Gravitational Waves and Nambu-Goldstone Bosons from Infrared-Finite Cosmic Strings

Author(s)

Fukuda, Hajime, Ge, Shuailiang, Harigaya, Keisuke

Abstract

Skyrmion lines and semi-local strings are examples of infrared-finite cosmic strings that arise in theories with spontaneously broken global symmetries. Unlike global $U(1)$ strings, they do not support the long-range Nambu-Goldstone boson (NGB) profile responsible for a logarithmically infrared-divergent string tension. We argue that NGB emission from their low-frequency oscillations is strongly suppressed. Consequently, their gravitational-wave signals may be comparable to those from local strings.

References
  • [1] T. W. B. Kibble, “Topology of Cosmic Domains and Strings,” J. Phys. A 9, 1387–1398 (1976).
  • [2] T. W. B. Kibble, “Some Implications of a Cosmological Phase Transition,” Phys. Rept. 67, 183 (1980).
  • [3] Alexander Vilenkin, “Cosmic Strings and Domain Walls,” Phys. Rept. 121, 263–315 (1985).
  • [4] W. H. Zurek, “Cosmological Experiments in Superfluid Helium?” Nature 317, 505–508 (1985).
  • [5] A. Vilenkin, “Cosmological Density Fluctuations Produced by Vacuum Strings,” Phys. Rev. Lett. 46, 1169– 1172 (1981), [Erratum: Phys.Rev.Lett. 46, 1496 (1981)].
  • [5] A. Vilenkin, “Cosmological Density Fluctuations Produced by Vacuum Strings,” Phys. Rev. Lett. 46, 1169– 1172 (1981), [Erratum: Phys.Rev.Lett. 46, 1496 (1981)].
  • [6] Tanmay Vachaspati and Alexander Vilenkin, “Gravitational Radiation from Cosmic Strings,” Phys. Rev. D 31, 3052 (1985).
  • [7] J. N. Moore, E. P. S. Shellard, and C. J. A. P. Martins, “On the evolution of Abelian-Higgs string networks,” Phys. Rev. D 65, 023503 (2002), arXiv:hep-ph/0107171.
  • [8] Gabriella Agazie et al. (NANOGrav), “The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background,” Astrophys. J. Lett. 951, L8 (2023), arXiv:2306.16213 [astro-ph.HE].
  • [9] Gabriella Agazie et al. (NANOGrav), “The NANOGrav 15 yr Data Set: Observations and Timing of 68 Millisecond Pulsars,” Astrophys. J. Lett. 951, L9 (2023), arXiv:2306.16217 [astro-ph.HE].
  • [10] Adeela Afzal et al. (NANOGrav), “The NANOGrav 15 yr Data Set: Search for Signals from New Physics,” Astrophys. J. Lett. 951, L11 (2023), [Erratum: Astrophys.J.Lett. 971, L27 (2024), Erratum: Astrophys.J. 971, L27 (2024)], arXiv:2306.16219 [astro-ph.HE].
  • [10] Adeela Afzal et al. (NANOGrav), “The NANOGrav 15 yr Data Set: Search for Signals from New Physics,” Astrophys. J. Lett. 951, L11 (2023), [Erratum: Astrophys.J.Lett. 971, L27 (2024), Erratum: Astrophys.J. 971, L27 (2024)], arXiv:2306.16219 [astro-ph.HE].
  • [10] Adeela Afzal et al. (NANOGrav), “The NANOGrav 15 yr Data Set: Search for Signals from New Physics,” Astrophys. J. Lett. 951, L11 (2023), [Erratum: Astrophys.J.Lett. 971, L27 (2024), Erratum: Astrophys.J. 971, L27 (2024)], arXiv:2306.16219 [astro-ph.HE].
  • [11] A. Vilenkin, “COSMOLOGICAL EVOLUTION OF MONOPOLES CONNECTED BY STRINGS,” Nucl. Phys. B 196, 240–258 (1982).
  • [12] A. Monin and M. B. Voloshin, “The Spontaneous breaking of a metastable string,” Phys. Rev. D 78, 065048 (2008), arXiv:0808.1693 [hep-th].
  • [13] Wilfried Buchmuller, Valerie Domcke, Hitoshi Murayama, and Kai Schmitz, “Probing the scale of grand unification with gravitational waves,” Phys. Lett. B 809, 135764 (2020), arXiv:1912.03695 [hep-ph].
  • [14] Wilfried Buchmuller, Valerie Domcke, and Kai Schmitz, “From NANOGrav to LIGO with metastable cosmic strings,” Phys. Lett. B 811, 135914 (2020), arXiv:2009.10649 [astro-ph.CO].
  • [15] Wilfried Buchmuller, Valerie Domcke, and Kai Schmitz, “Stochastic gravitational-wave background from metastable cosmic strings,” JCAP 12, 006 (2021), arXiv:2107.04578 [hep-ph].
  • [16] David I. Dunsky, Anish Ghoshal, Hitoshi Murayama, Yuki Sakakihara, and Graham White, “GUTs, hybrid topological defects, and gravitational waves,” Phys. Rev. D 106, 075030 (2022), arXiv:2111.08750 [hep-ph].
  • [17] Wilfried Buchmuller, Valerie Domcke, and Kai Schmitz, “Metastable cosmic strings,” JCAP 11, 020 (2023), arXiv:2307.04691 [hep-ph].
  • [18] Haipeng An, Boye Su, Hanwen Tai, Lian-Tao Wang, and Chen Yang, “Phase transition during inflation and the gravitational wave signal at pulsar timing arrays,” Phys. Rev. D 109, L121304 (2024), arXiv:2308.00070 [astroph.CO].
  • [19] George Lazarides, Rinku Maji, Ahmad Moursy, and Qaisar Shafi, “Inflation, superheavy metastable strings and gravitational waves in non-supersymmetric flipped SU(5),” JCAP 03, 006 (2024), arXiv:2308.07094 [hepph].
  • [20] Yunjia Bao, Keisuke Harigaya, and Lian-Tao Wang, “Crescendo beyond the horizon: more gravitational waves from domain walls bounded by inflated cosmic strings,” JHEP 11, 032 (2024), arXiv:2407.17525 [hepph].
  • [21] Akifumi Chitose, Masahiro Ibe, Satoshi Shirai, and Yaxuan Wen, “Cosmic strings in multi-step symmetry breaking,” JHEP 02, 166 (2026), arXiv:2506.15194 [hep-ph].
  • [22] James Ingoldby, Valentin V. Khoze, and Jessica Turner, “Metastable strings and gravitational waves in one-scale models,” JHEP 04, 094 (2026), arXiv:2511.08546 [hepph].
  • [23] Yunjia Bao, Tore Boybeyi, Vuk Mandic, and Lian-Tao Wang, “Searching stochastic gravitational wave background landscape across frequency bands,” Phys. Rev. D 113, 122003 (2026), arXiv:2511.19590 [gr-qc].
  • [24] Doa Hashemi Asl and Kai Schmitz, “New gravitationalwave templates for metastable cosmic strings: Loop breaking versus network collapse,” Phys. Rev. D 114, 035010 (2026), arXiv:2604.28097 [hep-ph].
  • [25] Steven Weinberg, “Nonlinear realizations of chiral symmetry,” Phys. Rev. 166, 1568–1577 (1968).
  • [26] Edward Witten, “Cosmic Superstrings,” Phys. Lett. B 153, 243–246 (1985).
  • [27] Alexander Vilenkin and Tanmay Vachaspati, “Radiation of Goldstone Bosons From Cosmic Strings,” Phys. Rev. D 35, 1138 (1987).
  • [28] R. L. Davis and E. P. S. Shellard, “Antisymmetric Tensors and Spontaneous Symmetry Breaking,” Phys. Lett. B 214, 219–222 (1988).
  • [29] T. H. R. Skyrme, “A Nonlinear field theory,” Proc. Roy. Soc. Lond. A 260, 127–138 (1961).
  • [30] B. M. A. G. Piette, B. J. Schroers, and W. J. Zakrzewski, “Multi - solitons in a two-dimensional Skyrme model,” Z. Phys. C 65, 165–174 (1995), arXiv:hep-th/9406160.
  • [31] B. M. A. G. Piette, B. J. Schroers, and W. J. Zakrzewski, “Dynamics of baby skyrmions,” Nucl. Phys. B 439, 205– 235 (1995), arXiv:hep-ph/9410256.
  • [32] G. H. Derrick, “Comments on nonlinear wave equations as models for elementary particles,” J. Math. Phys. 5, 1252–1254 (1964).
  • [33] T. Vachaspati and A. Achucarro, “Semilocal cosmic strings,” Phys. Rev. D 44, 3067–3071 (1991).
  • [34] John Preskill, “Semilocal defects,” Phys. Rev. D 46, 4218–4231 (1992), arXiv:hep-ph/9206216.
  • [35] Keisuke Harigaya and Yasunori Nomura, “Light Chiral Dark Sector,” Phys. Rev. D 94, 035013 (2016), arXiv:1603.03430 [hep-ph].
  • [36] Raymond T. Co, Keisuke Harigaya, and Yasunori Nomura, “Chiral Dark Sector,” Phys. Rev. Lett. 118, 101801 (2017), arXiv:1610.03848 [hep-ph].
  • [37] Roberto Contino, Alessandro Podo, and Filippo Revello, “Composite Dark Matter from Strongly-Interacting Chiral Dynamics,” JHEP 02, 091 (2021), arXiv:2008.10607 [hep-ph].
  • [38] Masahiro Ibe, Shin Kobayashi, and Keiichi Watanabe, “Chiral composite asymmetric dark matter,” JHEP 07, 220 (2021), arXiv:2105.07642 [hep-ph].
  • [39] Hajime Fukuda and Keisuke Harigaya, “Accidental Peccei-Quinn Symmetry from Chiral Gauge Symmetry and Mirror QCD,” (2026), arXiv:2604.24849 [hep-ph].
  • [40] Mark Hindmarsh, “Existence and stability of semilocal strings,” Phys. Rev. Lett. 68, 1263–1266 (1992).
  • [41] Mark Hindmarsh, “Semilocal topological defects,” Nucl. Phys. B 392, 461–492 (1993), arXiv:hep-ph/9206229.
  • [42] David Tong, “TASI lectures on solitons: Instantons, monopoles, vortices and kinks,” in Theoretical Advanced Study Institute in Elementary Particle Physics: Many Dimensions of String Theory (2005) arXiv:hepth/0509216.
  • [43] David P. Bennett and Francois R. Bouchet, “Evidence for a Scaling Solution in Cosmic String Evolution,” Phys. Rev. Lett. 60, 257 (1988).
  • [44] C. J. A. P. Martins and E. P. S. Shellard, “Quantitative string evolution,” Phys. Rev. D 54, 2535–2556 (1996), arXiv:hep-ph/9602271.
  • [45] Vitaly Vanchurin, Ken D. Olum, and Alexander Vilenkin, “Scaling of cosmic string loops,” Phys. Rev. D 74, 063527 (2006), arXiv:gr-qc/0511159.
  • [46] Jose J. Blanco-Pillado, Ken D. Olum, and Benjamin Shlaer, “Large parallel cosmic string simulations: New results on loop production,” Phys. Rev. D 83, 083514 (2011), arXiv:1101.5173 [astro-ph.CO].
  • [47] R. A. Battye and E. P. S. Shellard, “Global string radiation,” Nucl. Phys. B 423, 260–304 (1994), arXiv:astroph/9311017.
  • [48] Jose J. Blanco-Pillado and Ken D. Olum, “Stochastic gravitational wave background from smoothed cosmic string loops,” Phys. Rev. D 96, 104046 (2017), arXiv:1709.02693 [astro-ph.CO].
  • [49] Pierre Auclair et al., “Probing the gravitational wave background from cosmic strings with LISA,” JCAP 04, 034 (2020), arXiv:1909.00819 [astro-ph.CO].
  • [50] R. A. Leese and T. M. Samols, “Interaction of semilocal vortices,” Nucl. Phys. B 396, 639–669 (1993).
  • [51] Edward Abraham, “Charged semilocal vortices,” Nucl. Phys. B 399, 197–210 (1993).
  • [52] Yukihiro Kanda and Naoya Kitajima, “Emission of Nambu–Goldstone bosons from the semilocal string network,” Phys. Lett. B 873, 140230 (2026), arXiv:2510.07894 [hep-ph].
  • [53] Ana Achucarro and Tanmay Vachaspati, “Semilocal and electroweak strings,” Phys. Rept. 327, 347–426 (2000), arXiv:hep-ph/9904229.
  • [54] Yukihiro Kanda and Naoya Kitajima, “NambuGoldstone emissions from the cosmological evolution of global monopoles,” (2026), arXiv:2607.22481 [hep-ph].
  • [55] Mark Hindmarsh, Stephanie Stuckey, and Neil Bevis, “Abelian Higgs Cosmic Strings: Small Scale Structure and Loops,” Phys. Rev. D 79, 123504 (2009), arXiv:0812.1929 [hep-th].
  • [56] Mark Hindmarsh, Joanes Lizarraga, Ander Urio, and Jon Urrestilla, “Loop decay in Abelian-Higgs string networks,” Phys. Rev. D 104, 043519 (2021), arXiv:2103.16248 [astro-ph.CO].
  • [57] Ana Achucarro, Konrad Kuijken, Leandros Perivolaropoulos, and Tanmay Vachaspati, “Dynamical simulations of semilocal strings,” Nucl. Phys. B 388, 435–456 (1992).