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  • Letter
  • Open Access

Magnetic monopoles and high frequency gravitational waves from quasistable strings

Rinku Maji1,* and Qaisar Shafi2

  • 1Cosmology, Gravity and Astroparticle Physics Group, Center for Theoretical Physics of the Universe, Institute for Basic Science, Daejeon 34126, Republic of Korea
  • 2Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA

  • *Contact author: rinkumaji9792@gmail.com
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Phys. Rev. D 113, L111703 – Published 11 June, 2026

DOI: https://doi.org/10.1103/nz1z-xszk

Abstract

The spontaneous breaking of SO(10) via flipped SU(5) to the Standard Model yields a novel scenario in which the superheavy topologically stable grand unified theory (GUT) monopole carrying a single unit (2π/e) of Dirac magnetic charge emerges from the merger of a confined but topologically distinct monopole-antimonopole pair that are pulled together by a string. The SO(10) breaking via the subgroup SU(4)c×SU(2)L×SU(2)R, following a similar reasoning, produces a topologically stable monopole that carries two units (4π/e) of Dirac charge. We explore the cosmological consequences of this scenario by assuming that the monopoles and strings experience a limited number of inflationary e-foldings, before reentering the horizon and ultimately forming a network of quasistable strings bounded by monopole-antimonopole pairs. We identify regions of the parameter space that yield an observable number density of the GUT monopole from the collapse of the appropriate string segments. The gravitational waves emitted by these quasistable cosmic strings lie in the Hz to kHz range, which can be tested in a number of proposed and ongoing experiments.

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References (89)

  1. P. A. M. Dirac, Quantised singularities in the electromagnetic field, Proc. R. Soc. A 133, 60 (1931).
  2. G. ’t Hooft, Magnetic monopoles in unified gauge theories, Nucl. Phys. B79, 276 (1974).
  3. A. M. Polyakov, Particle spectrum in quantum field theory, JETP Lett. 20, 194 (1974).
  4. H. Georgi and S. L. Glashow, Unity of all elementary particle forces, Phys. Rev. Lett. 32, 438 (1974).
  5. H. Georgi, The state of the art—gauge theories, AIP Conf. Proc. 23, 575 (1975).
  6. H. Fritzsch and P. Minkowski, Unified interactions of leptons and hadrons, Ann. Phys. (N.Y.) 93, 193 (1975).
  7. M. Daniel, G. Lazarides, and Q. Shafi, SU(5) monopoles, magnetic symmetry and confinement, Nucl. Phys. B170, 156 (1980).
  8. C. P. Dokos and T. N. Tomaras, Monopoles and dyons in the SU(5) model, Phys. Rev. D 21, 2940 (1980).
  9. G. Lazarides, Q. Shafi, and W. P. Trower, Consequences of a monopole with Dirac magnetic charge, Phys. Rev. Lett. 49, 1756 (1982).
  10. J. C. Pati and A. Salam, Lepton number as the fourth color, Phys. Rev. D 10, 275 (1974); 11, 703(E) (1975).
  11. G. Lazarides, M. Magg, and Q. Shafi, Phase transitions and magnetic monopoles in SO(10), Phys. Lett. B 97, 87 (1980).
  12. G. Lazarides and Q. Shafi, Monopoles, strings, and necklaces in SO(10) and E6, J. High Energy Phys. 10 (2019) 193.
  13. G. Lazarides, R. Maji, and Q. Shafi, Quantum tunneling in the early universe: Stable magnetic monopoles from metastable cosmic strings, J. Cosmol. Astropart. Phys. 05 (2024) 128.
  14. T. W. Kephart and Q. Shafi, Magnetic monopoles and exotic states in SU(4)c×SU(2)L×SU(2)R, Phys. Rev. D 112, 075013 (2025).
  15. A. Moursy and Q. Shafi, Primordial monopoles, black holes and gravitational waves, J. Cosmol. Astropart. Phys. 08 (2024) 064.
  16. A. Afzal, Q. Shafi, and A. Tiwari, Gravitational wave emission from metastable current-carrying strings in E6, Phys. Lett. B 850, 138516 (2024).
  17. R. Maji, Q. Shafi, and A. Tiwari, Topological structures, dark matter and gravitational waves in E6, J. High Energy Phys. 08 (2024) 060.
  18. R. Maji and Q. Shafi, Superheavy metastable strings in SO(10), J. High Energy Phys. 06 (2025) 217.
  19. R. Maji and Q. Shafi, Superconducting strings in E6, Phys. Rev. D 112, L101903 (2025).
  20. T. W. B. Kibble, G. Lazarides, and Q. Shafi, Walls bounded by strings, Phys. Rev. D 26, 435 (1982).
  21. R. Maji and Q. Shafi, C-parity, magnetic monopoles, and higher frequency gravitational waves, Phys. Rev. D 111, 075027 (2025).
  22. W. Buchmuller, V. Domcke, H. Murayama, and K. Schmitz, Probing the scale of grand unification with gravitational waves, Phys. Lett. B 809, 135764 (2020).
  23. W. Buchmuller, V. Domcke, and K. Schmitz, Stochastic gravitational-wave background from metastable cosmic strings, J. Cosmol. Astropart. Phys. 12 (2021) 006.
  24. D. I. Dunsky, A. Ghoshal, H. Murayama, Y. Sakakihara, and G. White, GUTs, hybrid topological defects, and gravitational waves, Phys. Rev. D 106, 075030 (2022).
  25. G. Senjanović and M. Zantedeschi, Minimal Pati-Salam theory: From cosmic defects to gravitational waves and colliders, Phys. Rev. D 112, 055018 (2025).
  26. I. Jeong, J. Kersten, S. Scopel, and L. Velasco-Sevilla, Gravitational wave signals in a promising realization of SO(10) unification, Phys. Rev. D 113, 075017 (2026).
  27. A. Moursy and Q. Shafi, Waterfall phase in supersymmetric hybrid inflation, J. High Energy Phys. 01 (2026) 162.
  28. D. Bandyopadhyay, D. Borah, N. Das, and R. Samanta, High-quality axion dark matter at gravitational wave interferometers, arXiv:2509.14323.
  29. Y. Bao, T. Boybeyi, V. Mandic, and L.-T. Wang, Searching stochastic gravitational wave background landscape across frequency bands, arXiv:2511.19590.
  30. L. Tranchedone, E. Carragher, E. Hardy, and N. K. van IJcken, Metastable cosmic strings are broken at the start, arXiv:2601.04320.
  31. Y. B. Zeldovich and M. Y. Khlopov, On the concentration of relic magnetic monopoles in the universe, Phys. Lett. 79B, 239 (1978).
  32. J. Preskill, Cosmological production of superheavy magnetic monopoles, Phys. Rev. Lett. 43, 1365 (1979).
  33. G. Lazarides, Q. Shafi, and A. Tiwari, Composite topological structures in SO(10), J. High Energy Phys. 05 (2023) 119.
  34. X. Martin and A. Vilenkin, Gravitational wave background from hybrid topological defects, Phys. Rev. Lett. 77, 2879 (1996).
  35. G. Lazarides, R. Maji, and Q. Shafi, Gravitational waves from quasi-stable strings, J. Cosmol. Astropart. Phys. 08 (2022) 042.
  36. N. Aggarwal et al., Challenges and opportunities of gravitational wave searches above 10 kHz, Living Rev. Relativity 28, 10 (2025).
  37. Planck Collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); Planck Collaboration652, C4(E) (2021).
  38. M. Escudero Abenza, Precision early universe thermodynamics made simple: Neff and neutrino decoupling in the Standard Model and beyond, J. Cosmol. Astropart. Phys. 05 (2020) 048.
  39. K. Akita and M. Yamaguchi, A precision calculation of relic neutrino decoupling, J. Cosmol. Astropart. Phys. 08 (2020) 012.
  40. J. Froustey, C. Pitrou, and M. C. Volpe, Neutrino decoupling including flavour oscillations and primordial nucleosynthesis, J. Cosmol. Astropart. Phys. 12 (2020) 015.
  41. J. J. Bennett, G. Buldgen, P. F. De Salas, M. Drewes, S. Gariazzo, S. Pastor, and Y. Y. Y. Wong, Towards a precision calculation of Neff in the standard model II: Neutrino decoupling in the presence of flavour oscillations and finite-temperature QED, J. Cosmol. Astropart. Phys. 04 (2021) 073.
  42. N. Herman, A. Füzfa, L. Lehoucq, and S. Clesse, Detecting planetary-mass primordial black holes with resonant electromagnetic gravitational-wave detectors, Phys. Rev. D 104, 023524 (2021).
  43. N. Herman, L. Lehoucq, and A. Fúzfa, Electromagnetic antennas for the resonant detection of the stochastic gravitational wave background, Phys. Rev. D 108, 124009 (2023).
  44. R. Slansky, Group theory for unified model building, Phys. Rep. 79, 1 (1981).
  45. T. W. B. Kibble, G. Lazarides, and Q. Shafi, Strings in SO(10), Phys. Lett. 113B, 237 (1982).
  46. J. Chakrabortty, G. Lazarides, R. Maji, and Q. Shafi, Primordial monopoles and strings, inflation, and gravity waves, J. High Energy Phys. 02 (2021) 114.
  47. A. Preda, G. Senjanovic, and M. Zantedeschi, SO(10): A case for hadron colliders, Phys. Lett. B 838, 137746 (2023).
  48. R. Maji and Q. Shafi, Kinetic mixing, proton decay and gravitational waves in SO(10), J. High Energy Phys. 10 (2024) 157.
  49. A. Preda, G. Senjanović, and M. Zantedeschi, Minimal SO(10) near the edge: The importance of being effective, Phys. Rev. D 111, 015036 (2025).
  50. A. Preda, G. Senjanović, and M. Zantedeschi, SO(10) theory on the plateau: The importance of being renormalizable, arXiv:2502.21180.
  51. MACRO Collaboration, Final results of magnetic monopole searches with the MACRO experiment, Eur. Phys. J. C 25, 511 (2002).
  52. A. Vilenkin, Cosmic string dynamics with friction, Phys. Rev. D 43, 1060 (1991).
  53. J. Garriga and M. Sakellariadou, Effects of friction on cosmic strings, Phys. Rev. D 48, 2502 (1993).
  54. C. J. A. P. Martins and E. P. S. Shellard, String evolution with friction, Phys. Rev. D 53, R575 (1996).
  55. C. J. A. P. Martins and E. P. S. Shellard, Quantitative string evolution, Phys. Rev. D 54, 2535 (1996).
  56. C. J. A. P. Martins and E. P. S. Shellard, Extending the velocity dependent one scale string evolution model, Phys. Rev. D 65, 043514 (2002).
  57. Y. Gouttenoire, G. Servant, and P. Simakachorn, Beyond the standard models with cosmic strings, J. Cosmol. Astropart. Phys. 07 (2020) 032.
  58. J. J. Blanco-Pillado and K. D. Olum, Form of cosmic string cusps, Phys. Rev. D 59, 063508 (1999); 103, 029902(E) (2021).
  59. D. Matsunami, L. Pogosian, A. Saurabh, and T. Vachaspati, Decay of cosmic string loops due to particle radiation, Phys. Rev. Lett. 122, 201301 (2019).
  60. P. Auclair, D. A. Steer, and T. Vachaspati, Particle emission and gravitational radiation from cosmic strings: Observational constraints, Phys. Rev. D 101, 083511 (2020).
  61. T. Vachaspati and A. Vilenkin, Gravitational radiation from cosmic strings, Phys. Rev. D 31, 3052 (1985).
  62. A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, England, 2000).
  63. T. Damour and A. Vilenkin, Gravitational wave bursts from cusps and kinks on cosmic strings, Phys. Rev. D 64, 064008 (2001).
  64. V. Vanchurin, K. D. Olum, and A. Vilenkin, Scaling of cosmic string loops, Phys. Rev. D 74, 063527 (2006).
  65. C. Ringeval, M. Sakellariadou, and F. Bouchet, Cosmological evolution of cosmic string loops, J. Cosmol. Astropart. Phys. 02 (2007) 023.
  66. K. D. Olum and V. Vanchurin, Cosmic string loops in the expanding Universe, Phys. Rev. D 75, 063521 (2007).
  67. S. Olmez, V. Mandic, and X. Siemens, Gravitational-wave stochastic background from kinks and cusps on cosmic strings, Phys. Rev. D 81, 104028 (2010).
  68. J. J. Blanco-Pillado, K. D. Olum, and B. Shlaer, The number of cosmic string loops, Phys. Rev. D 89, 023512 (2014).
  69. J. J. Blanco-Pillado and K. D. Olum, Stochastic gravitational wave background from smoothed cosmic string loops, Phys. Rev. D 96, 104046 (2017).
  70. Y. Cui, M. Lewicki, D. E. Morrissey, and J. D. Wells, Probing the pre-BBN universe with gravitational waves from cosmic strings, J. High Energy Phys. 01 (2019) 081.
  71. E. Witten, Neutrino masses in the minimal O(10) theory, Phys. Lett. 91B, 81 (1980).
  72. G. Mentasti and M. Peloso, ET sensitivity to the anisotropic stochastic gravitational wave background, J. Cosmol. Astropart. Phys. 03 (2021) 080.
  73. T. Regimbau, M. Evans, N. Christensen, E. Katsavounidis, B. Sathyaprakash, and S. Vitale, Digging deeper: Observing primordial gravitational waves below the binary black hole produced stochastic background, Phys. Rev. Lett. 118, 151105 (2017).
  74. LIGO Scientific, Virgo, and KAGRA Collaboration, Constraints on cosmic strings using data from the third Advanced LIGO–Virgo observing run, Phys. Rev. Lett. 126, 241102 (2021).
  75. E. Thrane and J. D. Romano, Sensitivity curves for searches for gravitational-wave backgrounds, Phys. Rev. D 88, 124032 (2013).
  76. K. Schmitz, New sensitivity curves for gravitational-wave signals from cosmological phase transitions, J. High Energy Phys. 01 (2021) 097.
  77. KAGRA, LIGO Scientific, and VIRGO Collaborations, Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA, Living Rev. Relativity 21, 3 (2018).
  78. S. Sato et al., The status of DECIGO, J. Phys. Conf. Ser. 840, 012010 (2017).
  79. J. Crowder and N. J. Cornish, Beyond LISA: Exploring future gravitational wave missions, Phys. Rev. D 72, 083005 (2005).
  80. V. Corbin and N. J. Cornish, Detecting the cosmic gravitational wave background with the big bang observer, Classical Quantum Gravity 23, 2435 (2006).
  81. E. Aver, K. A. Olive, and E. D. Skillman, The effects of He I λ10830 on helium abundance determinations, J. Cosmol. Astropart. Phys. 07 (2015) 011.
  82. A. Peimbert, M. Peimbert, and V. Luridiana, The primordial helium abundance and the number of neutrino families, Rev. Mex. Astron. Astrofis. 52, 419 (2016), https://www.astroscu.unam.mx/rmaa/RMxAA..52-2/PDF/RMxAA..52-2_apeimbert.pdf.
  83. M. Maggiore, Gravitational wave experiments and early universe cosmology, Phys. Rep. 331, 283 (2000).
  84. N. Bartolo et al., Science with the space-based interferometer LISA. IV: Probing inflation with gravitational waves, J. Cosmol. Astropart. Phys. 12 (2016) 026.
  85. P. Amaro-Seoane et al., Laser interferometer space antenna, arXiv:1702.00786.
  86. G. Janssen et al., Gravitational wave astronomy with the SKA, Proc. Sci. AASKA14 (2015) 037 [arXiv:1501.00127].
  87. NANOGrav Collaboration, The NANOGrav 15 yr data set: Evidence for a gravitational-wave background, Astrophys. J. Lett. 951, L8 (2023).
  88. NANOGrav Collaboration, The NANOGrav 15 yr data set: Search for signals from new physics, Astrophys. J. Lett. 951, L11 (2023).
  89. G. Lazarides, R. Maji, and Q. Shafi, Superheavy quasistable strings and walls bounded by strings in the light of NANOGrav 15 year data, Phys. Rev. D 108, 095041 (2023).

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Phys. Rev. D 113, L111703– Published 11 June, 2026
  • Received 6 March 2026
  • Accepted 8 May 2026
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