075021 (2026).
  47. H. Takahashi and J. Wada, Asymmetric dark matter from low-scale spontaneous leptogenesis, arXiv:2601.01849.
  48. I. Affleck and M. Dine, A new mechanism for baryogenesis, Nucl. Phys. B249, 361 (1985).
  49. R. N. Mohapatra and N. Okada, Unified model for inflation, pseudo-Goldstone dark matter, neutrino mass, and baryogenesis, Phys. Rev. D 105, 035024 (2022).
  50. M. Berbig, Type II seesaw leptogenesis in a majoron background, J. High Energy Phys. 04 (2026) 116.
  51. E. K. Akhmedov, V. A. Rubakov, and A. Y. Smirnov, Baryogenesis via neutrino oscillations, Phys. Rev. Lett. 81, 1359 (1998).
  52. T. Asaka and M. Shaposhnikov, The νMSM, dark matter and baryon asymmetry of the universe, Phys. Lett. B 620, 17 (2005).
  53. A. Caputo, P. Hernandez, and N. Rius, Leptogenesis from oscillations and dark matter, Eur. Phys. J. C 79, 574 (2019).
  54. M. Escudero and S. J. Witte, The Hubble tension as a hint of leptogenesis and neutrino mass generation, Eur. Phys. J. C 81, 515 (2021).
  55. T. Brune, Leptogenesis in majoron models without domain walls, Phys. Rev. D 107, 096023 (2023).
  56. S. K. Manna and A. Sil, Majorons revisited: Light dark matter as a FIMP, Phys. Rev. D 108, 075026 (2023).
  57. S. F. King, S. K. Manna, R. Roshan, and A. Sil, Leptogenesis with majoron dark matter, Phys. Rev. D 111, 095008 (2025).
  58. T. Brune, Leptogenesis in a majoron plus triplet model, Phys. Rev. D 111, 115001 (2025).
  59. I. Vilja, Baryogenesis in the singlet majoron model, Phys. Lett. B 324, 197 (1994).
  60. P.-H. Gu and U. Sarkar, Leptogenesis bound on spontaneous symmetry breaking of global lepton number, Eur. Phys. J. C 71, 1560 (2011).
  61. P.-H. Gu, E. Ma, and U. Sarkar, Pseudo-majoron as dark matter, Phys. Lett. B 690, 145 (2010).
  62. D. Aristizabal Sierra, M. Tortola, J. W. F. Valle, and A. Vicente, Leptogenesis with a dynamical seesaw scale, J. Cosmol. Astropart. Phys. 07 (2014) 052.
  63. M. Reig, J. W. F. Valle, and M. Yamada, Light majoron cold dark matter from topological defects and the formation of boson stars, J. Cosmol. Astropart. Phys. 09 (2019) 029.
  64. K. Akita, G. Lambiase, M. Niibo, and M. Yamaguchi, Neutrino lines from MeV dark matter annihilation and decay in JUNO, J. Cosmol. Astropart. Phys. 10 (2022) 097.
  65. G. F. Giudice, A. Notari, M. Raidal, A. Riotto, and A. Strumia, Towards a complete theory of thermal leptogenesis in the SM and MSSM, Nucl. Phys. B685, 89 (2004).
  66. J. Heeck and D. Teresi, Cold keV dark matter from decays and scatterings, Phys. Rev. D 96, 035018 (2017).
  67. S. Boulebnane, J. Heeck, A. Nguyen, and D. Teresi, Cold light dark matter in extended Seesaw models, J. Cosmol. Astropart. Phys. 04 (2018) 006.
  68. C. Y. Tan, A. Dekker, and A. Drlica-Wagner, Mixed warm dark matter constraints using Milky Way satellite galaxy counts, Phys. Rev. D 111, 063079 (2025).
  69. C. Thorpe-Morgan, D. Malyshev, A. Santangelo, J. Jochum, B. Jäger, M. Sasaki, and S. Saeedi, THESEUS insights into axionlike particles, dark photon, and sterile neutrino dark matter, Phys. Rev. D 102, 123003 (2020).
  70. T. Shutt et al., The GammaTPC gamma-ray telescope concept, arXiv:2502.14841.
  71. I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J. P. Pinheiro, and T. Schwetz, nufit-6.0: Updated global analysis of three-flavor neutrino oscillations, J. High Energy Phys. 12 (2024) 216.
  72. F. Capozzi and G. Raffelt, Axion and neutrino bounds improved with new calibrations of the tip of the red-giant branch using geometric distance determinations, Phys. Rev. D 102, 083007 (2020).
  73. M. J. Dolan, F. J. Hiskens, and R. R. Volkas, Advancing globular cluster constraints on the axion-photon coupling, J. Cosmol. Astropart. Phys. 10 (2022) 096.
  74. Y. Farzan, Bounds on the coupling of the majoron to light neutrinos from supernova cooling, Phys. Rev. D 67, 073015 (2003).
  75. T. Brune and H. Päs, Massive majorons and constraints on the majoron-neutrino coupling, Phys. Rev. D 99, 096005 (2019).
  76. A. Caputo, H.-T. Janka, G. Raffelt, and E. Vitagliano, Low-energy supernovae severely constrain radiative particle decays, Phys. Rev. Lett. 128, 221103 (2022).
  77. M. Diamond, D. F. G. Fiorillo, G. Marques-Tavares, and E. Vitagliano, Axion-sourced fireballs from supernovae, Phys. Rev. D 107, 103029 (2023); 108, 049902(E) (2023).
  78. D. F. G. Fiorillo, G. G. Raffelt, and E. Vitagliano, Strong supernova 1987A constraints on bosons decaying to neutrinos, Phys. Rev. Lett. 131, 021001 (2023).
  79. D. Cadamuro and J. Redondo, Cosmological bounds on pseudo Nambu-Goldstone bosons, J. Cosmol. Astropart. Phys. 02 (2012) 032.
  80. M. Millea, L. Knox, and B. Fields, New bounds for axions and axion-like particles with keV-GeV masses, Phys. Rev. D 92, 023010 (2015).
  81. P. F. Depta, M. Hufnagel, and K. Schmidt-Hoberg, Robust cosmological constraints on axion-like particles, J. Cosmol. Astropart. Phys. 05 (2020) 009.
  82. M. Escudero Abenza, C. Garcia-Perez, and M. Ovchynnikov, Nucleosynthesis and CMB bounds on photophilic ALPs: A fresh look, Eur. Phys. J. C 86, 500 (2026).
  83. M. Escudero and S. J. Witte, A CMB search for the neutrino mass mechanism and its relation to the Hubble tension, Eur. Phys. J. C 80, 294 (2020).
  84. K. Bays et al. (Super-Kamiokande Collaboration), Supernova relic neutrino search at Super-Kamiokande, Phys. Rev. D 85, 052007 (2012).
  85. H. Zhang et al. (Super-Kamiokande Collaboration), Supernova relic neutrino search with neutron tagging at Super-Kamiokande-IV, Astropart. Phys. 60, 41 (2015).
  86. A. Albert et al., Results from the search for dark matter in the Milky Way with 9 years of data of the ANTARES neutrino telescope, Phys. Lett. B 769, 249 (2017); 796, 253(E) (2019).
  87. M. Agostini et al. (Borexino Collaboration), Search for low-energy neutrinos from astrophysical sources with Borexino, Astropart. Phys. 125, 102509 (2021).
  88. S. Abe et al. (KamLAND Collaboration), Limits on astrophysical antineutrinos with the KamLAND experiment, Astrophys. J. 925, 14 (2022).
  89. K. Abe et al. (Super-Kamiokande Collaboration), Diffuse supernova neutrino background search at Super-Kamiokande, Phys. Rev. D 104, 122002 (2021).
  90. R. Abbasi et al. (IceCube Collaboration), Indirect search for dark matter in the galactic centre with IceCube, in 37th International Cosmic Ray Conference (2021), arXiv:2107.11224.
  91. C. A. Argüelles, D. Delgado, A. Friedlander, A. Kheirandish, I. Safa, A. C. Vincent, and H. White, Dark matter decay to neutrinos, Phys. Rev. D 108, 123021 (2023).
  92. R. Abbasi et al. (IceCube Collaboration), Search for neutrino lines from dark matter annihilation and decay with IceCube, Phys. Rev. D 108, 102004 (2023).
  93. K. Perez, K. C. Y. Ng, J. F. Beacom, C. Hersh, S. Horiuchi, and R. Krivonos, Almost closing the νMSM sterile neutrino dark matter window with NuSTAR, Phys. Rev. D 95, 123002 (2017).
  94. K. C. Y. Ng, B. M. Roach, K. Perez, J. F. Beacom, S. Horiuchi, R. Krivonos, and D. R. Wik, New constraints on sterile neutrino dark matter from NuSTAR M31 observations, Phys. Rev. D 99, 083005 (2019).
  95. J. W. Foster, M. Kongsore, C. Dessert, Y. Park, N. L. Rodd, K. Cranmer, and B. R. Safdi, Deep search for decaying dark matter with XMM-Newton blank-sky observations, Phys. Rev. Lett. 127, 051101 (2021).
  96. A. Dekker, E. Peerbooms, F. Zimmer, K. C. Y. Ng, and S. Ando, Searches for sterile neutrinos and axionlike particles from the galactic halo with eROSITA, Phys. Rev. D 104, 023021 (2021).
  97. B. M. Roach, S. Rossland, K. C. Y. Ng, K. Perez, J. F. Beacom, B. W. Grefenstette, S. Horiuchi, R. Krivonos, and D. R. Wik, Long-exposure NuSTAR constraints on decaying dark matter in the galactic halo, Phys. Rev. D 107, 023009 (2023).
  98. F. Calore, A. Dekker, P. D. Serpico, and T. Siegert, Constraints on light decaying dark matter candidates from 16 yr of INTEGRAL/SPI observations, Mon. Not. R. Astron. Soc. 520, 4167 (2023); 538, 132(E) (2025).
  99. C. Fong, K. C. Y. Ng, and Q. Liu, Searching for particle dark matter with eROSITA early data, Phys. Rev. D 112, 083052 (2025).
  100. F. S. Queiroz and K. Sinha, The poker face of the majoron dark matter model: LUX to keV line, Phys. Lett. B 735, 69 (2014).
  101. C. O’Hare, cajohare/axionlimits: Axionlimits, https://cajohare.github.io/AxionLimits/ (2020).
  102. J. A. Adams, S. Sarkar, and D. W. Sciama, CMB anisotropy in the decaying neutrino cosmology, Mon. Not. R. Astron. Soc. 301, 210 (1998).
  103. N. Padmanabhan and D. P. Finkbeiner, Detecting dark matter annihilation with CMB polarization: Signatures and experimental prospects, Phys. Rev. D 72, 023508 (2005).
  104. T. R. Slatyer, N. Padmanabhan, and D. P. Finkbeiner, CMB constraints on WIMP annihilation: Energy absorption during the recombination epoch, Phys. Rev. D 80, 043526 (2009).
  105. V. Poulin, J. Lesgourgues, and P. D. Serpico, Cosmological constraints on exotic injection of electromagnetic energy, J. Cosmol. Astropart. Phys. 03 (2017) 043.
  106. T. R. Slatyer and C.-L. Wu, General constraints on dark matter decay from the cosmic microwave background, Phys. Rev. D 95, 023010 (2017).
  107. J. Baur, N. Palanque-Delabrouille, C. Yèche, C. Magneville, and M. Viel, Lyman-alpha forests cool warm dark matter, J. Cosmol. Astropart. Phys. 08 (2016) 012.
  108. C. Yèche, N. Palanque-Delabrouille, J. Baur, and H. du Mas des Bourboux, Constraints on neutrino masses from Lyman-alpha forest power spectrum with BOSS and XQ-100, J. Cosmol. Astropart. Phys. 06 (2017) 047.
  109. J. Baur, N. Palanque-Delabrouille, C. Yeche, A. Boyarsky, O. Ruchayskiy, E. Armengaud, and J. Lesgourgues, Constraints from Ly-α forests on non-thermal dark matter including resonantly-produced sterile neutrinos, J. Cosmol. Astropart. Phys. 12 (2017) 013.
  110. V. Iršič et al., New Constraints on the free-streaming of warm dark matter from intermediate and small scale Lyman-α forest data, Phys. Rev. D 96, 023522 (2017).
  111. Y. Sun, J. W. Foster, H. Liu, J. B. Muñoz, and T. R. Slatyer, Inhomogeneous energy injection in the 21-cm power spectrum: Sensitivity to dark matter decay, Phys. Rev. D 111, 043015 (2025).
  112. T. Simon, G. Franco Abellán, P. Du, V. Poulin, and Y. Tsai, Constraining decaying dark matter with BOSS data and the effective field theory of large-scale structures, Phys. Rev. D 106, 023516 (2022).
  113. A. Kamada, K. T. Inoue, and T. Takahashi, Constraints on mixed dark matter from anomalous strong lens systems, Phys. Rev. D 94, 023522 (2016).
  114. A. Schneider, Constraining noncold dark matter models with the global 21-cm signal, Phys. Rev. D 98, 063021 (2018).
  115. G. Parimbelli, G. Scelfo, S. K. Giri, A. Schneider, M. Archidiacono, S. Camera, and M. Viel, Mixed dark matter: Matter power spectrum and halo mass function, J. Cosmol. Astropart. Phys. 12 (2021) 044.
  116. R. An, E. O. Nadler, A. Benson, and V. Gluscevic, COZMIC. II. Cosmological zoom-in simulations with fractional non-CDM initial conditions, Astrophys. J. 986, 128 (2025).
  117. T. T. Q. Nguyen, P. De la Torre Luque, I. John, S. Balaji, P. Carenza, and T. Linden, INTEGRAL, eROSITA and Voyager constraints on light bosonic dark matter: ALPs, dark photons, scalars, B−L and Li−Lj vectors, Phys. Rev. D 113, 103010 (2026).
  118. M. Lattanzi and J. W. F. Valle, Decaying warm dark matter and neutrino masses, Phys. Rev. Lett. 99, 121301 (2007).
  119. M. Lattanzi, Decaying majoron dark matter and neutrino masses, AIP Conf. Proc. 966, 163 (2008).
  120. L. F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. 120B, 133 (1983).
  121. M. Dine and W. Fischler, The not so harmless axion, Phys. Lett. 120B, 137 (1983).
  122. J. Preskill, M. B. Wise, and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. 120B, 127 (1983).
  123. N. Blinov, M. J. Dolan, P. Draper, and J. Kozaczuk, Dark matter targets for axionlike particle searches, Phys. Rev. D 100, 015049 (2019).
  124. M. Blennow, E. Fernandez-Martinez, and B. Zaldivar, Freeze-in through portals, J. Cosmol. Astropart. Phys. 01 (2014) 003.
  125. T. W. B. Kibble, Topology of cosmic domains and strings, J. Phys. A 9, 1387 (1976).
  126. R. Davis, Cosmic axions from cosmic strings, Phys. Lett. B 180, 225 (1986).
  127. K. Chathirathas and T. Schwetz, How light can ALP dark matter be?, J. Cosmol. Astropart. Phys. 08 (2026) 041.
  128. M. Gorghetto, E. Hardy, and G. Villadoro, Axions from strings: The attractive solution, J. High Energy Phys. 07 (2018) 151.
  129. M. Gorghetto, E. Hardy, and G. Villadoro, More axions from strings, SciPost Phys. 10, 050 (2021).
  130. M. Buschmann, J. W. Foster, A. Hook, A. Peterson, D. E. Willcox, W. Zhang, and B. R. Safdi, Dark matter from axion strings with adaptive mesh refinement, Nat. Commun. 13, 1049 (2022).
  131. H. Kim and M. Son, More scalings from cosmic strings, J. High Energy Phys. 07 (2025) 052.
  132. K. Saikawa, J. Redondo, A. Vaquero, and M. Kaltschmidt, Spectrum of global string networks and the axion dark matter mass, J. Cosmol. Astropart. Phys. 10 (2024) 043.
  133. J. N. Benabou, M. Buschmann, J. W. Foster, and B. R. Safdi, Axion mass prediction from adaptive mesh refinement cosmological lattice simulations, Phys. Rev. Lett. 134, 241003 (2025).
  134. H. Kim, J. Park, and M. Son, Axion dark matter from cosmic string network, J. High Energy Phys. 07 (2024) 150.
  135. D. H. Lyth, Axions and inflation: Sitting in the vacuum, Phys. Rev. D 45, 3394 (1992).
  136. M. Beltran, J. Garcia-Bellido, and J. Lesgourgues, Isocurvature bounds on axions revisited, Phys. Rev. D 75, 103507 (2007).
  137. M. P. Hertzberg, M. Tegmark, and F. Wilczek, Axion cosmology and the energy scale of inflation, Phys. Rev. D 78, 083507 (2008).
  138. A. Arvanitaki, S. Dimopoulos, M. Galanis, L. Lehner, J. O. Thompson, and K. Van Tilburg, Large-misalignment mechanism for the formation of compact axion structures: Signatures from the QCD axion to fuzzy dark matter, Phys. Rev. D 101, 083014 (2020).
  139. B. Batell, A. Dasgupta, S. Dutta, and A. Ghalsasi, Majoron dark matter, high-scale seesaw, and leptogenesis, Phys. Rev. D 114, 055018 (2026).
  140. G. Ballesteros, J. Redondo, A. Ringwald, and C. Tamarit, Unifying inflation with the axion, dark matter, baryogenesis and the Seesaw mechanism, Phys. Rev. Lett. 118, 071802 (2017).
  141. Y. Bao, J. Fan, and L. Li, Opening up a window on the postinflationary QCD axion, Phys. Rev. Lett. 130, 241001 (2023).
  142. A. H. Sopov, C. Tamarit, and R. R. Volkas, The post-inflationary cosmology of the VISHν axion-majoron model, J. Cosmol. Astropart. Phys. 10 (2026) 007.
  143. R. R. Volkas, A. J. Davies, and G. C. Joshi, Naturalness of the invisible axion model, Phys. Lett. B 215, 133 (1988).
  144. R. Foot, A. Kobakhidze, K. L. McDonald, and R. R. Volkas, Poincaré protection for a natural electroweak scale, Phys. Rev. D 89, 115018 (2014).
  145. W. Buchmuller, P. Di Bari, and M. Plumacher, Leptogenesis for pedestrians, Ann. Phys. (Amsterdam) 315, 305 (2005).
  146. C. Hagedorn, R. N. Mohapatra, E. Molinaro, C. C. Nishi, and S. T. Petcov, CP violation in the lepton sector and implications for leptogenesis, Int. J. Mod. Phys. A 33, 1842006 (2018).
  147. A. Abada, S. Davidson, A. Ibarra, F. X. Josse-Michaux, M. Losada, and A. Riotto, Flavour matters in leptogenesis, J. High Energy Phys. 09 (2006) 010.
  148. S. Davidson and A. Ibarra, A lower bound on the right-handed neutrino mass from leptogenesis, Phys. Lett. B 535, 25 (2002).
  149. K. Moffat, S. Pascoli, S. T. Petcov, H. Schulz, and J. Turner, Three-flavored nonresonant leptogenesis at intermediate scales, Phys. Rev. D 98, 015036 (2018).
  150. A. Granelli, K. Moffat, Y. F. Perez-Gonzalez, H. Schulz, and J. Turner, ulysses: Universal LeptogeneSiS Equation Solver, Comput. Phys. Commun. 262, 107813 (2021).
  151. A. Granelli, C. Leslie, Y. F. Perez-Gonzalez, H. Schulz, B. Shuve, J. Turner, and R. Walker, ulysses, Universal LeptogeneSiS Equation Solver: Version 2, Comput. Phys. Commun. 291, 108834 (2023).
  152. F. Feroz and M. P. Hobson, Multimodal nested sampling: An efficient and robust alternative to MCMC methods for astronomical data analysis, Mon. Not. R. Astron. Soc. 384, 449 (2008).
  153. F. Feroz, M. P. Hobson, and M. Bridges, multinest: An efficient and robust Bayesian inference tool for cosmology and particle physics, Mon. Not. R. Astron. Soc. 398, 1601 (2009).
  154. F. Feroz, M. P. Hobson, E. Cameron, and A. N. Pettitt, Importance nested sampling and the multinest algorithm, Open J. Astrophys. 2, 10 (2019).
  155. J. A. Casas and A. Ibarra, Oscillating neutrinos and μ→e,γ, Nucl. Phys. B618, 171 (2001).
  156. I. Obata and T. T. Yanagida, Probing majoron dark matter with gravitational wave detectors, arXiv:2604.08193.
  157. C.-F. Chang and Y. Cui, Stochastic gravitational wave background from global cosmic strings, Phys. Dark Universe 29, 100604 (2020).
  158. P. Di Bari, S. F. King, and M. H. Rahat, Gravitational waves from phase transitions and cosmic strings in neutrino mass models with multiple majorons, J. High Energy Phys. 05 (2024) 068.
  159. K. Akita, K. Hamaguchi, H. Kitagawa, and T. Yokoyama, Minimal majoron dark matter, arXiv:2605.12946.
  160. J. Bonilla, A. de Giorgi, B. Gavela, L. Merlo, and M. Ramos, The cost of an ALP solution to the neutral B-anomalies, J. High Energy Phys. 02 (2023) 138.
  161. B. Pontecorvo, Neutrino experiments and the problem of conservation of leptonic charge, Zh. Eksp. Teor. Fiz. 53, 1717 (1967).
  162. Z. Maki, M. Nakagawa, and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28, 870 (1962).
  163. M. Badziak and M. Laletin, Precise predictions for the QCD axion contribution to dark radiation with full phase-space evolution, J. High Energy Phys. 02 (2025) 108.
  164. F. D’Eramo and A. Lenoci, Back to the phase space: Thermal axion dark radiation via couplings to standard model fermions, Phys. Rev. D 110, 116028 (2024).
  165. S. Blanchet, P. Di Bari, D. A. Jones, and L. Marzola, Leptogenesis with heavy neutrino flavours: From density matrix to Boltzmann equations, J. Cosmol. Astropart. Phys. 01 (2013) 041.
  166. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  167. J. Lopez-Pavon, E. Molinaro, and S. T. Petcov, Radiative corrections to light neutrino masses in low scale type I seesaw scenarios and neutrinoless double beta decay, J. High Energy Phys. 11 (2015) 030.
  168. G. Cardano, The Rules of Algebra: Ars Magna (Dover Publications, New York, 1993).
  169. 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).
  170. M. Berbig and A. Ghoshal, Impact of high-scale seesaw and leptogenesis on inflationary tensor perturbations as detectable gravitational waves, J. High Energy Phys. 05 (2023) 172.
  171. Z. A. Borboruah, F. F. Deppisch, A. Ghoshal, and L. Malhotra, Inflationary gravitational waves and laboratory searches as complementary probes of right-handed neutrinos, Phys. Rev. D 112, 056003 (2025).
  172. M. Chianese, G. Domènech, T. Papanikolaou, R. Samanta, and N. Saviano, Induced gravitational waves as cosmic tracers of leptogenesis, J. Cosmol. Astropart. Phys. 08 (2026) 021.
  173. H. Murayama, B. Noether, and J. Schütte-Engel, Observing leptogenesis in action with gravitational waves, J. Cosmol. Astropart. Phys. 12 (2025) 027.
  174. N. Aggarwal et al., Challenges and opportunities of gravitational-wave searches above 10 kHz, Living Rev. Relativity 28, 10 (2025).

Outline

Information

Phys. Rev. D 114, 075034– Published 27 October, 2026
  • Received 4 June 2026
  • Accepted 25 September 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