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High Energy Physics - Phenomenology · arXiv:2611.14593 v1 · submitted 10 Nov 2026 · 91 references

Strongly supercooled first-order phase transitions: monopole abundance, entropy production and homogeneity consistency

Chen Zhang, Yue Niu, Xin Zhang

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The paper says

“We investigate whether monopole production in the early universe from a first-order phase transition in a unified gauge theory can be significantly suppressed if the phase transition is subject to strong supercooling but still completes successfully.”

more of the abstract

This is facilitated by adopting a Gaussian nucleation model and assuming the false vacuum energy released is transferred to sectors which behave effectively as radiation in terms of cosmological evolution. We distinguish three criteria of phase-transition completion: the comoving measure completion (CMC) characterized by the eventual vanishing of the false-vacuum fraction (FVF), the physical volume completion (PVC) characterized by the eventual vanishing of the physical volume of false vacuum, and the asymptotic thermodynamic completion (ATC), which refers to the finiteness of total entropy production. Assuming an idealized Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology, it is shown that the three criteria share exactly the same completion boundary, away from which they are completely equivalent. It is further shown that monopole abundance can be arbitrarily suppressed for parameter points approaching the completion boundary from the successful side. Nevertheless, for parameter points too close to the completion boundary, justification of the self-consistency of a homogeneous FLRW cosmology is difficult. We propose the use of the Hubble-scale FVF root-mean-square fluctuation to diagnose the homogeneity consistency issue, and find that arbitrarily strong suppression of monopole abundance relative to a reasonable Kibble estimate is not justifiable in terms of homogeneity consistency. These findings also have implications for gravitational wave production in strongly supercooled phase transitions.

from the abstract

Pith says

Machine review · deepseek-v4-flash · 13 Nov 2026 · what was read was not recorded · not checked by a person

It can be wrong. Challenge this review or reply to it.

A solid, internally consistent analysis of monopole dilution in supercooled transitions, with a clear central result—but the quantitative bound depends on a heuristic homogeneity threshold that needs better justification or sensitivity testing. This line is wrong

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What would settle it

Recompute the homogeneity boundary in the q-γ plane for Ξ_F,crit = 0.1 and Ξ_F,crit = 0.3, keeping rbgm=0.1 and vw=1. For each boundary point, evaluate Y_hat. If Y_hat remains at the few-percent level for both thresholds, the concern is alleviated. If Y_hat drops below 1% for either threshold, the paper's claim of no arbitrary suppression is not robust.

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3 readings by deepseek-v4-flash · 13 Nov 2026

  1. Reader holds up confidence high
  2. Skeptic partly agrees 20 s · 26,348 tokens read, 2,420 written
  3. Editor wrote the verdict above 15 s · 27,094 tokens read, 1,256 written

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The review in full

The review in brief, machine-written

The paper's main contribution is twofold: it gives a clean proof that three completion criteria (CMC, PVC, ATC) coincide for Gaussian nucleation with radiation-like energy transfer, and it shows that homogeneity consistency (measured by Hubble-scale FVF fluctuations) places a lower bound of a few percent on the relative monopole yield. The math in the appendix is careful and self-contained; the numerical scans are consistent with the analytic story. This is a real step over earlier work, which often assumed arbitrarily strong suppression was possible.

The soft spot is the threshold ΞF,crit = 0.2 used to define the homogeneity boundary. The authors are upfront that this is heuristic and that ΞF only probes phase inhomogeneity, not metric perturbations. But they do not test sensitivity to this choice. If the critical value were 0.1 or 0.3, the boundary in Fig. 2 shifts, and the minimal Y_hat could change—possibly by more than a factor of a few. The central claim that 'arbitrarily strong suppression is not justifiable' survives, but the quantitative 'few percent' floor is less secure. A robustness scan or calibration against a known breakdown of FLRW would strengthen the paper.

Other assumptions (Gaussian nucleation, neglect of quantum tunneling) are stated clearly and are standard for this class of models; they limit the scope but do not undermine the logic.

Who is this for? Cosmologists and GUT model builders working on monopoles and phase transition phenomenology. The paper deserves a serious referee: the mathematics is substantial, the question is well-motivated, and the result is useful even if the quantitative threshold needs follow-up. I would send it to review.

The strongest objection

The central quantitative claim—that the relative monopole yield cannot be suppressed below a few percent while maintaining homogeneity consistency—depends on the choice Ξ_F,crit = 0.2 (Section 4, sentences b150–b152). The authors acknowledge that Ξ_F only probes phase inhomogeneity and that the threshold is heuristic, but they do not test sensitivity to this choice. If a different threshold (e.g., 0.1 or 0.3) were adopted, the homogeneity boundary in Fig. 2 would shift, and the minimal Y_hat along that boundary might change. Because the paper provides no physical calibration or robustness study for this threshold, the quantitative limit on monopole suppression is less secure than the headline claim suggests.

The reader's weakest assumption noted the heuristic homogeneity threshold as part of the concern. The present attack zooms in on the quantitative sensitivity of the main result to that specific threshold value, which the paper does not test. The paper is otherwise sound and transparent, so the finding does not alter the verdict but identifies a concrete robustness check that would strengthen confidence in the conclusion.

Pith's reading of the paper (a machine's summary, not the authors')

Magnetic monopoles are predicted by grand unified theories and would be produced during a cosmological phase transition. One proposed way to explain why we have not observed them is to make the phase transition strongly supercooled: the universe cools far below the critical temperature before bubbles of the new phase nucleate, releasing a huge amount of latent heat that dilutes monopoles. This paper asks how far the dilution can go.

The authors adopt a flexible parametrization (Gaussian bubble nucleation rate) and assume that the released vacuum energy goes into radiation-like sectors that do not disrupt the expansion history. They define three different ways to declare the transition complete: comoving measure (zero false vacuum fraction), physical volume (zero physical false vacuum volume), and thermodynamic (finite entropy production). For this model, all three criteria give the same boundary between a successful transition and a failed one. Near that boundary, the monopole yield can indeed become arbitrarily small.

However, the paper also checks whether a homogeneous FLRW universe remains a good approximation when only a few very large bubbles nucleate per Hubble volume. It introduces a fluctuation measure of the Hubble-scale false-vacuum fraction and sets a threshold (RMS fluctuation >0.2) as a flag for inconsistency. Parameter points that respect this homogeneity constraint turn out to have monopole yields no smaller than a few percent of the Kibble benchmark. Hence the strong suppression scenario is incompatible with maintaining a homogeneous cosmology, a necessary condition for the standard analysis.

Core claim. The paper's central claim is that arbitrarily strong suppression of monopole abundance relative to a reasonable Kibble estimate is not justifiable in terms of homogeneity consistency: along the boundary where the FLRW description remains self-consistent, the relative monopole yield is at least at the level of a few percent (Sentences b5, b29, b140).

The premise it rests on. The Gaussian nucleation model (Eq. 1) together with the assumption that false vacuum energy is transferred to sectors with effective equation of state w=1/3 (radiation-like) forms the backbone of the analysis. For strongly supercooled transitions, quantum tunneling may dominate at low temperatures, but this contribution is neglected (Section 2, sentence b46). Additionally, the homogeneity consistency indicator (Hubble-scale FVF RMS fluctuation) only probes phase inhomogeneity, not energy-momentum inhomogeneity that enters Einstein's equations; the threshold Ξ_F,crit = 0.2 is chosen heuristically (Section 4, sentences b150-b152). If either of these assumptions fails qualitatively, the quantitative limits on monopole suppression could change.

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The paper

Abstract

We investigate whether monopole production in the early universe from a first-order phase transition in a unified gauge theory can be significantly suppressed if the phase transition is subject to strong supercooling but still completes successfully. This is facilitated by adopting a Gaussian nucleation model and assuming the false vacuum energy released is transferred to sectors which behave effectively as radiation in terms of cosmological evolution. We distinguish three criteria of phase-transition completion: the comoving measure completion (CMC) characterized by the eventual vanishing of the false-vacuum fraction (FVF), the physical volume completion (PVC) characterized by the eventual vanishing of the physical volume of false vacuum, and the asymptotic thermodynamic completion (ATC), which refers to the finiteness of total entropy production. Assuming an idealized Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology, it is shown that the three criteria share exactly the same completion boundary, away from which they are completely equivalent. It is further shown that monopole abundance can be arbitrarily suppressed for parameter points approaching the completion boundary from the successful side. Nevertheless, for parameter points too close to the completion boundary, justification of the self-consistency of a homogeneous FLRW cosmology is difficult. We propose the use of the Hubble-scale FVF root-mean-square fluctuation to diagnose the homogeneity consistency issue, and find that arbitrarily strong suppression of monopole abundance relative to a reasonable Kibble estimate is not justifiable in terms of homogeneity consistency. These findings also have implications for gravitational wave production in strongly supercooled phase transitions.

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. No sentence in this record was written by a model.

abstract compiled · 2026-11-13

The authors' main claim, as the classifier picked it out 1.00

“We propose the use of the Hubble-scale FVF root-mean-square fluctuation to diagnose the homogeneity consistency issue, and find that arbitrarily strong suppression of monopole abundance relative to a reasonable Kibble estimate is not justifiable in terms of homogeneity consistency.”

How the main claim is stated: asserted 1.00

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.66 · mentions code or data availability 0.02

The abstract, sentence by sentence

This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.

SentenceRoleThe authors' own workStates the main conclusionStrength
We investigate whether monopole production in the early universe from a first-order phase transition in a unified gauge theory can be significantly suppressed if the phase transition is subject to strong supercooling but still completes successfully. contribution 0.90 0.60 0.09 hedged possibility 0.76
This is facilitated by adopting a Gaussian nucleation model and assuming the false vacuum energy released is transferred to sectors which behave effectively as radiation in terms of cosmological evolution. method 1.00 0.66 0.03 asserted 0.66
We distinguish three criteria of phase-transition completion: the comoving measure completion (CMC) characterized by the eventual vanishing of the false-vacuum fraction (FVF), the physical volume completion (PVC) characterized by the eventual vanishing of the physical volume of false vacuum, and the asymptotic thermodynamic completion (ATC), which refers to the finiteness of total entropy production. contribution 0.52 0.74 0.04 asserted 0.86
Assuming an idealized Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmology, it is shown that the three criteria share exactly the same completion boundary, away from which they are completely equivalent. result 1.00 0.93 0.10 asserted 1.00
It is further shown that monopole abundance can be arbitrarily suppressed for parameter points approaching the completion boundary from the successful side. result 1.00 0.93 0.24 asserted 0.97
Nevertheless, for parameter points too close to the completion boundary, justification of the self-consistency of a homogeneous FLRW cosmology is difficult. limitation 0.80 0.48 0.08 asserted 0.53
We propose the use of the Hubble-scale FVF root-mean-square fluctuation to diagnose the homogeneity consistency issue, and find that arbitrarily strong suppression of monopole abundance relative to a reasonable Kibble estimate is not justifiable in terms of homogeneity consistency. result 0.91 0.96 0.74 asserted 1.00
These findings also have implications for gravitational wave production in strongly supercooled phase transitions. interpretation 1.00 0.46 0.04 asserted 0.50

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98

What was examined, and what was not

Sources read

  • arXiv listing abstract v1

Not examined

  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers

Levels run

  • P abstract

Not run

  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

How the labels were made

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-11-13: 1 request, 6,516 input tokens.

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON

Figures (2)
Figure 1 of the paper
Figure 1. Evolution of characteristic quantities as a function of the number
Figure 2 of the paper
Figure 2. Upper panel: the boundary of phase transition completion and

Figures are the authors', reproduced from the paper.

References (91)
  1. [1] R. Foot, G. C. Joshi, H. Lew, R. R. V olkas, Charge quan- tization in the standard model and some of its exten- sions, Mod. Phys. Lett. A 5 (1990) 2721–2732. doi: 10.1142/S0217732390003176 on Pithdoi:10.1142/s0217732390003176
  2. [2] R. Foot, H. Lew, R. R. V olkas, Electric charge quantization, J. Phys. G 19 (1993) 361–372, [Erratum: J.Phys.G 19, 1067 (1993)]. arXiv:hep-ph/9209259, doi:10.1088/ 0954-3899/19/3/005 on PithPith's reviewarXiv
  3. [3] J. Preskill, Magnetic monopoles, Ann. Rev. Nucl. Part. Sci. 34 (1984) 461–530. doi:10.1146/annurev.ns.34. 120184.002333 on Pithdoi:10.1146/annurev.ns.34
  4. [4] Y . M. Shnir, Magnetic Monopoles, Texts and Monographs in Physics, Springer, Berlin/Heidelberg, 2005. doi:10. 1007/3-540-29082-6 on Pith
  5. [5] A. Rajantie, Introduction to Magnetic Monopoles, Con- temp. Phys. 53 (2012) 195–211. arXiv:1204.3077, doi:10.1080/00107514.2012.685693 on PithPith's reviewarXiv
  6. [6] L. Patrizii, M. Spurio, Status of Searches for Mag- netic Monopoles, Ann. Rev. Nucl. Part. Sci. 65 (2015) 279–302. arXiv:1510.07125, doi:10.1146/ annurev-nucl-102014-022137 on PithPith's reviewarXiv
  7. [7] N. E. Mavromatos, V . A. Mitsou, Magnetic monopoles revisited: Models and searches at colliders and in the Cos- mos, Int. J. Mod. Phys. A 35 (23) (2020) 2030012. arXiv: 2005.05100,doi:10.1142/S0217751X20300124 on PithPith's reviewarXiv
  8. [8] V . A. Mitsou, Magnetic monopoles: from Dirac to the Large Hadron Collider, Eur. Phys. J. ST 235 (25) (2026) 5481–5521. arXiv:2605.02869, doi:10.1140/epjs/ s11734-026-02463-z on PithPith's reviewarXiv
  9. [9] P. A. M. Dirac, Quantised singularities in the electromag- netic field, Proc. Roy. Soc. Lond. A 133 (821) (1931) 60– 72.doi:10.1098/rspa.1931.0130 on Pithdoi:10.1098/rspa.1931.0130
  10. [10] E. Witten, Comments on string theory, in: Challenges to the Standard Paradigm: Fundamental Physics and Cosmol- ogy, 2002.arXiv:hep-th/0212247 on PithPith's reviewarXiv
  11. [11] J. Polchinski, Monopoles, duality, and string theory, Int. J. Mod. Phys. A 19S1 (2004) 145–156. arXiv:hep-th/ 0304042,doi:10.1142/S0217751X0401866X on Pithdoi:10.1142/s0217751x0401866x
  12. [12] E. García-Valdecasas, M. Reece, M. Suzuki, Monopole breaking of Chern-Weil symmetries, SciPost Phys. 18 (5) (2025) 162. arXiv:2408.00067, doi:10.21468/ SciPostPhys.18.5.162 on PithPith's reviewarXiv
  13. [13] G. ’t Hooft, Magnetic Monopoles in Unified Gauge The- ories, Nucl. Phys. B 79 (1974) 276–284. doi:10.1016/ 0550-3213(74)90486-6 on Pith
  14. [14] A. M. Polyakov, Particle Spectrum in Quantum Field The- ory, JETP Lett. 20 (1974) 194–195 on Pith
  15. [15] T. W. B. Kibble, Topology of Cosmic Domains and Strings, J. Phys. A 9 (1976) 1387–1398. doi:10.1088/ 0305-4470/9/8/029 on Pith
  16. [16] A. Vilenkin, E. P. S. Shellard, Cosmic Strings and Other Topological Defects, Cambridge University Press, 2000 on Pith
  17. [17] E. J. Weinberg, Classical solutions in quantum field theory: Solitons and Instantons in High Energy Physics, Cambridge Monographs on Mathematical Physics, Cambridge University Press, 2012. doi:10.1017/ CBO9781139017787 on Pith
  18. [18] G. Lazarides, M. Magg, Q. Shafi, Phase Transitions and Magnetic Monopoles in SO(10), Phys. Lett. B 97 (1980) 87–92.doi:10.1016/0370-2693(80)90553-5 on Pithdoi:10.1016/0370-2693(80)90553-5
  19. [19] V . N. ¸ Seno˘guz, Q. Shafi, Primordial monopoles, proton decay, gravity waves and GUT inflation, Phys. Lett. B 752 (2016) 169–174. arXiv:1510.04442, doi:10.1016/j. physletb.2015.11.037 on PithPith's reviewarXiv
  20. [20] T. W. Kephart, G. K. Leontaris, Q. Shafi, Magnetic Monopoles and Free Fractionally Charged States at Accel- erators and in Cosmic Rays, JHEP 10 (2017) 176. arXiv: 1707.08067,doi:10.1007/JHEP10(2017)176 on PithPith's reviewarXiv
show 71 more
  1. [21] G. Lazarides, Q. Shafi, Monopoles, Strings, and Necklaces in S O(10) and E6, JHEP 10 (2019) 193. arXiv:1904. 06880,doi:10.1007/JHEP10(2019)193 on Pithdoi:10.1007/jhep10(2019)193
  2. [22] S. F. King, S. Pascoli, J. Turner, Y .-L. Zhou, Gravita- tional Waves and Proton Decay: Complementary Win- dows into Grand Unified Theories, Phys. Rev. Lett. 126 (2) (2021) 021802. arXiv:2005.13549, doi:10.1103/ PhysRevLett.126.021802 on PithPith's reviewarXiv
  3. [23] G. Lazarides, Q. Shafi, Triply Charged Monopole and Magnetic Quarks, Phys. Lett. B 818 (2021) 136363. arXiv:2101.01412, doi:10.1016/j.physletb. 2021.136363 on PithPith's reviewarXiv
  4. [24] T. W. Kephart, Q. Shafi, Magnetic monopoles and ex- otic states in S U(4)c×S U(2)L×S U(2)R, Phys. Rev. D 112 (7) (2025) 075013. arXiv:2503.18321, doi:10. 1103/y7cd-ds58 on PithPith's reviewarXiv
  5. [25] J. Preskill, Cosmological Production of Superheavy Mag- netic Monopoles, Phys. Rev. Lett. 43 (1979) 1365. doi: 10.1103/PhysRevLett.43.1365. 8 on Pithdoi:10.1103/physrevlett.43.1365
  6. [26] A. Rajantie, Magnetic monopoles from gauge the- ory phase transitions, Phys. Rev. D 68 (2003) 021301. arXiv:hep-ph/0212130, doi:10.1103/ PhysRevD.68.021301 on PithPith's reviewarXiv
  7. [27] H. Murayama, J. Shu, Topological Dark Matter, Phys. Lett. B 686 (2010) 162–165. arXiv:0905.1720, doi: 10.1016/j.physletb.2010.02.037 on PithPith's reviewarXiv
  8. [28] M. Hindmarsh, A. Lopez-Eiguren, R. Seppä, D. J. Weir, Numerical simulations of magnetic monopole evolution in an expanding universe (11 2025).arXiv:2511.14204 on PitharXiv
  9. [29] Y . Di, L. Bian, R.-G. Cai, Magnetic monopoles produced by first-order phase transition (10 2026). arXiv:2610. 29349 on Pith
  10. [30] M. S. Turner, E. N. Parker, T. J. Bogdan, Magnetic Monopoles and the Survival of Galactic Magnetic Fields, Phys. Rev. D 26 (1982) 1296. doi:10.1103/PhysRevD. 26.1296 on Pithdoi:10.1103/physrevd
  11. [31] F. C. Adams, M. Fatuzzo, K. Freese, G. Tarle, R. Watkins, M. S. Turner, Extension of the Parker bound on the flux of magnetic monopoles, Phys. Rev. Lett. 70 (1993) 2511– 2514.doi:10.1103/PhysRevLett.70.2511 on Pithdoi:10.1103/physrevlett.70.2511
  12. [32] T. Kobayashi, D. Perri, Parker bounds on monopoles with arbitrary charge from galactic and primordial magnetic fields, Phys. Rev. D 108 (8) (2023) 083005. arXiv:2307. 07553,doi:10.1103/PhysRevD.108.083005 on Pithdoi:10.1103/physrevd.108.083005
  13. [33] C. Zhang, S.-H. Zhang, B. Fu, J.-F. Zhang, X. Zhang, On the cosmological abundance of magnetic monopoles, JHEP 08 (2024) 220. arXiv:2404.04926, doi:10.1007/ JHEP08(2024)220 on PithPith's reviewarXiv
  14. [34] C. Zhang, C.-Y . Jiang, N. Jia, X. Zhang, Self-Consistent Parker Bound on Magnetic Monopoles (5 2026). arXiv: 2605.21281 on PithPith's reviewarXiv
  15. [35] P. B. Price, M. H. Salamon, Search for Supermassive Mag- netic Monopoles Using Mica Crystals, Phys. Rev. Lett. 56 (1986) 1226–1229. doi:10.1103/PhysRevLett.56. 1226 on Pithdoi:10.1103/physrevlett.56
  16. [36] M. Ambrosio, et al., Final results of magnetic monopole searches with the MACRO experiment, Eur. Phys. J. C 25 (2002) 511–522. arXiv:hep-ex/0207020, doi:10. 1140/epjc/s2002-01046-9 on PithPith's reviewarXiv
  17. [37] S. Burdin, M. Fairbairn, P. Mermod, D. Milstead, J. Pin- fold, T. Sloan, W. Taylor, Non-collider searches for stable massive particles, Phys. Rept. 582 (2015) 1–52. arXiv: 1410.1374,doi:10.1016/j.physrep.2015.03.004 on PithPith's reviewarXiv
  18. [38] A. Aab, et al., Search for ultrarelativistic magnetic monopoles with the Pierre Auger Observatory, Phys. Rev. D 94 (8) (2016) 082002. arXiv:1609.04451, doi: 10.1103/PhysRevD.94.082002 on PithPith's reviewarXiv
  19. [39] Y . Bai, S. Lu, N. Orlofsky, Searching for Magnetic Monopoles with the Earth’s Magnetic Field, Phys. Rev. Lett. 127 (10) (2021) 101801.arXiv:2103.06286,doi: 10.1103/PhysRevLett.127.101801 on PithPith's reviewarXiv
  20. [40] R. Abbasi, et al., Search for Relativistic Magnetic Monopoles with Eight Years of IceCube Data, Phys. Rev. Lett. 128 (5) (2022) 051101. arXiv:2109.13719, doi: 10.1103/PhysRevLett.128.051101 on PitharXiv
  21. [41] D. Perri, M. Doro, T. Kobayashi, Recasting experimental constraints on relativistic magnetic monopoles, Phys. Dark Univ. 50 (2025) 102134. arXiv:2507.05136, doi:10. 1016/j.dark.2025.102134 on PitharXiv
  22. [42] Z. Cao, et al., Search for Ultra-Relativistic Magnetic Monopoles with LHAASO-KM2A (10 2026). arXiv: 2610.30968 on PitharXiv
  23. [43] P. Langacker, S.-Y . Pi, Magnetic Monopoles in Grand Unified Theories, Phys. Rev. Lett. 45 (1980) 1. doi: 10.1103/PhysRevLett.45.1 on Pithdoi:10.1103/physrevlett.45.1
  24. [44] M. Izawa, K. Sato, Cosmological First Order Phase Transi- tion and Baryon - Monopole Problem, Prog. Theor. Phys. 68 (1982) 1574.doi:10.1143/PTP.68.1574 on Pithdoi:10.1143/ptp.68.1574
  25. [45] G. R. Dvali, H. Liu, T. Vachaspati, Sweeping away the monopole problem, Phys. Rev. Lett. 80 (1998) 2281–2284. arXiv:hep-ph/9710301, doi:10.1103/ PhysRevLett.80.2281 on PithPith's reviewarXiv
  26. [46] B. Bajc, A. Riotto, G. Senjanovic, Large lepton number of the universe and the fate of topological defects, Phys. Rev. Lett. 81 (1998) 1355–1358. arXiv:hep-ph/9710415, doi:10.1103/PhysRevLett.81.1355 on PithPith's reviewarXiv
  27. [47] D. Stojkovic, K. Freese, A Black hole solution to the cos- mological monopole problem, Phys. Lett. B 606 (2005) 251–257. arXiv:hep-ph/0403248, doi:10.1016/j. physletb.2004.12.019 on PithPith's reviewarXiv
  28. [48] C. Zhang, X. Zhang, Gravitational capture of magnetic monopoles by primordial black holes in the early uni- verse, JHEP 10 (2023) 037. arXiv:2302.07002, doi: 10.1007/JHEP10(2023)037 on PithPith's reviewarXiv
  29. [49] C. Zhang, X. Zhang, Magnetic monopole meets primordial black hole: an extended analysis, Eur. Phys. J. C 84 (1) (2024) 100. arXiv:2308.07166, doi:10.1140/epjc/ s10052-024-12383-8 on PithPith's reviewarXiv
  30. [50] D. Perri, Noninflationary solution to the monopole prob- lem, Phys. Rev. D 113 (2) (2026) 023547. arXiv:2509. 23726,doi:10.1103/zcp4-pkbw on Pithdoi:10.1103/zcp4-pkbw
  31. [51] A. H. Guth, S. H. H. Tye, Phase Transitions and Magnetic Monopole Production in the Very Early Universe, Phys. Rev. Lett. 44 (1980) 631, [Erratum: Phys.Rev.Lett. 44, 963 (1980)].doi:10.1103/PhysRevLett.44.631. 9 on Pithdoi:10.1103/physrevlett.44.631
  32. [52] M. B. Einhorn, K. Sato, Monopole Production in the Very Early Universe in a First Order Phase Transition, Nucl. Phys. B 180 (1981) 385–404. doi:10.1016/ 0550-3213(81)90057-2 on Pith
  33. [53] M. B. Hindmarsh, M. Lüben, J. Lumma, M. Pauly, Phase transitions in the early universe, SciPost Phys. Lect. Notes 24 (2021) 1. arXiv:2008.09136, doi:10.21468/ SciPostPhysLectNotes.24 on PithPith's reviewarXiv
  34. [54] X. Wang, F. P. Huang, X. Zhang, Phase transition dynamics and gravitational wave spectra of strong first-order phase transition in supercooled universe, JCAP 05 (2020) 045. arXiv:2003.08892, doi:10.1088/1475-7516/2020/ 05/045 on PithPith's reviewarXiv
  35. [55] A. Eichhorn, J. Lumma, J. M. Pawlowski, M. Reichert, M. Yamada, Universal gravitational-wave signatures from heavy new physics in the electroweak sector, JCAP 05 (2021) 006. arXiv:2010.00017, doi:10.1088/ 1475-7516/2021/05/006 on PithPith's reviewarXiv
  36. [56] P. Athron, C. Balázs, A. Fowlie, L. Morris, L. Wu, Cos- mological phase transitions: From perturbative particle physics to gravitational waves, Prog. Part. Nucl. Phys. 135 (2024) 104094. arXiv:2305.02357, doi:10.1016/j. ppnp.2023.104094 on PithPith's reviewarXiv
  37. [57] A. Megevand, S. Ramirez, Bubble nucleation and growth in very strong cosmological phase transitions, Nucl. Phys. B 919 (2017) 74–109. arXiv:1611.05853, doi:10.1016/ j.nuclphysb.2017.03.009 on PithPith's reviewarXiv
  38. [58] Z. Ning, X.-X. Zeng, R.-G. Cai, S.-J. Wang, Numerical simulations of primordial black hole formation via de- layed first-order phase transitions, JCAP 07 (2026) 073. arXiv:2601.21878, doi:10.1088/1475-7516/2026/ 07/073 on PithPith's reviewarXiv
  39. [59] M. S. Turner, E. J. Weinberg, L. M. Widrow, Bubble nucleation in first order inflation and other cosmologi- cal phase transitions, Phys. Rev. D 46 (1992) 2384–2403. doi:10.1103/PhysRevD.46.2384 on Pithdoi:10.1103/physrevd.46.2384
  40. [60] H.-K. Guo, S. Li, Y . Xiao, J. M. Yang, Y . Zhang, Estimating the uncertainty of cosmological first order phase transitions with numerical simulations of bubble nucleation, Phys. Rev. D 110 (6) (2024) 063541. arXiv:2310.04654, doi: 10.1103/PhysRevD.110.063541 on PithPith's reviewarXiv
  41. [61] L. Giombi, M. Hindmarsh, General relativistic bubble growth in cosmological phase transitions, JCAP 03 (2024) on Pith
  42. [62] arXiv:2307.12080, doi:10.1088/1475-7516/ 2024/03/059 on PithPith's reviewarXiv
  43. [63] L. Giombi, J. Dahl, M. Hindmarsh, Acoustic gravita- tional waves beyond leading-order in bubble over Hub- ble radius, JCAP 03 (2026) 024. arXiv:2504.08037, doi:10.1088/1475-7516/2026/03/024 on PithPith's reviewarXiv
  44. [64] P. Athron, C. Balázs, T. E. Gonzalo, M. Pearce, Falsify- ing Pati-Salam models with LIGO, Phys. Rev. D 109 (6) (2024) L061303. arXiv:2307.02544, doi:10.1103/ PhysRevD.109.L061303 on PithPith's reviewarXiv
  45. [65] P. Athron, C. Balázs, L. Morris, Supercool subtleties of cosmological phase transitions, JCAP 03 (2023) 006. arXiv:2212.07559, doi:10.1088/1475-7516/2023/ 03/006 on PitharXiv
  46. [66] J. Liu, L. Bian, R.-G. Cai, Z.-K. Guo, S.-J. Wang, Constraining First-Order Phase Transitions with Curvature Perturbations, Phys. Rev. Lett. 130 (5) (2023) 051001. arXiv:2208.14086, doi:10.1103/ PhysRevLett.130.051001 on PithPith's reviewarXiv
  47. [67] Y . Gouttenoire, T. V olansky, Primordial black holes from supercooled phase transitions, Phys. Rev. D 110 (4) (2024) 043514. arXiv:2305.04942, doi:10.1103/PhysRevD. 110.043514 on PithPith's reviewarXiv
  48. [68] M. Lewicki, P. Toczek, V . Vaskonen, Primordial black holes from strong first-order phase transitions, JHEP 09 (2023) 092. arXiv:2305.04924, doi:10.1007/ JHEP09(2023)092 on PithPith's reviewarXiv
  49. [69] M. Lewicki, P. Toczek, V . Vaskonen, Black holes and grav- itational waves from phase transitions in realistic models, Phys. Dark Univ. 50 (2025) 102075. arXiv:2412.10366, doi:10.1016/j.dark.2025.102075 on PitharXiv
  50. [70] T. Ghosh, K. Loho, S. Manna, Impact of Bubble Nucleation History and Friction on Primordial Black Hole Formation (8 2026).arXiv:2608.22846 on PithPith's reviewarXiv
  51. [71] A. H. Guth, E. J. Weinberg, Could the Universe Have Recovered from a Slow First Order Phase Transition?, Nucl. Phys. B 212 (1983) 321–364. doi:10.1016/ 0550-3213(83)90307-3 on Pith
  52. [72] H. Wang, R. Qin, L. Bian, False vacuum decay across the quantum-to-thermal crossover: A comparison of real- time observables, Phys. Rev. D 114 (3) (2026) L031903. arXiv:2506.18334,doi:10.1103/svt7-rfsz on PithPith's reviewarXiv
  53. [73] A. Kobakhidze, C. Lagger, A. Manning, J. Yue, Grav- itational waves from a supercooled electroweak phase transition and their detection with pulsar timing arrays, Eur. Phys. J. C 77 (8) (2017) 570. arXiv:1703.06552, doi:10.1140/epjc/s10052-017-5132-y on PithPith's reviewarXiv
  54. [74] J. Ellis, M. Lewicki, J. M. No, V . Vaskonen, Gravita- tional wave energy budget in strongly supercooled phase transitions, JCAP 06 (2019) 024. arXiv:1903.09642, doi:10.1088/1475-7516/2019/06/024 on PithPith's reviewarXiv
  55. [75] J. Ellis, M. Lewicki, V . Vaskonen, Updated predictions for gravitational waves produced in a strongly supercooled phase transition, JCAP 11 (2020) 020. arXiv:2007. 15586,doi:10.1088/1475-7516/2020/11/020. 10 on Pithdoi:10.1088/1475-7516/2020/11/020
  56. [76] M. Lewicki, V . Vaskonen, Gravitational wave spectra from strongly supercooled phase transitions, Eur. Phys. J. C 80 (11) (2020) 1003. arXiv:2007.04967, doi: 10.1140/epjc/s10052-020-08589-1 on PithPith's reviewarXiv
  57. [77] M. Lewicki, V . Vaskonen, Gravitational waves from bubble collisions and fluid motion in strongly supercooled phase transitions, Eur. Phys. J. C 83 (2) (2023) 109.arXiv:2208. 11697,doi:10.1140/epjc/s10052-023-11241-3 on Pithdoi:10.1140/epjc/s10052-023-11241-3
  58. [78] M. Kierkla, B. Swiezewska, T. V . I. Tenkanen, J. van de Vis, Gravitational waves from supercooled phase tran- sitions: dimensional transmutation meets dimensional reduction, JHEP 02 (2024) 234. arXiv:2312.12413, doi:10.1007/JHEP02(2024)234 on PithPith's reviewarXiv
  59. [79] P. Athron, A. Fowlie, C.-T. Lu, L. Morris, L. Wu, Y . Wu, Z. Xu, Can Supercooled Phase Transitions Explain the Gravitational Wave Background Observed by Pulsar Timing Arrays?, Phys. Rev. Lett. 132 (22) (2024) 221001. arXiv:2306.17239, doi:10.1103/ PhysRevLett.132.221001 on PithPith's reviewarXiv
  60. [80] P. Athron, L. Morris, Z. Xu, How robust are gravita- tional wave predictions from cosmological phase transi- tions?, JCAP 05 (2024) 075. arXiv:2309.05474, doi: 10.1088/1475-7516/2024/05/075 on PithPith's reviewarXiv
  61. [81] M. Lewicki, V . Vaskonen, Impact of cosmic expansion on gravitational wave spectra from strongly supercooled first-order phase transitions, Phys. Dark Univ. 53 (2026) 102425. arXiv:2511.15687, doi:10.1016/j.dark. 2026.102425 on PitharXiv
  62. [82] S. Baek, P. Ko, W.-I. Park, Hidden sector monopole, vector dark matter and dark radiation with Higgs portal, JCAP 10 (2014) 067. arXiv:1311.1035, doi:10.1088/ 1475-7516/2014/10/067 on PithPith's reviewarXiv
  63. [83] V . V . Khoze, G. Ro, Dark matter monopoles, vectors and photons, JHEP 10 (2014) 061. arXiv:1406.2291, doi: 10.1007/JHEP10(2014)061 on PithPith's reviewarXiv
  64. [84] M. Kawasaki, F. Takahashi, M. Yamada, Suppressing the QCD Axion Abundance by Hidden Monopoles, Phys. Lett. B 753 (2016) 677–681. arXiv:1511.05030, doi:10. 1016/j.physletb.2015.12.075 on PithPith's reviewarXiv
  65. [85] Y . Nomura, S. Rajendran, F. Sanches, Axion Isocurva- ture and Magnetic Monopoles, Phys. Rev. Lett. 116 (14) (2016) 141803. arXiv:1511.06347, doi:10.1103/ PhysRevLett.116.141803 on PithPith's reviewarXiv
  66. [86] M. L. Graesser, J. K. Osi ´nski, Hidden Sector Monopole Dark Matter with Matter Domination, JHEP 11 (2020) 133. arXiv:2007.07917, doi:10.1007/ JHEP11(2020)133 on PithPith's reviewarXiv
  67. [87] J. Yang, R. Zhou, L. Bian, Gravitational waves and monopoles dark matter from first-order phase transition, Phys. Lett. B 839 (2023) 137822. arXiv:2204.07540, doi:10.1016/j.physletb.2023.137822 on PithPith's reviewarXiv
  68. [88] R. Zhou, L. Bian, Gravitational waves and dark matter with Witten effect, Chin. Phys. C 49 (11) (2025) 115110.arXiv: 2501.09596,doi:10.1088/1674-1137/adfc36 on PithPith's reviewarXiv
  69. [89] F. Brümmer, G. Ferrante, T. Fischer, M. Frigerio, No room for minimal monopole dark matter, Phys. Rev. D 113 (9) (2026) L091701. arXiv:2509.21924, doi:10.1103/ bttg-zfr3 on PithPith's reviewarXiv
  70. [90] D. Liveoak, A. Maharana, J. D. Wells, Dark Monopoles, Bounds on Hidden Sectors, and Cosmological Implications (7 2026).arXiv:2607.20843 on PithPith's reviewarXiv
  71. [91] A. Mégevand, F. A. Membiela, Bubble wall correlations in cosmological phase transitions, Phys. Rev. D 102 (10) (2020) 103514. arXiv:2008.01873, doi:10.1103/ PhysRevD.102.103514. 11 Supplementary Material Appendix B. Proof of the propositions on relations between the three comp... on PithPith's reviewarXiv

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