- 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

Supersymmetric hybrid inflation and current-carrying metastable cosmic strings in SU(4)c×SU(2)L×U(1)R

Adeela Afzal1,*, Maria Mehmood1,†, Mansoor Ur Rehman2,‡, and Qaisar Shafi3

  • *Contact author: adeelaafzal555@gmail.com
  • †Contact author: mehmood.maria786@gmail.com
  • ‡Contact author: m.rehman@iu.edu.sa
PDF

Phys. Rev. D 112, 083545 – Published 23 October, 2025

DOI: https://doi.org/10.1103/d7zx-c7f7

Abstract

We construct a realistic supersymmetric model for superheavy metastable cosmic strings (CSs) that can be investigated in the current pulsar timing array (PTA) experiments. It is based on shifted μ-hybrid inflation in which the symmetry breaking SU(4)c×SU(2)L×U(1)R→SU(3)c×SU(2)L×U(1)B−L×U(1)R proceeds along an inflationary trajectory such that the topologically unstable primordial monopoles are inflated away. The breaking of U(1)B−L×U(1)R→U(1)Y after inflation ends yields the superheavy metastable CSs carrying the right handed neutrino zero modes that generate the stochastic gravitational wave background, which we show is consistent with the current PTA dataset and the LIGO O3 run. The scalar spectral index ns and the tensor-to-scalar ratio r are compatible with the Planck 2018 and Atacama Cosmology Telescope measurements. Both reheating and leptogenesis are briefly discussed.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (65)

  1. G. Agazie et al. (NANOGrav Collaboration), Astrophys. J. Lett. 951, L8 (2023).
  2. A. Afzal et al. (NANOGrav Collaboration), Astrophys. J. Lett. 951, L11 (2023).
  3. J. Antoniadis et al. (EPTA Collaboration), Astron. Astrophys. 678, A50 (2023).
  4. D. J. Reardon et al., Astrophys. J. Lett. 951, L6 (2023).
  5. H. Xu et al., Res. Astron. Astrophys. 23, 075024 (2023).
  6. W. Buchmuller, V. Domcke, and K. Schmitz, Phys. Lett. B 811, 135914 (2020).
  7. W. Buchmuller, V. Domcke, and K. Schmitz, J. Cosmol. Astropart. Phys. 12 (2021) 006.
  8. G. Lazarides, R. Maji, A. Moursy, and Q. Shafi, J. Cosmol. Astropart. Phys. 03 (2024) 006.
  9. W. Buchmuller, V. Domcke, and K. Schmitz, J. Cosmol. Astropart. Phys. 11 (2023) 020.
  10. S. Antusch, K. Hinze, S. Saad, and J. Steiner, Phys. Rev. D 108, 095053 (2023).
  11. W. Ahmed, M. U. Rehman, and U. Zubair, J. Cosmol. Astropart. Phys. 01 (2024) 049.
  12. G. Lazarides, R. Maji, and Q. Shafi, Phys. Rev. D 108, 095041 (2023).
  13. G. Lazarides, Q. Shafi, and A. Tiwari, J. High Energy Phys. 05 (2023) 119.
  14. G. R. Dvali, Q. Shafi, and R. K. Schaefer, Phys. Rev. Lett. 73, 1886 (1994).
  15. E. J. Copeland, A. R. Liddle, D. H. Lyth, E. D. Stewart, and D. Wands, Phys. Rev. D 49, 6410 (1994).
  16. V. N. Senoguz and Q. Shafi, Phys. Rev. D 71, 043514 (2005).
  17. M. U. Rehman, Q. Shafi, and J. R. Wickman, Phys. Lett. B 683, 191 (2010).
  18. W. Buchmuller, L. Covi, and D. Delepine, Phys. Lett. B 491, 183 (2000).
  19. M. Bastero-Gil, S. F. King, and Q. Shafi, Phys. Lett. B 651, 345 (2007).
  20. M. ur Rehman, V. N. Senoguz, and Q. Shafi, Phys. Rev. D 75, 043522 (2007).
  21. M. U. Rehman, Q. Shafi, and J. R. Wickman, Phys. Lett. B 688, 75 (2010).
  22. Q. Shafi and J. R. Wickman, Phys. Lett. B 696, 438 (2011).
  23. M. U. Rehman, Q. Shafi, and J. R. Wickman, Phys. Rev. D 83, 067304 (2011).
  24. M. Civiletti, M. U. Rehman, Q. Shafi, and J. R. Wickman, Phys. Rev. D 84, 103505 (2011).
  25. W. Buchmüller, V. Domcke, K. Kamada, and K. Schmitz, J. Cosmol. Astropart. Phys. 07 (2014) 054.
  26. W. Buchmuller, J. High Energy Phys. 04 (2021) 168.
  27. W. Ahmed, M. Junaid, S. Nasri, and U. Zubair, Phys. Rev. D 105, 115008 (2022).
  28. W. Ahmed, M. Moosa, S. Munir, and U. Zubair, J. High Energy Phys. 05 (2023) 011.
  29. M. A. Masoud, M. U. Rehman, and Q. Shafi, J. Cosmol. Astropart. Phys. 11 (2021) 022.
  30. N. Okada and Q. Shafi, Phys. Lett. B 775, 348 (2017).
  31. M. U. Rehman, Q. Shafi, and F. K. Vardag, Phys. Rev. D 96, 063527 (2017).
  32. N. Okada and Q. Shafi, Phys. Lett. B 787, 141 (2018).
  33. W. Ahmed, A. Karozas, and G. K. Leontaris, Phys. Rev. D 104, 055025 (2021).
  34. A. Afzal, W. Ahmed, M. U. Rehman, and Q. Shafi, Phys. Rev. D 105, 103539 (2022).
  35. G. Lazarides and Q. Shafi, J. High Energy Phys. 10 (2019) 193.
  36. G. Lazarides, M. U. Rehman, Q. Shafi, and F. K. Vardag, Phys. Rev. D 103, 035033 (2021).
  37. W. Ahmed, M. Mehmood, M. U. Rehman, and U. Zubair, J. Cosmol. Astropart. Phys. 09 (2025) 035.
  38. G. Aad et al. (ATLAS Collaboration), J. High Energy Phys. 06 (2023) 158.
  39. S. Antusch, K. Hinze, S. Saad, and J. Steiner, Phys. Rev. D 109, 055031 (2024).
  40. S. Khalil, M. U. Rehman, Q. Shafi, and E. A. Zaakouk, Phys. Rev. D 83, 063522 (2011).
  41. V. N. Senoguz and Q. Shafi, Phys. Lett. B 668, 6 (2008).
  42. V. N. Senoguz and Q. Shafi, Phys. Lett. B 596, 8 (2004).
  43. G. R. Dvali, G. Lazarides, and Q. Shafi, Phys. Lett. B 424, 259 (1998).
  44. G. Lazarides and N. D. Vlachos, Phys. Lett. B 441, 46 (1998).
  45. N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  46. Y. Akrami et al. (Planck Collaboration), Astron. Astrophys. 641, A10 (2020).
  47. E. Calabrese et al. (ACT Collaboration), arXiv:2503.14454.
  48. J. Garcia-Bellido and A. D. Linde, Phys. Rev. D 57, 6075 (1998).
  49. W. Buchmuller, V. Domcke, H. Murayama, and K. Schmitz, Phys. Lett. B 809, 135764 (2020).
  50. R. Abbott et al. (KAGRA Collaboration, Virgo Collaboration, and LIGO Scientific Collaboration), Phys. Rev. D 104, 022004 (2021).
  51. A. Afzal, Q. Shafi, and A. Tiwari, Phys. Lett. B 850, 138516 (2024).
  52. A. Monin and M. B. Voloshin, Phys. At. Nucl. 73, 703 (2010).
  53. A. Monin and M. B. Voloshin, Phys. Rev. D 78, 065048 (2008).
  54. L. Leblond, B. Shlaer, and X. Siemens, Phys. Rev. D 79, 123519 (2009).
  55. I. Y. Rybak and L. Sousa, J. Cosmol. Astropart. Phys. 11 (2022) 024.
  56. I. Y. Rybak and L. Sousa, Phys. Rev. D 111, 083502 (2025).
  57. R. Smits, M. Kramer, B. Stappers, D. R. Lorimer, J. Cordes, and A. Faulkner, Astron. Astrophys. 493, 1161 (2009).
  58. J. Garcia-Bellido, H. Murayama, and G. White, J. Cosmol. Astropart. Phys. 12 (2021) 023.
  59. Pau Amaro-Seoane et al., arXiv:1702.00786.
  60. M. Punturo et al., Classical Quantum Gravity 27, 194002 (2010).
  61. V. Corbin and N. J. Cornish, Classical Quantum Gravity 23, 2435 (2006).
  62. A. Sesana et al., Exp. Astron. 51, 1333 (2021).
  63. D. Reitze et al., Bull. Am. Astron. Soc. 51, 035 (2019).
  64. R. Maji and Q. Shafi, J. High Energy Phys. 06 (2025) 217.
  65. https://github.com/mansoorhep/2308.11410.

Outline

Information

Phys. Rev. D 112, 083545– Published 23 October, 2025
  • Received 6 August 2025
  • Accepted 27 September 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