\begin{document}$ S U(2)_d $\end{document} symmetry breaking in conjunction with the Witten effect. Furthermore, we examine the mass of hidden monopoles generated by phase transition as well as the impact of axion-monopole interactions on the axion mass. Following spontaneous breaking of the PQ symmetry, axions emitted by cosmic strings or domain walls as well as hidden monopoles generated during this transition may collectively contribute to the observed dark matter relic density. Additionally, the stochastic gravitational wave background generated by sub-GeV phase transitions and by the decay of axionic domain walls formed during sub-ZeV phase transitions could account for the low-frequency gravitational wave signals detected by PTA experiments."> Gravitational waves and dark matter with Witten effect -
  • [1]

    R. Caldwell, Y. Cui, H. K. Guoet al., Gen. Rel. Grav.54, 156 (2022), arXiv: 2203.07972[gr-qc]

  • [2]

    P. S. B. Dev and A. Mazumdar, Phys. Rev. D93, 104001 (2016), arXiv: 1602.04203[hep-ph]

  • [3]

    C. S. Machado, W. Ratzinger, P. Schwalleret al., Phys. Rev. D102, 075033 (2020), arXiv: 1912.01007[hep-ph]

  • [4]

    L. Delle Rose, G. Panico, M. Rediet al., JHEP04, 025 (2020), arXiv: 1912.06139[hep-ph]

  • [5]

    B. Von Harling, A. Pomarol, O. Pujolàset al., JHEP04, 195 (2020), arXiv: 1912.07587[hep-ph]

  • [6]

    B. P. Abbottet al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. D100, 061101 (2019), arXiv: 1903.02886[gr-qc]

  • [7]

    M. Punturo, M. Abernathy, F. Acerneseet al., Class. Quant. Grav.27, 194002 (2010)

  • [8]

    A. Salvio, JCAP12, 046 (2023), arXiv: 2307.04694[hep-ph]

  • [9]

    A. Salvio, Phys. Lett. B852, 138639 (2024), arXiv: 2312.04628[hep-ph]

  • [10]

    J. Antoniadiset al. (EPTA and InPTA: Collaborations), Astron. Astrophys.678, A50 (2023), arXiv: 2306.16214 [astro-ph.HE]

  • [11]

    D. J. Reardon, A. Zic, R. M. Shannonet al., Astrophys. J. Lett.951, L6 (2023), arXiv: 2306.16215[astro-ph.HE]

  • [12]

    G. Agazieet al. (NANOGrav Collaboration), Astrophys. J. Lett.951, L8 (2023), arXiv: 2306.16213[astro-ph.HE]

  • [13]

    H. Xu, S. Chen, Y. Guoet al., Res. Astron. Astrophys.23, 075024 (2023), arXiv: 2306.16216[astro-ph.HE]

  • [14]

    L. Bian, R. G. Cai, J. Liuet al., Phys. Rev. D103, L081301 (2021), arXiv: 2009.13893[astro-ph.CO]

  • [15]

    Y. Nakai, M. Suzuki, F. Takahashiet al., Phys. Lett. B816, 136238 (2021), arXiv: 2009.09754[astro-ph.CO]

  • [16]

    A. Addazi, Y. F. Cai, Q. Ganet al., Sci. China Phys. Mech. Astron.64, 290411 (2021), arXiv: 2009.10327[hep-ph]

  • [17]

    W. Ratzinger and P. Schwaller, SciPost Phys.10, 047 (2021), arXiv: 2009.11875[astro-ph.CO]

  • [18]

    D. Borah, A. Dasgupta, and S. K. Kang, JCAP12, 039 (2021), arXiv: 2109.11558[hep-ph]

  • [19]

    X. Xue, L. Bian, J. Shuet al., Phys. Rev. Lett.127, 251303 (2021), arXiv: 2110.03096[astro-ph.CO]

  • [20]

    Z. C. Chen, S. L. Li, P. Wuet al., Phys. Rev. D109, 043022 (2024), arXiv: 2312.01824[astro-ph.CO]

  • [21]

    S. He, L. Li, S. Wanget al., Sci. China Phys. Mech. Astron.68, 210411 (2025), arXiv: 2308.07257[hep-ph]

  • [22]

    Y. M. Wu, Z. C. Chen, and Q. G. Huang, Sci. China Phys. Mech. Astron.67, 240412 (2024), arXiv: 2307.03141 [astroph.CO]

  • [23]

    P. Athron, A. Fowlie, C. T. Luet al., Phys. Rev. Lett.132, 221001 (2024), arXiv: 2306.17239[hep-ph]

  • [24]

    A. Addazi, Y. F. Cai, A. Marcianoet al., Phys. Rev. D109, 015028 (2024), arXiv: 2306.17205[astro-ph.CO]

  • [25]

    R. D. Peccei and H. R. Quinn, Phys. Rev. Lett.38, 1440 (1977)

  • [26]

    R. D. Peccei and H. R. Quinn, Phys. Rev. D16, 1791 (1977)

  • [27]

    S. Weinberg, Phys. Rev. Lett.40, 223 (1978)

  • [28]

    F. Wilczek, Phys. Rev. Lett.40, 279 (1978)

  • [29]

    G. ’t Hooft, Phys. Rev. D14, 3432 (1976), [Erratum: Phys. Rev. D 18, 2199 (1978)].

  • [30]

    J. Preskill, M. B. Wise, and F. Wilczek, Phys. Lett. B120, 127 (1983)

  • [31]

    W. Fischler and J. Preskill, Phys. Lett. B125, 165 (1983)

  • [32]

    B. Julia and A. Zee, Phys. Rev. D11, 2227 (1975)

  • [33]

    K. S. Jeong, S. Nakagawa, F. Takahashiet al., Phys. Rev. D109, 015014 (2024), arXiv: 2309.16570[hep-ph]

  • [34]

    A. Banerjee and M. A. Buen-Abad, JHEP02, 078 (2025), arXiv: 2410.21369 [hep-ph]

  • [35]

    C. Zhang, S. H. Zhang, B. Fuet al., JHEP08, 220 (2024), arXiv: 2404.04926[hep-ph]

  • [36]

    Y. Bai, S. Lu, and N. Orlofsky, Phys. Rev. Lett.127, 101801 (2021), arXiv: 2103.06286[hep-ph]

  • [37]

    M. G. Aartsenet al. (IceCube Collaboration), Eur. Phys. J. C76, 133 (2016), arXiv: 1511.01350[astro-ph.HE]

  • [38]

    A. Aabet al. (Pierre Auger Collaboration), Phys. Rev. D94, 082002 (2016), arXiv: 1609.04451[astro-ph.HE]

  • [39]

    N. E. Mavromatos and V. A. Mitsou, Int. J. Mod. Phys. A35, 2030012 (2020), arXiv: 2005.05100[hep-ph]

  • [40]

    S. Nakagawa, F. Takahashi, and M. Yamada, Phys. Rev. Lett.127, 181103 (2021), arXiv: 2103.08153[hep-ph]

  • [41]

    M. L. Graesser, I. M. Shoemaker, and N. T. Arellano, JHEP03, 105 (2022), arXiv: 2105.05769[hep-ph]

  • [42]

    J. Fan, K. Fraser, M. Reeceet al., Phys. Rev. Lett.127, 131602 (2021), arXiv: 2105.09950[hep-ph]

  • [43]

    M. L. Graesser and J. K. Osinski, ′ JHEP11, 133 (2020), arXiv: 2007.07917[hep-ph]

  • [44]

    R. Daido, S. Y. Ho, and F. Takahashi, JHEP01, 185 (2020), arXiv: 1909.03627[hep-ph]

  • [45]

    R. Sato, F. Takahashi, and M. Yamada, Phys. Rev. D98, 043535 (2018), arXiv: 1805.10533[hep-ph]

  • [46]

    M. Kawasaki, F. Takahashi, and M. Yamada, Phys. Lett. B753, 677 (2016), arXiv: 1511.05030[hep-ph]

  • [47]

    T. Hiramatsu, M. Ibe, M. Suzukiet al., JHEP12, 122 (2021), arXiv: 2109.12771[hep-ph]

  • [48]

    C. Gomez Sanchez and B. Holdom, Phys. Rev. D83, 123524 (2011), arXiv: 1103.1632[hep-ph]

  • [49]

    Y. Nomura, S. Rajendran, and F. Sanches, Phys. Rev. Lett.116, 141803 (2016), arXiv: 1511.06347[hep-ph]

  • [50]

    H. Murayama and J. Shu, Phys. Lett. B686, 162 (2010), arXiv: 0905.1720[hep-ph]

  • [51]

    J. Evslin and S. B. Gudnason, arXiv: 1202.0560 [astroph.CO]

  • [52]

    J. Terning and C. B. Verhaaren, JHEP12, 152 (2019), arXiv: 1906.00014[hep-ph]

  • [53]

    S. Baek, P. Ko, and W. I. Park, JCAP10, 067 (2014), arXiv: 1311.1035[hep-ph]

  • [54]

    V. V. Khoze and G. Ro, JHEP10, 061 (2014), arXiv: 1406.2291[hep-ph]

  • [55]

    Y. Bai, M. Korwar, and N. Orlofsky, JHEP07, 167 (2020), arXiv: 2005.00503[hep-ph]

  • [56]

    G. ’t Hooft, Nucl. Phys. B79, 276 (1974)

  • [57]

    A. M. Polyakov, JETP Lett.20, 194 (1974)

  • [58]

    A. Vilenkin and A. E. Everett, Phys. Rev. Lett.48, 1867 (1982)

  • [59]

    Y. B. Zeldovich, I. Y. Kobzarev, and L. B. Okun, Zh. Eksp. Teor. Fiz.67, 3 (1974)

  • [60]

    P. Sikivie, Phys. Rev. Lett.48, 1156 (1982)

  • [61]

    A. Vilenkin, Phys. Rev. D23, 852 (1981)

  • [62]

    G. B. Gelmini, M. Gleiser, and E. W. Kolb, Phys. Rev. D39, 1558 (1989)

  • [63]

    S. E. Larsson, S. Sarkar, and P. L. White, Phys. Rev. D55, 5129 (1997), arXiv: hep-ph/9608319 [hep-ph]

  • [64]

    I. Baldes and C. Garcia-Cely, JHEP05, 190 (2019), arXiv: 1809.01198[hep-ph]

  • [65]

    E. Hall, T. Konstandin, R. McGeheeet al., JHEP04, 042 (2020), arXiv: 1910.08068[hep-ph]

  • [66]

    T. Ghosh, H. K. Guo, T. Hanet al., JHEP07, 045 (2021), arXiv: 2012.09758[hep-ph]

  • [67]

    B. Fornal, Y. Shirman, T. M. P. Taitet al., Phys. Rev. D96, 035001 (2017), arXiv: 1703.00199[hep-ph]

  • [68]

    T. Hambye, JHEP01, 028 (2009), arXiv: 0811.0172[hep-ph]

  • [69]

    C. Boehm, M. J. Dolan, and C. McCabe, Phys. Rev. D90, 023531 (2014), arXiv: 1404.4977[hep-ph]

  • [70]

    C. Gross, O. Lebedev, and Y. Mambrini, JHEP08, 158 (2015), arXiv: 1505.07480[hep-ph]

  • [71]

    P. Ko, T. Nomura, and H. Okada, Phys. Rev. D103, 095011 (2021), arXiv: 2007.08153[hep-ph]

  • [72]

    C.-H. Chen and T. Nomura, Phys. Lett. B746, 351 (2015), arXiv: 1501.07413[hep-ph]

  • [73]

    C.-H. Chen and T. Nomura, Phys. Rev. D93, 074019 (2016), arXiv: 1507.00886[hep-ph]

  • [74]

    C. W. Chiang, T. Nomura, and J. Tandean, JHEP01, 183 (2014), arXiv: 1306.0882[hep-ph]

  • [75]

    A. Salvio, Phys. Lett. B808, 135686 (2020), arXiv: 2003.10446[hep-ph]

  • [76]

    A. Ghoshal and A. Salvio, JHEP12, 049 (2020), arXiv: 2007.00005[hep-ph]

  • [77]

    M. Quiros, inICTP Summer School in High-Energy Physics and Cosmology, (1999) pp. 187–259,, arXiv: hep-ph/9901312

  • [78]

    X. Wang, F. P. Huang, and X. Zhang, JCAP05, 045 (2020), arXiv: 2003.08892[hep-ph]

  • [79]

    V. Guada, M. Nemevšek, and M. Pintar, Comput. Phys. Commun.256, 107480 (2020), arXiv: 2002.00881[hep-ph]

  • [80]

    L. Leitao, A. Megevand, and A. D. Sanchez, JCAP10, 024 (2012), arXiv: 1205.3070[astro-ph.CO]

  • [81]

    A. H. Guth and S. H. H. Tye, Phys. Rev. Lett.44, 631 (1980)

  • [82]

    A. H. Guth and E. J. Weinberg, Phys. Rev. D23, 876 (1981)

  • [83]

    M. B. Einhorn and K. Sato, Nucl. Phys. B180, 385 (1981)

  • [84]

    E. Witten, Phys. Lett. B86, 283 (1979)

  • [85]

    M. Kawasaki, F. Takahashi, and M. Yamada, JHEP01, 053 (2018), arXiv: 1708.06047[hep-ph]

  • [86]

    J. Preskill, Phys. Rev. Lett.43, 1365 (1979)

  • [87]

    J. T. Goldman, E. W. Kolb, and D. Toussaint, Phys. Rev. D23, 867 (1981)

  • [88]

    A. Vilenkin and E. P. S. Shellard,Cosmic Strings and Other Topological Defects(Cambridge University Press, 2000).

  • [89]

    Y. B. Zeldovich and M. Y. Khlopov, Phys. Lett. B79, 239 (1978)

  • [90]

    M. Yamaguchi, M. Kawasaki, and J. Yokoyama, Phys. Rev. Lett.82, 4578 (1999), arXiv: hep-ph/9811311

  • [91]

    T. Hiramatsu, M. Kawasaki, T. Sekiguchiet al., Phys. Rev. D83, 123531 (2011), arXiv: 1012.5502[hep-ph]

  • [92]

    Y. Jia and L. Bian, (2024),, arXiv: 2412.04218[hep-ph]

  • [93]

    J. E. Kim, Phys. Rev. Lett.43, 103 (1979)

  • [94]

    M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B166, 493 (1980)

  • [95]

    D. H. Lyth, Phys. Lett. B275, 279 (1992)

  • [96]

    M. Kawasaki, K. Saikawa, and T. Sekiguchi, Phys. Rev. D91, 065014 (2015), arXiv: 1412.0789[hep-ph]

  • [97]

    A. R. Zhitnitsky, Sov. J. Nucl. Phys.31, 260 (1980)

  • [98]

    Y. Li, L. Bian, R. G. Caiet al.,JCAP08, 091 (2025), arXiv: 2311.02011[astro-ph.CO]

  • [99]

    N. Aghanimet al. (Planck Collaboration), stron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv: 1807.06209[astro-ph.CO]

  • [100]

    K. Enqvist, J. Ignatius, K. Kajantieet al., Phys. Rev. D45, 3415 (1992)

  • [101]

    S. J. Huber and T. Konstandin, JCAP09, 022 (2008), arXiv: 0806.1828[hep-ph]

  • [102]

    M. Hindmarsh, S. J. Huber, K. Rummukainenet al., Phys. Rev. D92, 123009 (2015), arXiv: 1504.03291 [astroph.CO]

  • [103]

    M. B. Hindmarsh, M. Lüben, J. Lummaet al., SciPost Phys. Lect. Notes24, 1 (2021), arXiv: 2008.09136 [astro-ph.CO]

  • [104]

    C. Caprini, R. Durrer, and G. Servant, JCAP12, 024 (2009), arXiv: 0909.0622[astro-ph.CO]

  • [105]

    P. Binetruy, A. Bohe, C. Capriniet al., JCAP06, 027 (2012), arXiv: 1201.0983[gr-qc]

  • [106]

    D. J. Fixsen, Astrophys. J.707, 916 (2009), arXiv: 0911.1955[astro-ph.CO]

  • [107]

    J. Ellis, M. Lewicki, and J. M. No, JCAP07, 050 (2020), arXiv: 2003.07360[hep-ph]

  • [108]

    M. Hindmarsh, S. J. Huber, K. Rummukainenet al., Phys. Rev. D96, 103520 (2017), arXiv: 1704.05871[astro-ph.CO]

  • [109]

    C. Capriniet al., JCAP03, 024 (2020), arXiv: 1910.13125[astro-ph.CO]

  • [110]

    J. Ellis, M. Lewicki, J. M. Noet al., JCAP06, 024 (2019), arXiv: 1903.09642[hep-ph]

  • [111]

    T. Hiramatsu, M. Kawasaki, and K. Saikawa, JCAP02, 031 (2014), arXiv: 1309.5001[astro-ph.CO]

  • [112]

    K. Kadota, M. Kawasaki, and K. Saikawa, JCAP10, 041 (2015), arXiv: 1503.06998[hep-ph]

  • [113]

    M. Kawasaki, K. Kohri, and T. Moroi, Phys. Lett. B625, 7 (2005), arXiv: astro-ph/0402490

  • [114]

    M. Kawasaki, K. Kohri, and T. Moroi, Phys. Rev. D71, 083502 (2005), arXiv: astro-ph/0408426

  • [115]

    S. Chenet al. (EPTA Collaboration), Mon. Not. Roy. Astron. Soc.508, 4970 (2021), arXiv: 2110.13184[astro-ph.HE]

  • [116]

    B. Goncharovet al., Astrophys. J. Lett.917, L19 (2021), arXiv: 2107.12112[astro-ph.HE]

  • [117]

    Z. Arzoumanianet al. (NANOGrav Collaboration), Astrophys. J. Lett.905, L34 (2020), arXiv: 2009.04496 [astro-ph.HE]

  • [118]

    A. Sesanaet al., Exper. Astron.51, 1333 (2021), arXiv: 1908.11391[astro-ph.IM]

  • [119]

    P. Amaro-Seoaneet al. (LISA Collaboration), arXiv: 1702.00786 [astro-ph.IM]

  • [120]

    J. Baker, J. Bellovary, P. L. Benderet al., arXiv: 1907.06482[astro-ph.IM]

  • [121]

    W. R. Hu and Y. L. Wu, Natl. Sci. Rev.4, 685 (2017)

  • [122]

    W. H. Ruan, Z. K. Guo, R. G. Caiet al., Int. J. Mod. Phys. A35, 2050075 (2020), arXiv: 1807.09495[gr-qc]

  • [123]

    J. Luoet al. (TianQin Collaboration), Class. Quant. Grav.33, 035010 (2016), arXiv: 1512.02076[astro-ph.IM]

  • [124]

    N. Seto, S. Kawamura, and T. Nakamura, Phys. Rev. Lett.87, 221103 (2001), arXiv: astro-ph/0108011

  • [125]

    H. Kudoh, A. Taruya, T. Hiramatsuet al., Phys. Rev. D73, 064006 (2006), arXiv: gr-qc/0511145

  • [126]

    S. Kawamura, M. Ando, N. Setoet al., PTEP2021, 05A105 (2021), arXiv: 2006.13545[gr-qc]

  • [127]

    J. Crowder and N. J. Cornish, Phys. Rev. D72, 083005 (2005), arXiv: gr-qc/0506015

  • [128]

    A. G. Riess, S. Casertano, W. Yuanet al., Astrophys. J.855, 136 (2018), arXiv: 1801.01120 [astro-ph.SR]

  • [129]

    J. L. Bernal, L. Verde, and A. G. Riess, JCAP10, 019 (2016), arXiv: 1607.05617[astro-ph.CO]

  • [130]

    N. Blinov and G. Marques-Tavares, JCAP09, 029 (2020), arXiv: 2003.08387[astro-ph.CO]

  • [131]

    A. Mariotti, X. Nagels, A. Raseet al., arXiv: 2411.13494[hep-ph]

  • [132]

    M. Vanvlasselaer, arXiv: 2501.00491[hep-ph]

  • [133]

    R. T. Co and K. Harigaya, Phys. Rev. Lett.124, 111602 (2020), arXiv: 1910.02080[hep-ph]

  • [134]

    R. T. Co, T. Gherghetta, and K. Harigaya, JHEP10, 121 (2022), arXiv: 2206.00678[hep-ph]

  • [135]

    S. R. Coleman and E. J. Weinberg, Phys. Rev. D7, 1888 (1973)

  • [136]

    L. Dolan and R. Jackiw, Phys. Rev. D9, 3320 (1974)

  • [137]

    G. W. Anderson and L. J. Hall, Phys. Rev. D45, 2685 (1992)

  • [138]

    M. E. Carrington, Phys. Rev. D45, 2933 (1992)

  • [139]

    P. B. Arnold and O. Espinosa,Phys. Rev. D47, 3546 (1993), [Erratum: Phys.Rev.D 50, 6662 (1994)], arXiv: hep-ph/9212235 [hep-ph]

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