pith. machine review for the scientific record.
sign in

arxiv: 2509.23858 · v2 · submitted 2025-09-28 · ✦ hep-ph · astro-ph.CO

Revisiting constraints on magnetogenesis from baryon asymmetry

Yuta Hamada , Kyohei Mukaida , Fumio Uchida This is my paper

Pith reviewed 2026-05-18 11:52 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords magnetogenesisbaryon asymmetryintergalactic magnetic fieldselectroweak crossoverhelical magnetic fieldshypermagnetic fieldsprimordial cosmology
0
0 comments X

The pith

Maximally helical primordial magnetic fields can explain both intergalactic fields and baryon asymmetry.

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

This paper reexamines constraints linking primordial magnetic fields to the observed baryon asymmetry of the universe. It concludes that maximally helical hypermagnetic fields remain consistent with both the intergalactic magnetic fields and the matter excess, based on updated modeling of the electroweak era. For non-helical fields a narrow window survives only if Higgs dynamics during the electroweak crossover cancel helicity decay to a precision of roughly one part in a billion or better. The analysis revisits the baryon isocurvature issue for non-helical cases under the same conditions.

Core claim

Maximally helical fields can be the origin of both the intergalactic magnetic fields and the baryon asymmetry of the universe. There can be a window for non-helical fields to explain the origin of the intergalactic magnetic fields if the Higgs dynamics during the electroweak crossover compensate the helicity decay with a ≲10^{-9--10} precision.

What carries the argument

Helicity evolution of primordial U(1)_Y hypermagnetic fields across the electroweak crossover, including possible compensation by Higgs dynamics.

If this is right

  • Maximally helical fields can simultaneously source intergalactic magnetic fields and the baryon asymmetry.
  • Non-helical fields retain a viable window for explaining intergalactic fields under precise Higgs compensation.
  • The baryon isocurvature constraint for non-helical fields is relaxed when the same compensation holds.
  • Earlier exclusions of magnetogenesis scenarios from baryon asymmetry are lifted for helical fields.

Where Pith is reading between the lines

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

  • If future calculations show insufficient compensation by Higgs dynamics, non-helical magnetogenesis would be ruled out.
  • Measurements of the helicity of intergalactic magnetic fields could distinguish helical from non-helical origins.
  • The scenario ties magnetogenesis to the dynamics of the electroweak phase transition in a testable way.

Load-bearing premise

The hot electroweak theory must accurately describe helicity evolution and the Higgs field must supply the precise compensation for helicity decay in the non-helical case.

What would settle it

A calculation or lattice simulation showing that Higgs dynamics cannot compensate helicity decay to better than 10^{-9} precision during the electroweak crossover would eliminate the non-helical window.

Figures

Figures reproduced from arXiv: 2509.23858 by Fumio Uchida, Kyohei Mukaida, Yuta Hamada.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The baryon-overproduction constraint for maximally helical [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The baryon isocurvature constraint for non-helical ( [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
read the original abstract

Magnetic fields in the universe potentially serve as a messenger of primordial physics. The observationally suggested intergalactic magnetic fields may be a relic of helical primordial $\mathrm{U}(1)_Y$ magnetic fields, which may also explain the origin of the baryon asymmetry of the universe. This scenario has been considered to be not viable, which we revisit as well as the baryon isocurvature problem for non-helical primordial $\mathrm{U}(1)_Y$ magnetic fields, based on the recent discussion on the hot electroweak theory. We find that maximally helical fields can be the origin of both the intergalactic magnetic fields and the baryon asymmetry of the universe and that there can be a window for non-helical fields to explain the origin of the intergalactic magnetic fields if the Higgs dynamics during the electroweak crossover compensate the helicity decay with a $\lesssim10^{-9\text{--}-10}$ precision.

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

2 major / 2 minor

Summary. The manuscript revisits constraints on primordial U(1)_Y magnetogenesis arising from the need to generate the observed baryon asymmetry. It concludes that maximally helical fields can simultaneously source both the intergalactic magnetic fields and the baryon asymmetry, while non-helical fields remain viable if Higgs dynamics during the electroweak crossover compensate helicity decay to a precision of ≲10^{-9--10}. The analysis incorporates recent results on hot electroweak theory and addresses the baryon isocurvature problem for the non-helical case.

Significance. If the helicity-compensation modeling holds, the result would reopen viable parameter space for non-helical magnetogenesis and reinforce helical fields as a unified origin for cosmic magnetism and baryogenesis. The work usefully connects updated electroweak dynamics to observational constraints and could motivate targeted lattice studies of the crossover.

major comments (2)
  1. [Abstract and electroweak-crossover analysis] Abstract and the non-helical viability claim: the window for non-helical U(1)_Y fields is stated to exist only if Higgs dynamics compensate helicity decay to ≲10^{-9--10} precision. This tolerance is adopted from external recent literature on hot electroweak theory without an independent derivation, error budget, or quantitative check of the cancellation (e.g., from sphaleron or vev evolution) shown in the manuscript. If the actual mismatch exceeds this level, the non-helical window closes and the central claim for non-helical magnetogenesis fails.
  2. [Helicity evolution and crossover section] Helicity-evolution modeling: the paper relies on the accuracy of recent hot-electroweak-theory results for the evolution of magnetic helicity through the crossover. A self-contained estimate of the residual helicity after compensation, including any dependence on the precise timing of the Higgs vev growth, would be needed to substantiate that the required 10^{-9--10} precision is dynamically achievable rather than assumed.
minor comments (2)
  1. [Introduction and field-strength definitions] Clarify the precise definition of 'maximally helical' and the normalization of the magnetic-field strength used when comparing to intergalactic-field bounds.
  2. [Abstract and introduction] Add explicit citations to the specific recent hot-electroweak-theory papers invoked for the compensation mechanism already in the abstract and introduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which help clarify the presentation of our results on constraints from baryon asymmetry for primordial U(1)_Y magnetogenesis. We address each major comment below, indicating revisions where appropriate to strengthen the discussion of the electroweak crossover inputs.

read point-by-point responses

  1. Referee: [Abstract and electroweak-crossover analysis] Abstract and the non-helical viability claim: the window for non-helical U(1)_Y fields is stated to exist only if Higgs dynamics compensate helicity decay to ≲10^{-9--10} precision. This tolerance is adopted from external recent literature on hot electroweak theory without an independent derivation, error budget, or quantitative check of the cancellation (e.g., from sphaleron or vev evolution) shown in the manuscript. If the actual mismatch exceeds this level, the non-helical window closes and the central claim for non-helical magnetogenesis fails.

    Authors: We appreciate the referee's emphasis on this point. The ≲10^{-9--10} precision is drawn from recent results in hot electroweak theory on helicity evolution through the crossover, which we cite explicitly. Our analysis applies these established results to the magnetogenesis and baryogenesis context rather than re-deriving the underlying dynamics. In the revised manuscript we have expanded the abstract and the electroweak-crossover section to state the conditional nature of the non-helical window more clearly, to summarize the physical origin of the compensation (sphaleron suppression combined with Higgs vev growth), and to note the main sources of uncertainty reported in the cited literature. A full independent derivation and error budget would require dedicated lattice computations that lie beyond the scope of the present work; we therefore present the non-helical viability as conditional on these theoretical inputs. revision: partial

  2. Referee: [Helicity evolution and crossover section] Helicity-evolution modeling: the paper relies on the accuracy of recent hot-electroweak-theory results for the evolution of magnetic helicity through the crossover. A self-contained estimate of the residual helicity after compensation, including any dependence on the precise timing of the Higgs vev growth, would be needed to substantiate that the required 10^{-9--10} precision is dynamically achievable rather than assumed.

    Authors: We agree that additional detail on the helicity evolution would improve transparency. In the revised version we have added a concise estimate in the helicity-evolution section that illustrates the residual helicity after compensation, using the standard-model Higgs potential and the crossover timing parameters taken from the hot-electroweak literature. The estimate shows how the required suppression level can be reached when the vev growth and sphaleron rate follow the standard crossover dynamics, and we discuss the sensitivity to the precise timing of the transition. This remains an order-of-magnitude assessment based on existing results; we explicitly note that a higher-precision, fully self-contained calculation would benefit from future lattice studies of the crossover. revision: partial

Circularity Check

0 steps flagged

Minor reliance on external electroweak literature; no load-bearing self-reduction or fitted prediction visible.

full rationale

The paper conditions its non-helical window on Higgs dynamics achieving ≲10^{-9--10} compensation during the electroweak crossover, drawing from recent hot electroweak theory discussions. This is presented as an external modeling input rather than a quantity fitted or redefined within the paper itself. No quoted derivation reduces a central prediction to a self-citation chain, ansatz smuggled via prior author work, or input parameter renamed as output. The helical case is framed as viable independently. The overall chain remains self-contained against external benchmarks, warranting only a low score for possible unexamined author overlap in the cited electroweak literature.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available; limited visibility into parameters or assumptions. The claimed precision level for helicity compensation appears as a derived bound rather than an input fit. No new particles or forces are introduced.

axioms (1)
  • domain assumption Recent discussions of the hot electroweak theory accurately describe helicity evolution and Higgs dynamics during the crossover.
    Invoked to reopen the non-helical window; location implied in abstract discussion of electroweak crossover.

pith-pipeline@v0.9.0 · 5696 in / 1276 out tokens · 28769 ms · 2026-05-18T11:52:38.054602+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

65 extracted references · 65 canonical work pages · 39 internal anchors

  1. [1]

    Cosmological Magnetic Fields: Their Generation, Evolution and Observation

    R. Durrer and A. Neronov, “Cosmological Magnetic Fields: Their Generation, Evolution and Observation, ”Astron. Astrophys. Rev.21(2013) 62,arXiv:1303.7121 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  2. [2]

    A Study of the Intergalactic Magnetic Field using Extragalactic Ultra–High-Energy Gamma-Ray Sources,

    M. Honda, “A Study of the Intergalactic Magnetic Field using Extragalactic Ultra–High-Energy Gamma-Ray Sources, ” Astrophysical Journal339(1989) 629

    work page 1989

  3. [3]

    Detecting intergalactic magnetic fields using time delays in pulses of𝛾-rays,

    R. Plaga, “Detecting intergalactic magnetic fields using time delays in pulses of𝛾-rays, ”Nature374no. 6521, (1995) 430–432

    work page 1995

  4. [4]

    Evidence for strong extragalactic magnetic fields from Fermi observations of TeV blazars

    A. Neronov and I. Vovk, “Evidence for strong extragalactic magnetic fields from Fermi observations of TeV blazars, ” Science328(2010) 73–75,arXiv:1006.3504 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  5. [5]

    The intergalactic magnetic field constrained by Fermi/LAT observations of the TeV blazar 1ES 0229+200

    F. Tavecchio, G. Ghisellini, L. Foschini, G. Bonnoli, G. Ghirlanda, and P. Coppi, “The intergalactic magnetic field constrained by Fermi/LAT observations of the TeV blazar 1ES 0229+200, ”Mon. Not. Roy. Astron. Soc.406(2010) L70–L74, arXiv:1004.1329 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  6. [6]

    Extreme TeV blazars and the intergalactic magnetic field

    F. Tavecchio, G. Ghisellini, G. Bonnoli, and L. Foschini, “Extreme TeV blazars and the intergalactic magnetic field, ” Mon. Not. Roy. Astron. Soc.414(2011) 3566, arXiv:1009.1048 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  7. [7]

    Lower limit on the strength and filling factor of extragalactic magnetic fields

    K. Dolag, M. Kachelriess, S. Ostapchenko, and R. Tomas, “Lower limit on the strength and filling factor of extragalactic magnetic fields, ”Astrophys. J. Lett.727(2011) L4, arXiv:1009.1782 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  8. [8]

    Determination of intergalactic magnetic fields from gamma ray data

    W. Essey, S. Ando, and A. Kusenko, “Determination of intergalactic magnetic fields from gamma ray data, ”Astropart. Phys.35(2011) 135–139,arXiv:1012.5313 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  9. [9]

    EGMF Constraints from Simultaneous GeV-TeV Observations of Blazars

    A. M. Taylor, I. Vovk, and A. Neronov, “Extragalactic magnetic fields constraints from simultaneous GeV-TeV observations of blazars, ”Astron. Astrophys.529(2011) A144, arXiv:1101.0932 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  10. [10]

    Time Delay of Cascade Radiation for TeV Blazars and the Measurement of the Intergalactic Magnetic Field

    C. D. Dermer, M. Cavadini, S. Razzaque, J. D. Finke, J. Chiang, and B. Lott, “Time Delay of Cascade Radiation for TeV Blazars and the Measurement of the Intergalactic Magnetic Field, ” Astrophys. J. Lett.733(2011) L21,arXiv:1011.6660 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  11. [11]

    Fermi/LAT observations of 1ES 0229+200: implications for extragalactic magnetic fields and background light

    I. Vovk, A. M. Taylor, D. Semikoz, and A. Neronov, “Fermi/LAT observations of 1ES 0229+200: implications for extragalactic magnetic fields and background light, ” Astrophys. J. Lett.747(2012) L14,arXiv:1112.2534 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  12. [12]

    Lower Bounds on Magnetic Fields in Intergalactic Voids from Long-Term GeV-TeV Light Curves of the Blazar Mrk 421

    K. Takahashi, M. Mori, K. Ichiki, S. Inoue, and H. Takami, “Lower Bounds on Magnetic Fields in Intergalactic Voids from Long-term GeV-TeV Light Curves of the Blazar Mrk 421, ” Astrophys. J. Lett.771(2013) L42,arXiv:1303.3069 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  13. [13]

    Constraints on the Intergalactic Magnetic Field with Gamma-Ray Observations of Blazars

    J. D. Finke, L. C. Reyes, M. Georganopoulos, K. Reynolds, M. Ajello, S. J. Fegan, and K. McCann, “Constraints on the Intergalactic Magnetic Field with Gamma-Ray Observations of Blazars, ”Astrophys. J.814no. 1, (2015) 20, arXiv:1510.02485 [astro-ph.HE]. [14]Fermi-LATCollaboration, M. Ackermannet al., “The Search for Spatial Extension in High-latitude Sourc...

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  14. [14]

    Multimessenger Constraints on Intergalactic Magnetic Fields from the Flare of TXS 0506+056,

    R. Alves Batista and A. Saveliev, “Multimessenger Constraints on Intergalactic Magnetic Fields from the Flare of TXS 0506+056, ”Astrophys. J. Lett.902no. 1, (2020) L11, arXiv:2009.12161 [astro-ph.HE]. [16]MAGICCollaboration, V. A. Acciariet al., “A lower bound on intergalactic magnetic fields from time variability of 1ES 0229+200 from MAGIC and Fermi/LAT ...

    work page arXiv 2020

  15. [15]

    The Cosmological Impact of Luminous TeV Blazars I: Implications of Plasma Instabilities for the Intergalactic Magnetic Field and Extragalactic Gamma-Ray Background

    A. E. Broderick, P. Chang, and C. Pfrommer, “The Cosmological Impact of Luminous TeV Blazars I: Implications of Plasma Instabilities for the Intergalactic Magnetic Field and Extragalactic Gamma-Ray Background, ”Astrophys. J.752 (2012) 22,arXiv:1106.5494 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  16. [16]

    Plasma Effects on Fast Pair Beams in Cosmic Voids,

    R. Schlickeiser, D. Ibscher, and M. Supsar, “Plasma Effects on Fast Pair Beams in Cosmic Voids, ”Astrophys. J.758no. 2, (2012) 102

    work page 2012

  17. [17]

    Plasma effects on fast pair beams II. Reactive versus kinetic instability of parallel electrostatic wave

    R. Schlickeiser, S. Krakau, and M. Supsar, “Plasma Effects on Fast Pair Beams. II. Reactive versus Kinetic Instability of Parallel Electrostatic Waves, ”Astrophys. J.777(2013) 49, arXiv:1308.4594 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  18. [18]

    The Effect of Nonlinear Landau Damping on Ultrarelativistic Beam Plasma Instabilities

    P. Chang, A. E. Broderick, C. Pfrommer, E. Puchwein, A. Lamberts, and M. Shalaby, “The Effect of Nonlinear Landau Damping on Ultrarelativistic Beam Plasma Instabilities, ” Astrophys. J.797no. 2, (2014) 110,arXiv:1410.3797 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  19. [19]

    The electrostatic instability for realistic pair distributions in blazar/EBL cascades

    S. Vafin, I. Rafighi, M. Pohl, and J. Niemiec, “The electrostatic instability for realistic pair distributions in blazar/EBL cascades, ”Astrophys. J.857no. 1, (2018) 43, arXiv:1803.02990 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  20. [20]

    Inflation Produced, Large Scale Magnetic Fields,

    M. S. Turner and L. M. Widrow, “Inflation Produced, Large Scale Magnetic Fields, ”Phys. Rev. D37(1988) 2743

    work page 1988

  21. [21]

    Cosmological ’seed’ magnetic field from inflation,

    B. Ratra, “Cosmological ’seed’ magnetic field from inflation, ” Astrophys. J. Lett.391(1992) L1–L4

    work page 1992

  22. [22]

    Primordial magnetic fields from pseudo-Goldstone bosons

    W. D. Garretson, G. B. Field, and S. M. Carroll, “Primordial magnetic fields from pseudoGoldstone bosons, ”Phys. Rev. D 46(1992) 5346–5351,arXiv:hep-ph/9209238

    work page internal anchor Pith review Pith/arXiv arXiv 1992

  23. [23]

    Magnetohydrodynamic Effects of a First-Order Cosmological Phase Transition,

    C. J. Hogan, “Magnetohydrodynamic Effects of a First-Order Cosmological Phase Transition, ”Phys. Rev. Lett.51(1983) 1488–1491

    work page 1983

  24. [24]

    Magnetic Field Generation During the Cosmological QCD Phase Transition,

    J. M. Quashnock, A. Loeb, and D. N. Spergel, “Magnetic Field Generation During the Cosmological QCD Phase Transition, ” Astrophys. J. Lett.344(1989) L49–L51

    work page 1989

  25. [25]

    Primordial magnetic fields generated in the quark - hadron transition,

    B.-l. Cheng and A. V. Olinto, “Primordial magnetic fields generated in the quark - hadron transition, ”Phys. Rev. D50 (1994) 2421–2424

    work page 1994

  26. [26]

    Magnetic fields from cosmological phase transitions,

    T. Vachaspati, “Magnetic fields from cosmological phase transitions, ”Phys. Lett. B265(1991) 258–261

    work page 1991

  27. [27]

    Evolution of the Baryon Asymmetry through the Electroweak Crossover in the Presence of a Helical Magnetic Field

    K. Kamada and A. J. Long, “Evolution of the Baryon Asymmetry through the Electroweak Crossover in the Presence of a Helical Magnetic Field, ”Phys. Rev. D94no. 12, (2016) 123509,arXiv:1610.03074 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  28. [28]

    Baryon isocurvature constraints on the primordial hypermagnetic fields,

    K. Kamada, F. Uchida, and J. Yokoyama, “Baryon isocurvature constraints on the primordial hypermagnetic fields, ”JCAP04 (2021) 034,arXiv:2012.14435 [astro-ph.CO]

    work page arXiv 2021

  29. [29]

    Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe,

    A. D. Sakharov, “Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, ”Pisma Zh. Eksp. Teor. Fiz.5(1967) 32–35

    work page 1967

  30. [30]

    Ingredients and Equations for Making a Magnetic Field in the Early Universe

    S. Davidson, “Ingredients and equations for making a magnetic field in the early universe, ”Phys. Lett. B380(1996) 253–256,arXiv:astro-ph/9605086

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  31. [31]

    Axial vector vertex in spinor electrodynamics,

    S. L. Adler, “Axial vector vertex in spinor electrodynamics, ” Phys. Rev.177(1969) 2426–2438

    work page 1969

  32. [32]

    A PCAC puzzle:𝜋0 →𝛾𝛾in the𝜎 model,

    J. S. Bell and R. Jackiw, “A PCAC puzzle:𝜋0 →𝛾𝛾in the𝜎 model, ”Nuovo Cim. A60(1969) 47–61

    work page 1969

  33. [33]

    Planck 2018 results. VI. Cosmological parameters

    G. ’t Hooft, “Magnetic Monopoles in Unified Gauge Theories, ” Nucl. Phys. B79(1974) 276–284. [36]PlanckCollaboration, N. Aghanimet al., “Planck 2018 results. VI. Cosmological parameters, ”Astron. Astrophys.641 (2020) A6,arXiv:1807.06209 [astro-ph.CO]. [Erratum: Astron.Astrophys. 652, C4 (2021)]

    work page internal anchor Pith review Pith/arXiv arXiv 1974

  34. [34]

    Big Bang Nucleosynthesis Constraint on Baryonic Isocurvature Perturbations

    K. Inomata, M. Kawasaki, A. Kusenko, and L. Yang, “Big Bang Nucleosynthesis Constraint on Baryonic Isocurvature Perturbations, ”JCAP12(2018) 003,arXiv:1806.00123 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  35. [35]

    Primordial Magnetic Fields, Right Electrons, and the Abelian Anomaly

    M. Joyce and M. E. Shaposhnikov, “Primordial magnetic fields, right-handed electrons, and the Abelian anomaly, ”Phys. Rev. Lett.79(1997) 1193–1196,arXiv:astro-ph/9703005

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  36. [36]

    Primordial Hypermagnetic Fields and Triangle Anomaly

    M. Giovannini and M. E. Shaposhnikov, “Primordial hypermagnetic fields and triangle anomaly, ”Phys. Rev. D57 (1998) 2186–2206,arXiv:hep-ph/9710234

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  37. [37]

    Primordial magnetic fields, anomalous isocurvature fluctuations and Big Bang nucleosynthesis

    M. Giovannini and M. E. Shaposhnikov, “Primordial magnetic fields, anomalous isocurvature fluctuations and big bang nucleosynthesis, ”Phys. Rev. Lett.80(1998) 22–25, arXiv:hep-ph/9708303

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  38. [38]

    Large-scale magnetic fields can explain the baryon asymmetry of the Universe

    T. Fujita and K. Kamada, “Large-scale magnetic fields can explain the baryon asymmetry of the Universe, ”Phys. Rev. D 93no. 8, (2016) 083520,arXiv:1602.02109 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  39. [39]

    Baryogenesis from Decaying Magnetic Helicity

    K. Kamada and A. J. Long, “Baryogenesis from decaying magnetic helicity, ”Phys. Rev. D94no. 6, (2016) 063501, arXiv:1606.08891 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  40. [40]

    Baryon asymmetry constraints on magnetic field from the Electroweak epoch,

    T. Boyer and A. Neronov, “Baryon asymmetry constraints on magnetic field from the Electroweak epoch, ” arXiv:2504.07937 [astro-ph.CO]

    work page arXiv

  41. [41]

    Symmetries of Hot SM, Magnetic Flux & Baryogenesis from Helicity Decay,

    Y. Hamada, K. Mukaida, and F. Uchida, “Symmetries of Hot SM, Magnetic Flux & Baryogenesis from Helicity Decay, ” arXiv:2507.01576 [hep-ph]

    work page arXiv

  42. [42]

    Is There a Hot Electroweak Phase Transition at $m_H\gsim m_W$?

    K. Kajantie, M. Laine, K. Rummukainen, and M. E. Shaposhnikov, “Is there a hot electroweak phase transition at 𝑚𝐻≳𝑚𝑊?, ”Phys. Rev. Lett.77(1996) 2887–2890, arXiv:hep-ph/9605288

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  43. [43]

    Where the electroweak phase transition ends

    M. Gurtler, E.-M. Ilgenfritz, and A. Schiller, “Where the electroweak phase transition ends, ”Phys. Rev. D56(1997) 3888–3895,arXiv:hep-lat/9704013

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  44. [44]

    The universality class of the electroweak theory

    K. Rummukainen, M. Tsypin, K. Kajantie, M. Laine, and M. E. Shaposhnikov, “The Universality class of the electroweak theory, ”Nucl. Phys. B532(1998) 283–314, arXiv:hep-lat/9805013

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  45. [45]

    Endpoint of the hot electroweak phase transition

    F. Csikor, Z. Fodor, and J. Heitger, “Endpoint of the hot electroweak phase transition, ”Phys. Rev. Lett.82(1999) 21–24, arXiv:hep-ph/9809291

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  46. [46]

    The endpoint of the first-order phase transition of the SU(2) gauge-Higgs model on a 4-dimensional isotropic lattice

    Y. Aoki, F. Csikor, Z. Fodor, and A. Ukawa, “The Endpoint of the first order phase transition of the SU(2) gauge Higgs model on a four-dimensional isotropic lattice, ”Phys. Rev. D60 (1999) 013001,arXiv:hep-lat/9901021

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  47. [47]

    The Standard Model cross-over on the lattice

    M. D’Onofrio and K. Rummukainen, “Standard model cross-over on the lattice, ”Phys. Rev. D93no. 2, (2016) 025003, arXiv:1508.07161 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  48. [48]

    The Sphaleron Rate in the Minimal Standard Model

    M. D’Onofrio, K. Rummukainen, and A. Tranberg, “Sphaleron Rate in the Minimal Standard Model, ”Phys. Rev. Lett.113 no. 14, (2014) 141602,arXiv:1404.3565 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  49. [49]

    Magnetic Helicity, Magnetic Monopoles, and Higgs Winding,

    H. Fukuda, Y. Hamada, K. Kamada, K. Mukaida, and F. Uchida, “Magnetic Helicity, Magnetic Monopoles, and Higgs Winding, ”.To appear

    work page

  50. [50]

    Large-scale magnetic fields from hydromagnetic turbulence in the very early universe

    A. Brandenburg, K. Enqvist, and P. Olesen, “Large scale magnetic fields from hydromagnetic turbulence in the very 7 early universe, ”Phys. Rev. D54(1996) 1291–1300, arXiv:astro-ph/9602031

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  51. [51]

    New comprehensive description of the scaling evolution of the cosmological magneto-hydrodynamic system,

    F. Uchida, M. Fujiwara, K. Kamada, and J. Yokoyama, “New comprehensive description of the scaling evolution of the cosmological magneto-hydrodynamic system, ” arXiv:2405.06194 [astro-ph.CO]

    work page arXiv

  52. [52]

    Updated constraint on a primordial magnetic field during big bang nucleosynthesis and a formulation of field effects

    M. Kawasaki and M. Kusakabe, “Updated constraint on a primordial magnetic field during big bang nucleosynthesis and a formulation of field effects, ”Phys. Rev. D86(2012) 063003,arXiv:1204.6164 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  53. [53]

    Constraining small-scale primordial magnetic fields from the abundance of primordial black holes,

    A. Kushwaha and T. Suyama, “Constraining small-scale primordial magnetic fields from the abundance of primordial black holes, ”JCAP12(2024) 012,arXiv:2405.19693 [astro-ph.CO]

    work page arXiv 2024

  54. [54]

    Revisiting constraints on primordial magnetic fields from spectral distortions of cosmic microwave background,

    F. Uchida, K. Kamada, and H. Tashiro, “Revisiting constraints on primordial magnetic fields from spectral distortions of cosmic microwave background, ”Phys. Lett. B865(2025) 139456,arXiv:2411.03183 [astro-ph.CO]. [58]PlanckCollaboration, P. A. R. Adeet al., “Planck 2015 results. XIX. Constraints on primordial magnetic fields, ”Astron. Astrophys.594(2016) ...

    work page arXiv 2025

  55. [55]

    Constraints on primordial magnetic fields from their impact on the ionization history with Planck 2018,

    D. Paoletti, J. Chluba, F. Finelli, and J. A. Rubiño-Martin, “Constraints on primordial magnetic fields from their impact on the ionization history with Planck 2018, ”Mon. Not. Roy. Astron. Soc.517no. 3, (2022) 3916–3927, arXiv:2204.06302 [astro-ph.CO]

    work page arXiv 2018

  56. [56]

    Stringent Limit on Primordial Magnetic Fields from the Cosmic Microwave Background Radiation

    K. Jedamzik and A. Saveliev, “Stringent Limit on Primordial Magnetic Fields from the Cosmic Microwave Background Radiation, ”Phys. Rev. Lett.123no. 2, (2019) 021301, arXiv:1804.06115 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  57. [57]

    Cosmological Magnetic Fields Limits in an Inhomogeneous Universe

    P. Blasi, S. Burles, and A. V. Olinto, “Cosmological magnetic fields limits in an inhomogeneous universe, ”Astrophys. J. Lett. 514(1999) L79–L82,arXiv:astro-ph/9812487

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  58. [58]

    Limit on the intergalactic magnetic field from the ultrahigh-energy cosmic ray hotspot in the Perseus-Pisces region,

    A. Neronov, D. Semikoz, and O. Kalashev, “Limit on the intergalactic magnetic field from the ultrahigh-energy cosmic ray hotspot in the Perseus-Pisces region, ”Phys. Rev. D108 no. 10, (2023) 103008,arXiv:2112.08202 [astro-ph.HE]

    work page arXiv 2023

  59. [59]

    Sensitivity of gamma-ray telescopes for detection of magnetic fields in intergalactic medium

    A. Neronov and D. V. Semikoz, “Sensitivity of gamma-ray telescopes for detection of magnetic fields in intergalactic medium, ”Phys. Rev. D80(2009) 123012, arXiv:0910.1920 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  60. [60]

    The Evolution of Cosmic Magnetic Fields: From the Very Early Universe, to Recombination, to the Present

    R. Banerjee and K. Jedamzik, “The Evolution of cosmic magnetic fields: From the very early universe, to recombination, to the present, ”Phys. Rev. D70(2004) 123003, arXiv:astro-ph/0410032

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  61. [61]

    Evolution of hydromagnetic turbulence from the electroweak phase transition

    A. Brandenburg, T. Kahniashvili, S. Mandal, A. Roper Pol, A. G. Tevzadze, and T. Vachaspati, “Evolution of hydromagnetic turbulence from the electroweak phase transition, ”Phys. Rev. D96no. 12, (2017) 123528, arXiv:1711.03804 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  62. [62]

    Cosmic-void observations reconciled with primordial magnetogenesis,

    D. N. Hosking and A. A. Schekochihin, “Cosmic-void observations reconciled with primordial magnetogenesis, ” Nature Commun.14no. 1, (2023) 7523, arXiv:2203.03573 [astro-ph.CO]

    work page arXiv 2023

  63. [63]

    Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence,

    U. Frisch, A. Pouquet, J. Leorat, and A. Mazure, “Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence, ”Journal of Fluid Mechanics68(1975) 769–778

    work page 1975

  64. [64]

    Reconnection-Controlled Decay of Magnetohydrodynamic Turbulence and the Role of Invariants,

    D. N. Hosking and A. A. Schekochihin, “Reconnection-Controlled Decay of Magnetohydrodynamic Turbulence and the Role of Invariants, ”Phys. Rev. X11no. 4, (2021) 041005,arXiv:2012.01393 [physics.flu-dyn]. [69]Particle Data GroupCollaboration, S. Navaset al., “Review of particle physics, ”Phys. Rev. D110no. 3, (2024) 030001

    work page arXiv 2021

  65. [65]

    Mukhanov,Physical Foundations of Cosmology

    V. Mukhanov,Physical Foundations of Cosmology. Cambridge University Press, Oxford, 2005. Assumptions on the magnetic field In this appendix section, we explain the assumptions we have made implicitly in the main text. First, we model the dissipation of the unconfined magnetic helic- ity as d(𝜅2⃗𝐴c /⋅⃗𝐵c /) d𝑡 ≃ −2𝑎−1𝜅2⃗𝐸c /⋅⃗𝐵c / = −2𝑎−1𝜅2𝜎−1 c / ⃗𝐵c /⋅⃗∇...

    work page 2005