NANOGrav hints for first-order confinement-deconfinement phase transition in different QCD-matter scenarios

Author(s)

Chen, Zu-Cheng, Li, Shou-Long, Wu, Puxun, Yu, Hongwei

Abstract

Recent observations from several pulsar timing array (PTA) collaborations have unveiled compelling evidence for a stochastic signal in the nanohertz band. This signal aligns remarkably with a gravitational wave (GW) background, potentially originating from the first-order color charge confinement phase transition. Distinct quantum chromodynamics (QCD) matters, such as quarks or gluons, and diverse phase transition processes thereof can yield disparate GW energy density spectra. In this letter, employing the Bayesian analysis on the NANOGrav 15-year data set, we explore the compatibility with the observed PTA signal of the GW from phase transitions of various QCD matter scenarios in the framework of the holographic QCD. We find that the PTA signal can be effectively explained by the GW from the confinement-deconfinement phase transition of pure quark systems in a hard wall model of the holographic QCD where the bubble dynamics, one important source of the GWs, is of the Jouguet detonations. Notably, our analysis decisively rules out the plausibility of the pure gluon QCD-matter scenario and the non-runaway bubble dynamics model for the phase transition in explaining the observed PTA signal.

Figures

\textbf{Left panel:} Bayesian posteriors for model parameters $\alpha$ and $T_*$ in the Jouguet detonation bubble scenario, using the NANOGrav 15-year data set. We show the $1\sigma$, $2\sigma$, and $5\sigma$ contours in the two-dimensional plot. The five holographical models are also indicated in the parameter space. \textbf{Right panel:} Posterior predictive distributions for the GW spectrum derived from the NANOGrav 15-year data set. The grey region represents the $5\sigma$ confidence interval, while the brown violins depict free spectrum data from the NANOGrav 15-year data set. Additionally, We show the GW spectra from the QCD-matter confinement-deconfinement phase transition in the Jouguet detonation bubble case from five holographical models.

\textbf{Left panel:} Bayesian posteriors for model parameters $\alpha$ and $T_*$ in the Jouguet detonation bubble scenario, using the NANOGrav 15-year data set. We show the $1\sigma$, $2\sigma$, and $5\sigma$ contours in the two-dimensional plot. The five holographical models are also indicated in the parameter space. \textbf{Right panel:} Posterior predictive distributions for the GW spectrum derived from the NANOGrav 15-year data set. The grey region represents the $5\sigma$ confidence interval, while the brown violins depict free spectrum data from the NANOGrav 15-year data set. Additionally, We show the GW spectra from the QCD-matter confinement-deconfinement phase transition in the Jouguet detonation bubble case from five holographical models.


\textbf{Left panel:} Bayesian posteriors for model parameters $\alpha$ and $T_*$ in the Jouguet detonation bubble scenario, using the NANOGrav 15-year data set. We show the $1\sigma$, $2\sigma$, and $5\sigma$ contours in the two-dimensional plot. The five holographical models are also indicated in the parameter space. \textbf{Right panel:} Posterior predictive distributions for the GW spectrum derived from the NANOGrav 15-year data set. The grey region represents the $5\sigma$ confidence interval, while the brown violins depict free spectrum data from the NANOGrav 15-year data set. Additionally, We show the GW spectra from the QCD-matter confinement-deconfinement phase transition in the Jouguet detonation bubble case from five holographical models.

\textbf{Left panel:} Bayesian posteriors for model parameters $\alpha$ and $T_*$ in the Jouguet detonation bubble scenario, using the NANOGrav 15-year data set. We show the $1\sigma$, $2\sigma$, and $5\sigma$ contours in the two-dimensional plot. The five holographical models are also indicated in the parameter space. \textbf{Right panel:} Posterior predictive distributions for the GW spectrum derived from the NANOGrav 15-year data set. The grey region represents the $5\sigma$ confidence interval, while the brown violins depict free spectrum data from the NANOGrav 15-year data set. Additionally, We show the GW spectra from the QCD-matter confinement-deconfinement phase transition in the Jouguet detonation bubble case from five holographical models.


Same as \Fig{posts_Jouguet} but for the non-runaway bubble case.

Same as \Fig{posts_Jouguet} but for the non-runaway bubble case.


Same as \Fig{posts_Jouguet} but for the non-runaway bubble case.

Same as \Fig{posts_Jouguet} but for the non-runaway bubble case.


References
  • [1] B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. X 9, 031040 (2019), arXiv:1811.12907 [astro-ph.HE].
  • [2] R. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. X 11, 021053 (2021), arXiv:2010.14527 [gr-qc].
  • [3] R. Abbott et al. (LIGO Scientific, VIRGO, KAGRA), (2021), arXiv:2111.03606 [gr-qc].
  • [4] B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. D 100, 104036 (2019), arXiv:1903.04467 [gr-qc].
  • [5] R. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. D 103, 122002 (2021), arXiv:2010.14529 [gr-qc].
  • [6] R. Abbott et al. (LIGO Scientific, VIRGO, KAGRA), (2021), arXiv:2112.06861 [gr-qc].
  • [7] B. P. Abbott et al. (LIGO Scientific, Virgo), Astrophys. J. Lett. 882, L24 (2019), arXiv:1811.12940 [astroph.HE].
  • [8] R. Abbott et al. (LIGO Scientific, Virgo), Astrophys. J. Lett. 913, L7 (2021), arXiv:2010.14533 [astro-ph.HE].
  • [9] Z.-C. Chen, C. Yuan, and Q.-G. Huang, Phys. Lett. B 829, 137040 (2022), arXiv:2108.11740 [astro-ph.CO].
  • [10] R. Abbott et al. (KAGRA, VIRGO, LIGO Scientific), Phys. Rev. X 13, 011048 (2023), arXiv:2111.03634 [astro-ph.HE].
  • [11] Z.-C. Chen, S.-S. Du, Q.-G. Huang, and Z.-Q. You, JCAP 03, 024 (2023), arXiv:2205.11278 [astro-ph.CO].
  • [12] M. V. Sazhin, Soviet Astronomy 22, 36 (1978).
  • [13] S. L. Detweiler, Astrophys. J. 234, 1100 (1979).
  • [14] R. S. Foster and D. C. Backer, Astrophys. J. 361, 300 (1990).
  • [15] G. Agazie et al. (NANOGrav), Astrophys. J. Lett. 951, L8 (2023), arXiv:2306.16213 [astro-ph.HE].
  • [16] G. Agazie et al. (NANOGrav), Astrophys. J. Lett. 951, L9 (2023), arXiv:2306.16217 [astro-ph.HE].
  • [17] A. Zic et al., (2023), arXiv:2306.16230 [astro-ph.HE].
  • [18] D. J. Reardon et al., Astrophys. J. Lett. 951, L6 (2023), arXiv:2306.16215 [astro-ph.HE].
  • [19] J. Antoniadis et al. (EPTA), Astron. Astrophys. 678, A48 (2023), arXiv:2306.16224 [astro-ph.HE].
  • [20] J. Antoniadis et al. (EPTA, InPTA:), Astron. Astrophys. 678, A50 (2023), arXiv:2306.16214 [astro-ph.HE].
  • [21] H. Xu et al., Res. Astron. Astrophys. 23, 075024 (2023), arXiv:2306.16216 [astro-ph.HE].
  • [22] R. w. Hellings and G. s. Downs, Astrophys. J. Lett. 265, L39 (1983).
  • [23] Z.-C. Chen, C. Yuan, and Q.-G. Huang, Phys. Rev. Lett. 124, 251101 (2020), arXiv:1910.12239 [astroph.CO].
  • [24] S. Vagnozzi, Mon. Not. Roy. Astron. Soc. 502, L11 (2021), arXiv:2009.13432 [astro-ph.CO].
  • [25] A. S. Sakharov, Y. N. Eroshenko, and S. G. Rubin, Phys. Rev. D 104, 043005 (2021), arXiv:2104.08750 [hep-ph].
  • [26] M. Benetti, L. L. Graef, and S. Vagnozzi, Phys. Rev. D 105, 043520 (2022), arXiv:2111.04758 [astro-ph.CO].
  • [27] Z.-C. Chen, Y.-M. Wu, and Q.-G. Huang, Astrophys. J. 936, 20 (2022), arXiv:2205.07194 [astro-ph.CO].
  • [28] A. Ashoorioon, K. Rezazadeh, and A. Rostami, Phys. Lett. B 835, 137542 (2022), arXiv:2202.01131 [astroph.CO].
  • [29] Y.-M. Wu, Z.-C. Chen, Q.-G. Huang, X. Zhu, N. D. R. Bhat, Y. Feng, G. Hobbs, R. N. Manchester, C. J. Russell, and R. M. Shannon (PPTA), Phys. Rev. D 106, L081101 (2022), arXiv:2210.03880 [astro-ph.CO].
  • [30] M. Falxa et al. (IPTA), Mon. Not. Roy. Astron. Soc. 521, 5077 (2023), arXiv:2303.10767 [gr-qc].
  • [31] V. Dandoy, V. Domcke, and F. Rompineve, SciPost Phys. Core 6, 060 (2023), arXiv:2302.07901 [astroph.CO].
  • [32] E. Madge, E. Morgante, C. Puchades-Ibáñez, N. Ramberg, W. Ratzinger, S. Schenk, and P. Schwaller, JHEP 10, 171 (2023), arXiv:2306.14856 [hep-ph].
  • [33] A. Afzal et al. (NANOGrav), Astrophys. J. Lett. 951, L11 (2023), arXiv:2306.16219 [astro-ph.HE].
  • [34] J. Antoniadis et al. (EPTA), (2023), arXiv:2306.16227 [astro-ph.CO].
  • [35] X. Niu and M. H. Rahat, (2023), arXiv:2307.01192 [hep-ph].
  • [36] Y.-C. Bi, Y.-M. Wu, Z.-C. Chen, and Q.-G. Huang, Sci. China Phys. Mech. Astron. 66, 120402 (2023), arXiv:2307.00722 [astro-ph.CO].
  • [37] S. Wang, Z.-C. Zhao, and Q.-H. Zhu, (2023), arXiv:2307.03095 [astro-ph.CO].
  • [38] L. Liu, Z.-C. Chen, and Q.-G. Huang, JCAP 11, 071 (2023), arXiv:2307.14911 [astro-ph.CO].
  • [39] S. Vagnozzi, JHEAp 39, 81 (2023), arXiv:2306.16912 [astro-ph.CO].
  • [40] C. Fu, J. Liu, X.-Y. Yang, W.-W. Yu, and Y. Zhang, (2023), arXiv:2308.15329 [astro-ph.CO].
  • [41] C. Han, K.-P. Xie, J. M. Yang, and M. Zhang, (2023), arXiv:2306.16966 [hep-ph].
  • [42] Y.-Y. Li, C. Zhang, Z. Wang, M.-Y. Cui, Y.-L. S. Tsai, Q. Yuan, and Y.-Z. Fan, (2023), arXiv:2306.17124 [astro-ph.HE].
  • [43] G. Franciolini, D. Racco, and F. Rompineve, (2023), arXiv:2306.17136 [astro-ph.CO].
  • [44] Z.-Q. Shen, G.-W. Yuan, Y.-Y. Wang, and Y.-Z. Wang, (2023), arXiv:2306.17143 [astro-ph.HE].
  • [45] N. Kitajima, J. Lee, K. Murai, F. Takahashi, and W. Yin, (2023), arXiv:2306.17146 [hep-ph].
  • [46] G. Franciolini, A. Iovino, Junior., V. Vaskonen, and H. Veermae, Phys. Rev. Lett. 131, 201401 (2023), arXiv:2306.17149 [astro-ph.CO].
  • [47] A. Addazi, Y.-F. Cai, A. Marciano, and L. Visinelli, (2023), arXiv:2306.17205 [astro-ph.CO].
  • [48] Y.-F. Cai, X.-C. He, X.-H. Ma, S.-F. Yan, and G.-W. Yuan, (2023), 10.1016/j.scib.2023.10.027, arXiv:2306.17822 [gr-qc].
  • [49] K. Inomata, K. Kohri, and T. Terada, (2023), arXiv:2306.17834 [astro-ph.CO].
  • [50] K. Murai and W. Yin, JHEP 10, 062 (2023), arXiv:2307.00628 [hep-ph].
  • [51] S.-P. Li and K.-P. Xie, Phys. Rev. D 108, 055018 (2023), arXiv:2307.01086 [hep-ph].
  • [52] L. A. Anchordoqui, I. Antoniadis, and D. Lust, (2023), arXiv:2307.01100 [hep-ph].
  • [53] L. Liu, Z.-C. Chen, and Q.-G. Huang, (2023), arXiv:2307.01102 [astro-ph.CO].
  • [54] D. G. Figueroa, M. Pieroni, A. Ricciardone, and P. Simakachorn, (2023), arXiv:2307.02399 [astroph.CO].
  • [55] Z. Yi, Q. Gao, Y. Gong, Y. Wang, and F. Zhang, Sci. China Phys. Mech. Astron. 66, 120404 (2023), arXiv:2307.02467 [gr-qc].
  • [56] Z.-C. Zhao, Q.-H. Zhu, S. Wang, and X. Zhang, (2023), arXiv:2307.13574 [astro-ph.CO].
  • [57] Y.-M. Wu, Z.-C. Chen, and Q.-G. Huang, (2023), arXiv:2307.03141 [astro-ph.CO].
  • [58] L. Bian, S. Ge, J. Shu, B. Wang, X.-Y. Yang, and J. Zong, (2023), arXiv:2307.02376 [astro-ph.HE].
  • [59] M. Geller, S. Ghosh, S. Lu, and Y. Tsai, (2023), arXiv:2307.03724 [hep-ph].
  • [60] S. Antusch, K. Hinze, S. Saad, and J. Steiner, (2023), arXiv:2307.04595 [hep-ph].
  • [61] G. Ye and A. Silvestri, (2023), arXiv:2307.05455 [astroph.CO].
  • [62] S. A. Hosseini Mansoori, F. Felegray, A. Talebian, and M. Sami, JCAP 08, 067 (2023), arXiv:2307.06757 [astro-ph.CO].
  • [63] J.-H. Jin, Z.-C. Chen, Z. Yi, Z.-Q. You, L. Liu, and Y. Wu, JCAP 09, 016 (2023), arXiv:2307.08687 [astroph.CO].
  • [64] Z. Zhang, C. Cai, Y.-H. Su, S. Wang, Z.-H. Yu, and H.-H. Zhang, Phys. Rev. D 108, 095037 (2023), arXiv:2307.11495 [hep-ph].
  • [65] S. Choudhury, (2023), arXiv:2307.03249 [astro-ph.CO].
  • [66] Z. Yi, Z.-Q. You, Y. Wu, Z.-C. Chen, and L. Liu, (2023), arXiv:2308.14688 [astro-ph.CO].
  • [67] M. A. Gorji, M. Sasaki, and T. Suyama, Phys. Lett. B 846, 138214 (2023), arXiv:2307.13109 [astro-ph.CO].
  • [68] B. Das, N. Jaman, and M. Sami, Phys. Rev. D 108, 103510 (2023), arXiv:2307.12913 [gr-qc].
  • [69] J. Ellis, M. Fairbairn, G. Franciolini, G. Hütsi, A. Iovino, M. Lewicki, M. Raidal, J. Urrutia, V. Vaskonen, and H. Veermäe, (2023), arXiv:2308.08546 [astroph.CO].
  • [70] S. Balaji, G. Domènech, and G. Franciolini, JCAP 10, 041 (2023), arXiv:2307.08552 [gr-qc].
  • [71] R. Maji and W.-I. Park, (2023), arXiv:2308.11439 [hepph].
  • [72] N. Bhaumik, R. K. Jain, and M. Lewicki, (2023), arXiv:2308.07912 [astro-ph.CO].
  • [73] S. Basilakos, D. V. Nanopoulos, T. Papanikolaou, E. N. Saridakis, and C. Tzerefos, (2023), arXiv:2307.08601 [hep-th].
  • [74] H.-L. Huang, Y. Cai, J.-Q. Jiang, J. Zhang, and Y.-S. Piao, (2023), arXiv:2306.17577 [gr-qc].
  • [75] J.-Q. Jiang, Y. Cai, G. Ye, and Y.-S. Piao, (2023), arXiv:2307.15547 [astro-ph.CO].
  • [76] P. Di Bari and M. H. Rahat, (2023), arXiv:2307.03184 [hep-ph].
  • [77] M. Aghaie, G. Armando, A. Dondarini, and P. Panci, (2023), arXiv:2308.04590 [astro-ph.CO].
  • [78] K. Harigaya, K. Inomata, and T. Terada, (2023), arXiv:2309.00228 [astro-ph.CO].
  • [79] K. D. Lozanov, S. Pi, M. Sasaki, V. Takhistov, and A. Wang, (2023), arXiv:2310.03594 [astro-ph.CO].
  • [80] S. Choudhury, K. Dey, A. Karde, S. Panda, and M. Sami, (2023), arXiv:2310.11034 [astro-ph.CO].
  • [81] J. Cang, Y. Gao, Y. Liu, and S. Sun, (2023), arXiv:2309.15069 [astro-ph.CO].
  • [82] L. Liu, Y. Wu, and Z.-C. Chen, (2023), arXiv:2310.16500 [astro-ph.CO].
  • [83] S. He, L. Li, S. Wang, and S.-J. Wang, (2023), arXiv:2308.07257 [hep-ph].
  • [84] L. Zu, C. Zhang, Y.-Y. Li, Y.-C. Gu, Y.-L. S. Tsai, and Y.-Z. Fan, (2023), arXiv:2306.16769 [astro-ph.HE].
  • [85] K. T. Abe and Y. Tada, (2023), arXiv:2307.01653 [astro-ph.CO].
  • [86] T. Ghosh, A. Ghoshal, H.-K. Guo, F. Hajkarim, S. F. King, K. Sinha, X. Wang, and G. White, (2023), arXiv:2307.02259 [astro-ph.HE].
  • [87] Y. Gouttenoire, Phys. Rev. Lett. 131, 171404 (2023), arXiv:2307.04239 [hep-ph].
  • [88] S.-L. Li, L. Shao, P. Wu, and H. Yu, Phys. Rev. D 104, 043510 (2021), arXiv:2101.08012 [astro-ph.CO].
  • [89] A. Kosowsky, M. S. Turner, and R. Watkins, Phys. Rev. D 45, 4514 (1992).
  • [90] A. Kosowsky, M. S. Turner, and R. Watkins, Phys. Rev. Lett. 69, 2026 (1992).
  • [91] A. Kosowsky and M. S. Turner, Phys. Rev. D 47, 4372 (1993), arXiv:astro-ph/9211004.
  • [92] M. Kamionkowski, A. Kosowsky, and M. S. Turner, Phys. Rev. D 49, 2837 (1994), arXiv:astro-ph/9310044.
  • [93] C. Caprini, R. Durrer, and G. Servant, Phys. Rev. D 77, 124015 (2008), arXiv:0711.2593 [astro-ph].
  • [94] M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Phys. Rev. Lett. 112, 041301 (2014), arXiv:1304.2433 [hep-ph].
  • [95] J. T. Giblin, Jr. and J. B. Mertens, JHEP 12, 042 (2013), arXiv:1310.2948 [hep-th].
  • [96] J. T. Giblin and J. B. Mertens, Phys. Rev. D 90, 023532 (2014), arXiv:1405.4005 [astro-ph.CO].
  • [97] A. Kosowsky, A. Mack, and T. Kahniashvili, Phys. Rev. D 66, 024030 (2002), arXiv:astro-ph/0111483.
  • [98] C. Caprini and R. Durrer, Phys. Rev. D 74, 063521 (2006), arXiv:astro-ph/0603476.
  • [99] T. Kahniashvili, A. Kosowsky, G. Gogoberidze, and Y. Maravin, Phys. Rev. D 78, 043003 (2008), arXiv:0806.0293 [astro-ph].
  • [100] T. Kahniashvili, L. Campanelli, G. Gogoberidze, Y. Maravin, and B. Ratra, Phys. Rev. D 78, 123006 (2008), [Erratum: Phys.Rev.D 79, 109901 (2009)], arXiv:0809.1899 [astro-ph].
  • [100] T. Kahniashvili, L. Campanelli, G. Gogoberidze, Y. Maravin, and B. Ratra, Phys. Rev. D 78, 123006 (2008), [Erratum: Phys.Rev.D 79, 109901 (2009)], arXiv:0809.1899 [astro-ph].
  • [101] T. Kahniashvili, L. Kisslinger, and T. Stevens, Phys. Rev. D 81, 023004 (2010), arXiv:0905.0643 [astroph.CO].
  • [102] L. Kisslinger and T. Kahniashvili, Phys. Rev. D 92, 043006 (2015), arXiv:1505.03680 [astro-ph.CO].
  • [103] S. J. Huber and T. Konstandin, JCAP 09, 022 (2008), arXiv:0806.1828 [hep-ph].
  • [104] C. Caprini, R. Durrer, and G. Servant, JCAP 12, 024 (2009), arXiv:0909.0622 [astro-ph.CO].
  • [105] C. Caprini et al., JCAP 04, 001 (2016), arXiv:1512.06239 [astro-ph.CO].
  • [106] M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Phys. Rev. D 92, 123009 (2015), arXiv:1504.03291 [astro-ph.CO].
  • [107] P. J. Steinhardt, Phys. Rev. D 25, 2074 (1982).
  • [108] A. Nicolis, Class. Quant. Grav. 21, L27 (2004), arXiv:gr-qc/0303084.
  • [109] J. R. Espinosa, T. Konstandin, J. M. No, and G. Servant, JCAP 06, 028 (2010), arXiv:1004.4187 [hep-ph].
  • [110] C. P. Herzog, Phys. Rev. Lett. 98, 091601 (2007), arXiv:hep-th/0608151.
  • [111] M. Ahmadvand and K. Bitaghsir Fadafan, Phys. Lett. B 772, 747 (2017), arXiv:1703.02801 [hep-th].
  • [112] M. Ahmadvand and K. Bitaghsir Fadafan, Phys. Lett. B 779, 1 (2018), arXiv:1707.05068 [hep-th].
  • [113] Y. Chen, M. Huang, and Q.-S. Yan, JHEP 05, 178 (2018), arXiv:1712.03470 [hep-ph].
  • [114] B. Allen and J. D. Romano, Phys. Rev. D 59, 102001 (1999), arXiv:gr-qc/9710117.
  • [115] N. Aghanim et al. (Planck), Astron. Astrophys. 641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO].
  • [115] N. Aghanim et al. (Planck), Astron. Astrophys. 641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO].
  • [116] S. Takeda, Y. Kuramashi, and A. Ukawa, Phys. Rev. D 85, 096008 (2012), arXiv:1111.6363 [hep-lat].
  • [117] M. Fromm, J. Langelage, S. Lottini, and O. Philipsen, JHEP 01, 042 (2012), arXiv:1111.4953 [hep-lat].
  • [118] H.-T. Ding, PoS LATTICE2016, 022 (2017), arXiv:1702.00151 [hep-lat].
  • [119] J. M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998), arXiv:hep-th/9711200.
  • [120] S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B 428, 105 (1998), arXiv:hep-th/9802109.
  • [121] E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998), arXiv:hep-th/9802150.
  • [122] J. Erlich, E. Katz, D. T. Son, and M. A. Stephanov, Phys. Rev. Lett. 95, 261602 (2005), arXiv:hepph/0501128.
  • [123] S. W. Hawking and D. N. Page, Commun. Math. Phys. 87, 577 (1983).
  • [124] L. Randall and G. Servant, JHEP 05, 054 (2007), arXiv:hep-ph/0607158.
  • [125] S. Rezapour, K. Bitaghsir Fadafan, and M. Ahmadvand, Annals Phys. 437, 168731 (2022), arXiv:2006.04265 [hep-th].
  • [126] J. S. Speagle, Mon. Not. Roy. Astron. Soc. 493, 3132 (2020), arXiv:1904.02180 [astro-ph.IM].
  • [127] G. Ashton et al., Astrophys. J. Suppl. 241, 27 (2019), arXiv:1811.02042 [astro-ph.IM].
  • [128] I. M. Romero-Shaw et al., Mon. Not. Roy. Astron. Soc. 499, 3295 (2020), arXiv:2006.00714 [astro-ph.IM].
  • [129] E. Reya, Rev. Mod. Phys. 46, 545 (1974).
  • [130] Y. Bai and M. Korwar, Phys. Rev. D 105, 095015 (2022), arXiv:2109.14765 [hep-ph].