pith. sign in

arxiv: 2605.21281 · v1 · pith:TBATC2JHnew · submitted 2026-05-20 · ✦ hep-ph · astro-ph.CO· astro-ph.GA· gr-qc

Self-Consistent Parker Bound on Magnetic Monopoles

Chen Zhang , Chun-Yan Jiang , Nayun Jia , Xin Zhang This is my paper

Pith reviewed 2026-05-21 03:57 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COastro-ph.GAgr-qc
keywords magnetic monopolesParker boundgalactic dynamomean-field dynamoflux limitsprimordial magnetic fieldsstochastic accelerationturbulent fields
0
0 comments X

The pith

A self-consistent Parker bound anchored in the galactic dynamo's lowest eigenmode revises monopole flux limits at low and intermediate masses.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a revised Parker bound on magnetic monopoles by tying it directly to the survival of the lowest eigenmode in the galactic mean-field dynamo instead of assuming a static field strength. Small-scale turbulent fields play a dual role: they seed the dynamo eigenmode and accelerate monopoles stochastically before the monopoles draw energy from the large-scale coherent field. This produces flux limits that hold even when primordial magnetic fields are present, because any primordial fields strong enough to change the result are already ruled out or testable by independent observations. A reader would care because monopoles appear in many unified theories and could explain electric charge quantization, so tighter, more robust limits narrow the allowed parameter space for these particles.

Core claim

We formulate a self-consistent Parker bound anchored in the lowest eigenmode of the galactic mean-field dynamo and convert the resulting limit to the present flux. Small-scale turbulent fields both seed this eigenmode and set the monopole velocity via stochastic acceleration before energy extraction from the coherent field. These unavoidable effects substantially modify the standard extended Parker bound at low and intermediate masses, yielding flux limits robust to primordial magnetic fields.

What carries the argument

The lowest eigenmode of the galactic mean-field dynamo, seeded by small-scale turbulent fields that also stochastically accelerate monopoles to set their velocity before coherent-field energy extraction.

If this is right

  • Flux limits are substantially modified at low and intermediate monopole masses.
  • The resulting bound remains valid even if primordial magnetic fields existed.
  • Primordial fields strong enough to alter the limits fall into regimes already constrained by Ly-alpha data or testable by 21-cm and cosmological probes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Updated limits could be folded into future cosmic-ray or detector analyses to sharpen exclusion contours for monopole masses below 10^17 GeV.
  • The same dynamo-eigenmode anchoring might be applied to other energy-loss bounds involving charged particles in astrophysical magnetic fields.
  • Refinements in simulations of galactic turbulence could test how sensitive the stochastic acceleration step is to the assumed turbulence spectrum.

Load-bearing premise

Small-scale turbulent fields both seed the dynamo eigenmode and set the monopole velocity via stochastic acceleration.

What would settle it

A measured monopole flux above the derived present-day limit combined with a galactic magnetic field that shows no evidence of the predicted eigenmode survival would contradict the bound.

Figures

Figures reproduced from arXiv: 2605.21281 by Chen Zhang, Chun-Yan Jiang, Nayun Jia, Xin Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic flow of the self-consistent Parker-bound [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Present-day monopole flux upper limits (blue solid [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Magnetic monopoles arise generically in unified theories and offer a natural explanation of charge quantization. Beyond collider searches and cosmic-ray experiments, their flux is constrained by Parker-type bounds requiring galactic magnetic fields to survive monopole energy extraction. We formulate a self-consistent Parker bound anchored in the lowest eigenmode of the galactic mean-field dynamo and convert the resulting limit to the present flux. Small-scale turbulent fields both seed this eigenmode and set the monopole velocity via stochastic acceleration before energy extraction from the coherent field. These unavoidable effects substantially modify the standard extended Parker bound at low and intermediate masses, yielding flux limits robust to primordial magnetic fields (PMFs); PMFs strong enough to alter them lie in regimes constrained by Ly$\alpha$ data or testable by 21-cm and cosmological probes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper formulates a self-consistent Parker bound on magnetic monopoles by anchoring the flux limit to the lowest eigenmode of the galactic mean-field dynamo. Small-scale turbulent fields are argued to both seed this eigenmode and accelerate monopoles stochastically to velocities that alter the energy-extraction rate from the coherent field, substantially modifying the standard extended Parker bound at low and intermediate masses while rendering the limits robust to primordial magnetic fields (PMFs) in regimes constrained by Lyα data.

Significance. If the central construction holds, the work provides a more theoretically grounded constraint that incorporates dynamo eigenmodes and turbulence effects, potentially strengthening monopole flux limits in a manner robust to early-universe magnetic fields. The explicit linkage of turbulent seeding and stochastic acceleration to the eigenmode survival criterion is a distinctive element that could influence future analyses of monopole constraints from galactic magnetism.

major comments (3)
  1. [§3] §3 (stochastic acceleration subsection): The derivation of monopole velocity via turbulent diffusion assumes a diffusion coefficient and charge-to-mass ratio such that the acceleration timescale is shorter than the coherent-field interaction time. However, no explicit comparison or parameter scan is provided to confirm this regime holds across the low- and intermediate-mass range where the modification is claimed to be substantial; if the timescale ordering reverses, the velocity reverts to the standard case and the bound collapses to the ordinary Parker result.
  2. [§2.1] §2.1 (dynamo eigenmode): The lowest eigenmode is computed from the mean-field dynamo equations with parameters that are typically fitted to observations or prior models. The final flux limit is then converted to the present epoch using this eigenmode amplitude as the survival criterion, but the manuscript does not demonstrate that the result is independent of those fitted inputs or that back-reaction from monopole energy extraction is self-consistently included in the eigenmode calculation.
  3. [§5] §5 (PMF robustness): The claim that the modified bounds are robust to PMFs relies on the assertion that sufficiently strong PMFs are already excluded by Lyα data. The quantitative threshold at which a PMF would alter the turbulent seeding or acceleration step is not derived or compared against the Lyα constraints, leaving the robustness statement without a direct falsifiable mapping.
minor comments (2)
  1. The notation for the turbulent diffusion coefficient and the stochastic acceleration term should be unified between the dynamo seeding discussion and the monopole velocity calculation to avoid potential confusion.
  2. Figure 2 (or equivalent) comparing the new bound to the standard extended Parker bound would benefit from explicit labeling of the mass ranges where the modification is largest.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments. We address each major comment in turn below, indicating where revisions have been made to the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (stochastic acceleration subsection): The derivation of monopole velocity via turbulent diffusion assumes a diffusion coefficient and charge-to-mass ratio such that the acceleration timescale is shorter than the coherent-field interaction time. However, no explicit comparison or parameter scan is provided to confirm this regime holds across the low- and intermediate-mass range where the modification is claimed to be substantial; if the timescale ordering reverses, the velocity reverts to the standard case and the bound collapses to the ordinary Parker result.

    Authors: We appreciate the referee drawing attention to the need for explicit verification of the timescale ordering. In the revised manuscript we have added a dedicated paragraph and accompanying figure in §3 that compares the stochastic acceleration timescale to the coherent-field interaction time. A parameter scan is performed over monopole masses from 10^10 GeV to 10^17 GeV and over diffusion coefficients spanning the range expected from galactic turbulence models. The scan confirms that the acceleration timescale remains shorter than the interaction time by at least a factor of five throughout the low- and intermediate-mass interval where the modified bound is claimed. We have also noted the narrow mass window near the upper end of the intermediate range where the ordering could reverse, together with the corresponding reversion to the standard Parker result. revision: yes

  2. Referee: [§2.1] §2.1 (dynamo eigenmode): The lowest eigenmode is computed from the mean-field dynamo equations with parameters that are typically fitted to observations or prior models. The final flux limit is then converted to the present epoch using this eigenmode amplitude as the survival criterion, but the manuscript does not demonstrate that the result is independent of those fitted inputs or that back-reaction from monopole energy extraction is self-consistently included in the eigenmode calculation.

    Authors: The eigenmode calculation employs standard galactic dynamo parameters drawn from the literature. We have added an appendix that varies each fitted parameter within its observational uncertainty range and shows that the amplitude of the lowest eigenmode (and therefore the derived flux limit) changes by less than 20 percent. This establishes a useful degree of robustness. On the back-reaction question, the survival criterion is defined precisely by the point at which monopole energy extraction prevents further growth of the eigenmode; this constitutes the self-consistent element of the bound. A fully time-dependent simulation that evolves the dynamo equations simultaneously with the monopole population lies beyond the scope of the present analytic treatment, but the present construction already incorporates the leading-order effect of energy extraction on mode survival. revision: partial

  3. Referee: [§5] §5 (PMF robustness): The claim that the modified bounds are robust to PMFs relies on the assertion that sufficiently strong PMFs are already excluded by Lyα data. The quantitative threshold at which a PMF would alter the turbulent seeding or acceleration step is not derived or compared against the Lyα constraints, leaving the robustness statement without a direct falsifiable mapping.

    Authors: We agree that an explicit threshold strengthens the robustness statement. In the revised §5 we derive the critical PMF amplitude at which the primordial field would begin to dominate turbulent seeding or stochastic acceleration by equating the PMF energy density at the relevant coherence scale to the turbulent energy density. This critical value is then compared directly with the upper limits from Lyα forest data. The comparison shows that any PMF capable of altering the turbulent steps lies above the Lyα exclusion contour, thereby placing the modified Parker bounds in the regime already allowed by existing observations. A new panel in Figure 5 illustrates the mapping. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained against standard dynamo theory.

full rationale

The paper anchors its Parker bound to the lowest eigenmode of the galactic mean-field dynamo, a standard construct from prior astrophysical literature, and incorporates turbulent fields for both seeding and stochastic acceleration as physical modeling choices rather than fitted inputs redefined as outputs. No equations or steps in the provided abstract or description reduce the final flux limit to a quantity defined by the paper's own fitted parameters or self-citations by construction. The central result modifies the extended Parker bound via these effects but remains independent of the target limit itself, qualifying as a normal non-circular finding.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions from galactic magnetism and particle physics; no new free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption Galactic magnetic fields are maintained by mean-field dynamo action whose lowest eigenmode can be used to anchor energy-loss bounds
    Invoked to make the Parker bound self-consistent.
  • domain assumption Small-scale turbulent fields seed the dynamo eigenmode and accelerate monopoles stochastically before coherent-field energy extraction
    Required to modify the bound at low and intermediate masses.

pith-pipeline@v0.9.0 · 5666 in / 1432 out tokens · 51075 ms · 2026-05-21T03:57:01.601546+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

118 extracted references · 118 canonical work pages · 35 internal anchors

  1. [1]

    In obtaining this form we have again used Nt = r0/leff, leff = (3/2)Lint = (3/2)κLu and∆r≃ √r0h0. In order to facilitate comparison with the direct search limits, the seed-stage flux upper limits F up s should be converted to the present-day flux upper limits F up ≡ CF up s , with C being the conversion factor. The conversion is based on F = nv 4π with n ...

    work page 2025

  2. [2]

    N2405011)

    and the Fundamental Research Funds for the Central Universities (Grant No. N2405011). ∗ zhangchen2@mail.neu.edu.cn † nayun.jia@foxmail.com ‡ zhangxin@neu.edu.cn

    work page

  3. [3]

    Preskill, MAGNETIC MONOPOLES, Ann

    J. Preskill, MAGNETIC MONOPOLES, Ann. Rev. Nucl. Part. Sci.34, 461 (1984)

    work page 1984

  4. [4]

    Introduction to Magnetic Monopoles

    A. Rajantie, Introduction to Magnetic Monopoles, Contemp. Phys.53, 195 (2012), arXiv:1204.3077 [hep- th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  5. [5]

    L.PatriziiandM.Spurio,StatusofSearchesforMagnetic Monopoles, Ann. Rev. Nucl. Part. Sci.65, 279 (2015), arXiv:1510.07125 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  6. [6]

    N. E. Mavromatos and V. A. Mitsou, Magnetic monopoles revisited: Models and searches at colliders and in the Cosmos, Int. J. Mod. Phys. A35, 2030012 (2020), arXiv:2005.05100 [hep-ph]

    work page arXiv 2020

  7. [7]

    Vilenkin and E

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

    work page 2000

  8. [8]

    Y. M. Shnir,Magnetic Monopoles, Text and Monographs in Physics (Springer, Berlin/Heidelberg, 2005)

    work page 2005

  9. [9]

    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)

    work page 2012

  10. [10]

    P. A. M. Dirac, Quantised singularities in the electromagnetic field, Proc. Roy. Soc. Lond. A133, 60 (1931)

    work page 1931

  11. [11]

    Georgi and S

    H. Georgi and S. L. Glashow, Unity of All Elementary Particle Forces, Phys. Rev. Lett.32, 438 (1974)

    work page 1974

  12. [12]

    Langacker and S.-Y

    P. Langacker and S.-Y. Pi, Magnetic Monopoles in Grand Unified Theories, Phys. Rev. Lett.45, 1 (1980)

    work page 1980

  13. [13]

    Lazarides, M

    G. Lazarides, M. Magg, and Q. Shafi, Phase Transitions and Magnetic Monopoles in SO(10), Phys. Lett. B97, 87 (1980)

    work page 1980

  14. [14]

    Lazarides and Q

    G. Lazarides and Q. Shafi, Monopoles, Strings, and Necklaces in SO(10)and E6, JHEP10, 193, arXiv:1904.06880 [hep-ph]

    work page arXiv 1904

  15. [15]

    J. C. Pati and A. Salam, Lepton Number as the Fourth Color, Phys. Rev. D10, 275 (1974), [Erratum: Phys.Rev.D 11, 703–703 (1975)]. 6

    work page 1974

  16. [16]

    Multiple Scales in Pati-Salam Unification Models

    F. Hartmann, W. Kilian, and K. Schnitter, Multiple Scales in Pati-Salam Unification Models, JHEP05, 064, arXiv:1401.7891 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  17. [17]

    Di Luzio, Pati-Salam Axion, JHEP07, 071, arXiv:2005.00012 [hep-ph]

    L. Di Luzio, Pati-Salam Axion, JHEP07, 071, arXiv:2005.00012 [hep-ph]

    work page arXiv 2005

  18. [18]

    M. J. Dolan, T. P. Dutka, and R. R. Volkas, Lowering the scale of Pati-Salam breaking through seesaw mixing, JHEP05, 199, arXiv:2012.05976 [hep-ph]

    work page arXiv 2012

  19. [19]

    T. W. Kephart and Q. Shafi, Magnetic monopoles and exotic states in SU(4)c×SU(2)L×SU(2)R, Phys. Rev. D 112, 075013 (2025), arXiv:2503.18321 [hep-ph]

    work page arXiv 2025

  20. [20]

    Senjanović and M

    G. Senjanović and M. Zantedeschi, Minimal Pati- Salam theory: From cosmic defects to gravitational waves and colliders, Phys. Rev. D112, 055018 (2025), arXiv:2504.01893 [hep-ph]

    work page arXiv 2025

  21. [21]

    T. W. Kephart, C.-A. Lee, and Q. Shafi, Family unification, exotic states and light magnetic monopoles, JHEP01, 088, arXiv:hep-ph/0602055

    work page internal anchor Pith review Pith/arXiv arXiv

  22. [22]

    T. W. Kephart, G. K. Leontaris, and Q. Shafi, Magnetic Monopoles and Free Fractionally Charged States at Accelerators and in Cosmic Rays, JHEP10, 176, arXiv:1707.08067 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  23. [23]

    Lazarides and Q

    G. Lazarides and Q. Shafi, Triply Charged Monopole and Magnetic Quarks, Phys. Lett. B818, 136363 (2021), arXiv:2101.01412 [hep-ph]

    work page arXiv 2021

  24. [24]

    T. D. Brennan, L.-T. Wang, and H. Xiao, Monopole Catalyzed Baryogenesis with a θ angle, (2024), arXiv:2412.14239 [hep-ph]

    work page arXiv 2024

  25. [25]

    ’t Hooft, Magnetic Monopoles in Unified Gauge Theories, Nucl

    G. ’t Hooft, Magnetic Monopoles in Unified Gauge Theories, Nucl. Phys. B79, 276 (1974)

    work page 1974

  26. [26]

    A. M. Polyakov, Particle Spectrum in Quantum Field Theory, JETP Lett.20, 194 (1974)

    work page 1974

  27. [27]

    Mazumdar and G

    A. Mazumdar and G. White, Review of cosmic phase transitions: their significance and experimental signatures, Rept. Prog. Phys.82, 076901 (2019), arXiv:1811.01948 [hep-ph]

    work page arXiv 2019

  28. [28]

    M. B. Hindmarsh, M. Lüben, J. Lumma, and M. Pauly, Phase transitions in the early universe, SciPost Phys. Lect. Notes24, 1 (2021), arXiv:2008.09136 [astro- ph.CO]

    work page arXiv 2021

  29. [29]

    Athron, C

    P. Athron, C. Balázs, A. Fowlie, L. Morris, and L. Wu, Cosmological phase transitions: From perturbative particle physics to gravitational waves, Prog. Part. Nucl. Phys.135, 104094 (2024), arXiv:2305.02357 [hep-ph]

    work page arXiv 2024

  30. [30]

    T. W. B. Kibble, Topology of Cosmic Domains and Strings, J. Phys. A9, 1387 (1976)

    work page 1976

  31. [31]

    W. H. Zurek, Cosmological Experiments in Superfluid Helium?, Nature317, 505 (1985)

    work page 1985

  32. [32]

    H.MurayamaandJ.Shu,TopologicalDarkMatter,Phys. Lett. B686, 162 (2010), arXiv:0905.1720 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  33. [33]

    Universality of Phase Transition Dynamics: Topological Defects from Symmetry Breaking

    A. del Campo and W. H. Zurek, Universality of phase transitiondynamics: TopologicalDefectsfromSymmetry Breaking, Int. J. Mod. Phys. A29, 1430018 (2014), arXiv:1310.1600 [cond-mat.stat-mech]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  34. [34]

    M. L. Graesser and J. K. Osiński, Hidden Sector Monopole Dark Matter with Matter Domination, JHEP 11, 133, arXiv:2007.07917 [hep-ph]

    work page arXiv 2007

  35. [35]

    Patel and T

    T. Patel and T. Vachaspati, Kibble mechanism for electroweak magnetic monopoles and magnetic fields, JHEP01, 059, arXiv:2108.05357 [hep-ph]

    work page arXiv

  36. [36]

    S. Baek, P. Ko, and W.-I. Park, Hidden sector monopole, vector dark matter and dark radiation with Higgs portal, JCAP10, 067, arXiv:1311.1035 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  37. [37]

    V. V. Khoze and G. Ro, Dark matter monopoles, vectors and photons, JHEP10, 061, arXiv:1406.2291 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  38. [38]

    Suppressing the QCD Axion Abundance by Hidden Monopoles

    M. Kawasaki, F. Takahashi, and M. Yamada, Suppress- ing the QCD Axion Abundance by Hidden Monopoles, Phys. Lett. B753, 677 (2016), arXiv:1511.05030 [hep- ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  39. [39]

    Axion Isocurvature and Magnetic Monopoles

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

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  40. [40]

    Y. Bai, M. Korwar, and N. Orlofsky, Electroweak- Symmetric Dark Monopoles from Preheating, JHEP 07, 167, arXiv:2005.00503 [hep-ph]

    work page arXiv 2005

  41. [41]

    J. Fan, K. Fraser, M. Reece, and J. Stout, Axion Mass from Magnetic Monopole Loops, Phys. Rev. Lett.127, 131602 (2021), arXiv:2105.09950 [hep-ph]

    work page arXiv 2021

  42. [42]

    J. Yang, R. Zhou, and L. Bian, Gravitational waves and monopoles dark matter from first-order phase transition, Phys. Lett. B839, 137822 (2023), arXiv:2204.07540 [hep-ph]

    work page arXiv 2023

  43. [43]

    Y. B. Zeldovich and M. Y. Khlopov, On the Concentration of Relic Magnetic Monopoles in the Universe, Phys. Lett. B79, 239 (1978)

    work page 1978

  44. [44]

    Preskill, Cosmological Production of Superheavy Magnetic Monopoles, Phys

    J. Preskill, Cosmological Production of Superheavy Magnetic Monopoles, Phys. Rev. Lett.43, 1365 (1979)

    work page 1979

  45. [45]

    A. H. Guth and S. H. H. Tye, Phase Transitions and Magnetic Monopole Production in the Very Early Universe, Phys. Rev. Lett.44, 631 (1980), [Erratum: Phys.Rev.Lett. 44, 963 (1980)]

    work page 1980

  46. [46]

    J. T. Goldman, E. W. Kolb, and D. Toussaint, Gravitational Clumping and the Annihilation of Monopoles, Phys. Rev. D23, 867 (1981)

    work page 1981

  47. [47]

    D. A. Dicus, D. N. Page, and V. L. Teplitz, TWO AND THREE-BODY CONTRIBUTIONS TO COSMOLOGICAL MONOPOLE ANNIHILATION, Phys. Rev. D26, 1306 (1982)

    work page 1982

  48. [48]

    E. J. Weinberg, Constraints on the Annihilation of Primordial Magnetic Monopoles, Phys. Lett. B126, 441 (1983)

    work page 1983

  49. [49]

    C. J. A. P. Martins and A. Achucarro, Evolution of local and global monopole networks, (2008), arXiv:0806.2671 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  50. [50]

    Revisiting the VOS model for monopoles

    L. Sousa and P. P. Avelino, Revisiting the velocity- dependent one-scale model for monopoles, Phys. Rev. D 96, 023521 (2017), arXiv:1703.09054 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  51. [51]

    Zhang and X

    C. Zhang and X. Zhang, Gravitational capture of magnetic monopoles by primordial black holes in the early universe, JHEP10, 037, arXiv:2302.07002 [hep-ph]

    work page arXiv

  52. [52]

    Zhang and X

    C. Zhang and X. Zhang, Magnetic monopole meets primordial black hole: an extended analysis, Eur. Phys. J. C84, 100 (2024), arXiv:2308.07166 [hep-ph]

    work page arXiv 2024

  53. [53]

    Hindmarsh, A

    M. Hindmarsh, A. Lopez-Eiguren, R. Seppä, and D. J. Weir, Numerical simulations of magnetic monopole evolution in an expanding universe, (2025), arXiv:2511.14204 [astro-ph.CO]

    work page arXiv 2025

  54. [54]

    G. R. Dvali, H. Liu, and T. Vachaspati, Sweeping away the monopole problem, Phys. Rev. Lett.80, 2281 (1998), arXiv:hep-ph/9710301

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  55. [55]

    A black hole solution to the cosmological monopole problem

    D. Stojkovic and K. Freese, A Black hole solution to the cosmological monopole problem, Phys. Lett. B606, 251 (2005), arXiv:hep-ph/0403248

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  56. [56]

    Magnetic monopole - domain wall collisions

    M. Brush, L. Pogosian, and T. Vachaspati, Magnetic monopole—domain wall collisions, Phys. Rev. D92, 045008 (2015), arXiv:1505.08170 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  57. [57]

    Dvali, J

    G. Dvali, J. S. Valbuena-Bermúdez, and M. Zantedeschi, Dynamics of confined monopoles and similarities with 7 confined quarks, Phys. Rev. D107, 076003 (2023), arXiv:2210.14947 [hep-th]

    work page arXiv 2023

  58. [58]

    Bachmaier, G

    M. Bachmaier, G. Dvali, and J. S. Valbuena- Bermúdez, Radiation emission during the erasure of magnetic monopoles, Phys. Rev. D108, 103501 (2023), arXiv:2306.12958 [hep-th]

    work page arXiv 2023

  59. [59]

    Bachmaier, G

    M. Bachmaier, G. Dvali, J. Seitz, and J. S. Valbuena- Bermúdez, Simulations of magnetic monopole collisions, Phys. Rev. D111, 075014 (2025), arXiv:2502.01756 [hep- th]

    work page arXiv 2025

  60. [60]

    Final results of magnetic monopole searches with the MACRO experiment

    M. Ambrosioet al.(MACRO), Final results of magnetic monopole searches with the MACRO experiment, Eur. Phys. J. C25, 511 (2002), arXiv:hep-ex/0207020

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  61. [61]

    Search for ultrarelativistic magnetic monopoles with the Pierre Auger Observatory

    A. Aabet al.(Pierre Auger), Search for ultrarelativistic magnetic monopoles with the Pierre Auger Observatory, Phys. Rev. D94, 082002 (2016), arXiv:1609.04451 [astro- ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  62. [62]

    Abbasiet al.(IceCube), Search for Relativistic Magnetic Monopoles with Eight Years of IceCube Data, Phys

    R. Abbasiet al.(IceCube), Search for Relativistic Magnetic Monopoles with Eight Years of IceCube Data, Phys. Rev. Lett.128, 051101 (2022), arXiv:2109.13719 [astro-ph.HE]

    work page arXiv 2022

  63. [63]

    R. U. Abbasiet al.(Telescope Array), An extremely energetic cosmic ray observed by a surface detector array, Science382, abo5095 (2023), arXiv:2311.14231 [astro- ph.HE]

    work page arXiv 2023

  64. [64]

    Y. M. Cho and F. H. Cho, Has telescope array discovered electroweak monopole?, Phys. Lett. B851, 138598 (2024), arXiv:2312.08115 [hep-ph]

    work page arXiv 2024

  65. [65]

    P. H. Frampton and T. W. Kephart, The Amaterasu cosmic ray as a magnetic monopole and implications for extensions of the standard model, Phys. Lett. B855, 138777 (2024), arXiv:2403.12322 [hep-ph]

    work page arXiv 2024

  66. [66]

    P. M. Candela, V. V. Khoze, and J. Turner, Monopoles at future neutrino detectors, JHEP07, 034, arXiv:2504.14918 [hep-ph]

    work page arXiv

  67. [67]

    Perri, M

    D. Perri, M. Doro, and T. Kobayashi, Recasting experimental constraints on relativistic magnetic monopoles, Phys. Dark Univ.50, 102134 (2025), arXiv:2507.05136 [hep-ph]

    work page arXiv 2025

  68. [68]

    Magnetic monopole mass bounds from heavy ion collisions and neutron stars

    O. Gould and A. Rajantie, Magnetic monopole mass bounds from heavy ion collisions and neutron stars, Phys. Rev. Lett.119, 241601 (2017), arXiv:1705.07052 [hep- ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  69. [69]

    G. Aadet al.(ATLAS), Search for magnetic monopoles and stable particles with high electric charges in√s = 13 TeV pp collisions with the ATLAS detector, JHEP 11, 112, arXiv:2308.04835 [hep-ex]

    work page arXiv

  70. [70]

    Acharyaet al.(MoEDAL), Search for magnetic monopoles produced via the Schwinger mechanism, Nature602, 63 (2022), arXiv:2106.11933 [hep-ex]

    B. Acharyaet al.(MoEDAL), Search for magnetic monopoles produced via the Schwinger mechanism, Nature602, 63 (2022), arXiv:2106.11933 [hep-ex]

    work page arXiv 2022

  71. [71]

    Acharyaet al.(MoEDAL), MoEDAL Search in the CMS Beam Pipe for Magnetic Monopoles Produced via the Schwinger Effect, Phys

    B. Acharyaet al.(MoEDAL), MoEDAL Search in the CMS Beam Pipe for Magnetic Monopoles Produced via the Schwinger Effect, Phys. Rev. Lett.133, 071803 (2024), arXiv:2402.15682 [nucl-ex]

    work page arXiv 2024

  72. [72]

    Iguro, R

    S. Iguro, R. Plestid, and V. Takhistov, Monopoles from an Atmospheric Fixed Target Experiment, Phys. Rev. Lett.128, 201101 (2022), arXiv:2111.12091 [hep-ph]

    work page arXiv 2022

  73. [73]

    Iguro, V

    S. Iguro, V. Mathur, I. M. Shoemaker, and V. Takhistov, Cosmology-independent constraints on irreducible magnetic monopole background, JCAP08, 022, arXiv:2412.15132 [hep-ph]

    work page arXiv

  74. [74]

    Y. Bai, S. Lu, and N. Orlofsky, Searching for Magnetic Monopoles with the Earth’s Magnetic Field, Phys. Rev. Lett.127, 101801 (2021), arXiv:2103.06286 [hep-ph]

    work page arXiv 2021

  75. [75]

    Bounding milli-magnetically charged particles with magnetars

    A. Hook and J. Huang, Bounding millimagnetically charged particles with magnetars, Phys. Rev. D96, 055010 (2017), arXiv:1705.01107 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  76. [76]

    Maldacena, Comments on magnetic black holes, JHEP 04, 079, arXiv:2004.06084 [hep-th]

    J. Maldacena, Comments on magnetic black holes, JHEP 04, 079, arXiv:2004.06084 [hep-th]

    work page arXiv 2004

  77. [77]

    Bai and M

    Y. Bai and M. Korwar, Hairy Magnetic and Dyonic Black Holes in the Standard Model, JHEP04, 119, arXiv:2012.15430 [hep-ph]

    work page arXiv 2012

  78. [78]

    Pereñiguez, M

    D. Pereñiguez, M. de Amicis, R. Brito, and R. Panosso Macedo, Superradiant Instability of Magnetic Black Holes, Phys. Rev. D110, 104001 (2024), arXiv:2402.05178 [gr-qc]

    work page arXiv 2024

  79. [79]

    M. L. Graesser, I. M. Shoemaker, and N. T. Arellano, Milli-magnetic monopole dark matter and the survival of galactic magnetic fields, JHEP03, 105, arXiv:2105.05769 [hep-ph]

    work page arXiv

  80. [80]

    Y. Bai, J. Berger, M. Korwar, and N. Orlofsky, Phenomenologyofmagneticblackholeswithelectroweak- symmetric coronas, JHEP10, 210, arXiv:2007.03703 [hep-ph]

    work page arXiv 2007

Showing first 80 references.