Pith. sign in

REVIEW 3 major objections 5 minor 4 cited by

A source of chirality keeps the chiral plasma instability alive below 80 TeV, generating helical magnetic fields.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 17:28 UTC pith:ZQDESHBE

load-bearing objection A credible proof-of-principle for sourced CPI magnetogenesis below 80 TeV, with an honest analytic formula and one good 1024^3 run—but the source is a toy and the fiducial parameters sit close to the edge of the regime where the mechanism works. the 3 major comments →

arxiv 2512.09177 v1 pith:ZQDESHBE submitted 2025-12-09 hep-ph astro-ph.CO

Primordial magnetic field from chiral plasma instability with sourcing

Murman Gurgenidze , Andrew J. Long , Alberto Roper Pol , Axel Brandenburg , Tina Kahniashvili This is my paper
classification hep-ph astro-ph.CO
keywords chiral plasma instabilityprimordial magnetic fieldschiral magnetic effectmagnetogenesischiral magnetohydrodynamicselectroweak epochmagnetic helicitychirality sourcing
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper claims that the usual death sentence for chiral magnetogenesis—washout of any chiral asymmetry once the plasma cools below about 80 TeV—can be lifted if something actively sources chirality while the washout reactions run. Using a toy model in which a metastable scalar decays with a slight right-versus-left asymmetry, the authors add a peaked source term to chiral magnetohydrodynamics and show, analytically and in 1024^3 direct simulations, that the chiral plasma instability then grows a helical magnetic field even in the washout regime. The resultant comoving magnetic helicity is controlled by a compact formula, hM ≈ sqrt(e) Sbar/(λ tφ Γ5^2), which the simulation confirms. This matters because it reopens CPI magnetogenesis at electroweak temperatures, where baryogenesis models typically live, and yields a relic field that, though too weak for blazar observations, may seed galactic dynamos.

Core claim

The central claim: with a chirality source present, the chiral plasma instability operates below 80 TeV despite the chirality-violating scatterings being in equilibrium. The source shifts the equilibrium chiral chemical potential to the nonzero value ⟨µ5⟩ ≈ S5/Γ5, so the asymmetry is not erased; as the source grows in time, the instability scale sweeps from k_cross toward larger k_φ, amplifying a helical magnetic field. The paper's central analytical result is the saturated helicity density hM ≈ sqrt(e) Sbar/(λ tφ Γ5^2), Eq. (27), and direct simulation of the χMHD equations gives hM = 2.89e-5 E* l*^-2, in close agreement with that formula.

What carries the argument

The load-bearing object is the sourced chiral chemical potential equation in χMHD, where the source S5(t) balances the erasure rate Γ5. The chosen source, S5 = Sbar (t/tφ) exp[-(t² - tφ²)/(2tφ²)], peaks at time tφ and is motivated by out-of-equilibrium decay of a metastable scalar with asymmetric right/left branching. The key identity is Eq. (27), which converts the peak-source value into magnetic helicity; it carries the argument by giving a parameter-free prediction once Sbar, λ, tφ, and Γ5 are fixed.

Load-bearing premise

The scenario depends on a chirality source of sufficient amplitude and lifetime that the instability begins before the source fades (t_cross << t_φ); the paper motivates this with a toy metastable scalar and fiducial parameters, but no established particle physics model is shown to guarantee such a source.

What would settle it

Reduce the source amplitude or lifetime so that t_cross ≥ t_φ in the same χMHD setup; the seed magnetic field should decay without any CPI growth. Alternatively, a more precise computation of the chirality erasure rate Γ5 that is significantly larger than the adopted 1.3e-2 y_e^2 T would suppress the predicted helicity as Γ5^-2, in direct conflict with the quoted fiducial number.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Sourced chirality makes CPI magnetogenesis possible below 80 TeV, including at the electroweak and QCD phase transitions, provided the source outlives the instability onset.
  • With Standard Model fiducial parameters, the relic comoving helicity is about (3.8e-21 G)^2 Mpc a0^3, too small for blazar constraints but enough in principle to seed galactic magnetic fields.
  • The analytical formula hM ≈ sqrt(e) Sbar/(λ tφ Γ5^2) is confirmed by 1024^3 simulations to within a factor of a few, validating the scaling with source amplitude, source lifetime, feedback strength, and erasure rate.
  • Larger chiral feedback (larger λ) suppresses the final field, consistent with the simulations and with the back-reaction in the chemical potential equation.
  • Chirality sourcing from decay of heavy scalars provides a concrete microphysical origin for the otherwise-unsourced CPI scenarios studied earlier at lower temperatures.

Where Pith is reading between the lines

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

  • If the mechanism holds, any baryogenesis model at or below the electroweak scale that produces a net chiral asymmetry will inevitably leave a helical magnetic relic; the sign of the relic helicity would trace the sign of the underlying chirality violation.
  • Because the helicity scales as Γ5^-2, a factor-of-two uncertainty in the electron Yukawa washout rate becomes a factor-of-four uncertainty in the field prediction, making a sharper calculation of Γ5 a high-leverage target.
  • The analytic condition t_cross << t_φ should define a quantitative phase boundary between magnetogenesis and no magnetogenesis; a parameter scan across this boundary in simulations would give a testable threshold.
  • Before electroweak symmetry breaking the relevant field is hypermagnetic rather than electromagnetic; whether Eq. (27) survives with order-one modifications in the hypercharge sector is a natural next check.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper argues that the chiral plasma instability (CPI) can generate helical magnetic fields even below the nominal 80 TeV chirality-erasure temperature, provided that a source continuously replenishes the chiral chemical potential. A phenomenological source term is motivated by a toy model of a metastable scalar decaying with a chirality asymmetry. The authors derive an approximate formula, Eq. (27), for the saturated comoving magnetic helicity, and test it against a single 1024^3 χMHD simulation (run A*) plus a few lower-resolution parameter variants. Extrapolating to Standard Model parameters gives a helicity equivalent to B ≈ 3.8×10^-21 G on Mpc scales, too weak for blazar constraints but possibly relevant for galactic dynamo seeding.

Significance. If correct, the paper identifies a genuine loophole in the standard lore and provides a useful analytical formula (Eq. (27)) for estimating the helicity produced by any future, better-motivated chiral source. The qualitative mechanism—a source can outpace washout and allow the CPI to operate at low temperatures—is plausible and is supported by the 1024^3 simulation. The paper also follows good open-science practice: the Pencil Code is publicly available, the simulation data are released with a DOI, and the analysis routines are promised in a public package. These are real strengths. However, the quantitative prediction is strongly dependent on the source amplitude and lifetime, which are free parameters in a toy model. The numerical validation is performed at parameters far from the SM benchmark, with no convergence study, and the time-scale ordering that underlies Eq. (27) is only marginally satisfied. The paper is therefore best viewed as a proof-of-principle with a provisional fitting formula, not as a robust early-universe prediction.

major comments (3)
  1. [§VII, Table II, Eq. (27)] The central quantitative result, Eq. (27), is validated by a single 1024^3 run (A*) with parameters λ=1e8, η=1e-6, Γ5=1e3, Sbar=4e7, tφ=0.05, which differ from the recommended SM values by 12–29 orders of magnitude (Table II). No convergence study is presented: run A (N=256) has kmax=5e3 < kcross≈7.4e3, so it cannot resolve the CPI; a 512^3 or 2048^3 run is needed to check discretization error. The agreement between Eq. (27) and the simulation (factor ≈1.5) is encouraging but not compelling without at least one additional resolution or parameter variation. In particular, Eq. (27) has no η dependence, yet η differs by 12 orders between the simulation and the fiducial physical value; this should be justified or tested.
  2. [§V.c, Eq. (18), §VI] The derivation of Eq. (27) assumes the ordering Γ5^{-1} << tcross << tφ. For the fiducial SM parameters, Eq. (32) gives tcross≈0.026 t* and tφ=0.05 t*, so tcross/tφ≈0.52. This is not a strong inequality, and the sourcing window is short. More seriously, the condition tcross < tφ translates into a lower bound on the source amplitude; the paper does not state this bound. Using Eq. (18), a source weaker than ϵβΩφ ≲ 4×10^-6 (for the fiducial Γ5, η, tφ) would make tcross > tφ, and no magnetic field would be generated. The paper should explicitly discuss this allowed parameter window, and ideally test Eq. (27) for tcross/tφ values close to unity, where the approximate quasi-steady treatment may fail.
  3. [§II, §VI] The chiral source is a phenomenological input with free parameters ϵ, β, Ωφ, mφ, tφ. The toy scalar in Section II is not realized in any concrete particle physics model, and the fiducial values ϵβΩφ=1e-5, mφ=100 GeV, tφ=0.05 t* are described as 'reasonable' but are effectively arbitrary. Consequently, the quantitative prediction in Eq. (38) is not a first-principles prediction of the early universe; it is a mapping from an assumed source to a magnetic helicity. The authors do state that the source parameters are free, but the abstract and conclusion could be read as claiming more. The paper should make the proof-of-principle character explicit and discuss what classes of baryogenesis/scalar-decay models could supply the required amplitude and lifetime without violating the small-chemical-potential constraint.
minor comments (5)
  1. [§II, Eq. (1) and surrounding text] There is a typo in the text: 'e_R^+ denotes a left-chiral positron' should read 'right-chiral positron.' Also, please double-check the definitions of ΓL and the positron chirality assignments in Eq. (1).
  2. [§II, Eq. (6)] The symbol 'e' is used both for the electric charge (earlier) and for the base of the natural logarithm (Eq. (6)). This is confusing; use 'exp(1)' or a distinct notation such as 'e_N' for Euler's number.
  3. [§V.c, Eq. (18)] The statement “Γ5^{-1} << tcross << tφ” is not reflected in the numerical ordering given after Eq. (32); the list there omits tcross. Including tcross in the ordered list would make the marginality of the condition immediately visible.
  4. [§VII, Fig. 4] The claim of 'excellent agreement' (factor ≈1.5 between Eq. (27) and the run A* value) is acceptable in a first comparison, but the wording is slightly strong given that only one run is used and the uncertainties from the finite resolution and from the neglect of the second term in Eq. (26) are not quantified.
  5. [§I, Introduction] The paper would benefit from a brief statement, early on, that the existence of a chirality source is an assumption and that the results define a framework for evaluating any concrete model that provides such a source.

Circularity Check

0 steps flagged

No significant circularity: hM is a model output, not a fitted input; the central claim is an acknowledged conditional proof-of-principle.

full rationale

Walked the derivation chain. The source S5(t) is introduced in Sec. II from a microscopic toy model (Eqs. 3-6) with independent parameters (epsilon, beta, Omega_phi, m_phi, t_phi); the chirality source is an external forcing in the stated chiMHD equations (7); the CPI growth follows from the standard linearized equation (12). Eq. (27) is obtained by time-integrating the chirality conservation law (22) together with the washout-balance approximation (17); it is not obtained by assuming the final hM. The 1024^3 run A* solves the same field equations, so agreement between Eq. (27) and Eq. (35) validates the analytic approximation; it is a consistency check of the model equations, not a circular prediction of a fitted parameter. Eq. (38) is a parametric evaluation of Eq. (27) with explicitly labeled fiducial choices; the proportionality of hM to Sbar (and hence to epsilon beta Omega_phi/m_phi and t_phi^-3) is honest parameter dependence, not a self-definitional reduction, since Sbar is defined by independent microphysical inputs and hM is the output. The paper explicitly acknowledges the key limitation: 'If instead t_cross > t_phi then the source turns off before the CPI occurs, and there is no magnetic field amplification' (Sec. V), and 'When selecting parameters, it is important to ensure that the time scale for the CPI is short compared to the lifetime of this scalar field' (Sec. VIII). The marginal ordering t_cross/t_phi ~ 0.5 at the fiducial point is a fine-tuning/robustness concern, not a circularity. Self-citations, e.g. Refs. [14,15,56,63], are not load-bearing: the chiMHD equations are stated in the paper, lambda_star follows from Eq. (10), and Gamma_5,star is taken from the independent Ref. [41]. No uniqueness theorem, ansatz-by-citation, or renamed known result is used. No circular step was found.

Axiom & Free-Parameter Ledger

8 free parameters · 9 axioms · 1 invented entities

The central result rests on χMHD equations from prior literature plus a hand-inserted source term. The source is the main unpaid input: its amplitude, lifetime, chiral asymmetry, and abundance are free parameters. The SM estimates for λ, Γ5, η, and D5 come from cited prior work. No new entity is predicted with independent evidence; the toy scalar is an invented entity.

free parameters (8)
  • chiral source amplitude Sbar (via ϵβΩφ/mφ) = fiducial ϵβΩφ=1e-5, mφ=100 GeV; simulation Sbar=4e7 l*-1 t*-1
    Controls the strength of chirality production; hM ∝ Sbar in Eq. (27). No independent measurement fixes it.
  • source decay time tφ = fiducial 0.05 t*; simulation 0.05 t*
    Sets when the source peaks and whether t_cross < tφ; hM ∝ tφ^-3 in Eq. (38).
  • chirality-violation parameter ϵ = not fixed; combined ϵβΩφ=1e-5 fiducial
    Encodes asymmetry between ΓR and ΓL; chosen by hand.
  • branching ratio β = not fixed; combined with ϵ and Ωφ
    Fraction of ϕ decays into chiral pairs; chosen by hand.
  • Ωφ energy fraction = not fixed; combined ϵβΩφ=1e-5 fiducial
    Abundance of the decaying particle; chosen by hand.
  • mφ scalar mass = 100 GeV fiducial
    Mass of the toy scalar; enters source amplitude and hM scaling; chosen by hand.
  • simulation parameters (η, λ, Γ5, Sbar, tφ) in runs A/A* = Table II values, e.g., λ=1e8, Γ5=1e3, η=1e-6
    Chosen for numerical feasibility, not from the SM; Eq. (27) is validated at these values and then extrapolated.
  • initial vector-potential noise amplitude = 1e-12 E*^1/2 l*^-1/2
    Seed magnetic field; final helicity is assumed independent of the seed amplitude.
axioms (9)
  • domain assumption χMHD equations (7a-d) with constitutive relations including the chiral magnetic effect current J_cme = c μ~5 B
    Assumes fluid description, subrelativistic bulk flow, electrical neutrality, and linear constitutive relations; taken from prior literature.
  • standard math Axial anomaly relation ∂µ j5^µ = -2(α/(4πℏ)) Fµν F~µν
    QED anomaly used in Eq. (8); standard.
  • domain assumption Chiral charge density n5 ≈ (kB^2/(ℏ^3 c^3)) μ5 T^2/3 for μ5 << T
    Small-chiral-chemical-potential assumption used throughout; violation would break the conversion between n5 and μ5.
  • ad hoc to paper Chiral source is homogeneous and has shape S5(t) = Sbar (t/tφ) exp[-(t^2-tφ^2)/(2tφ^2)]
    Motivated by a toy decaying scalar, but no specific particle physics model is pinned down; this is central to keeping CPI active below 80 TeV.
  • ad hoc to paper Toy scalar ϕ decays out of equilibrium with ΓR ≠ ΓL, and inverse processes are shut off
    Needed for the S5 formula; not guaranteed by the SM or by a specified BSM model.
  • domain assumption Comoving erasure rate Γ5 is constant during sourcing
    Assumed in the staged evolution; physically Γ5_phys ∝ y_e^2 T, and the comoving value is roughly constant only for T ∝ 1/a. Stated before Eq. (16).
  • domain assumption Time-scale ordering Γ5^-1 << t_cross << tφ
    Needed for the three-stage analytic solution; if not satisfied, either no quasi-equilibrium or no CPI.
  • domain assumption Radiation domination, p=ρ/3, and subrelativistic fluid |u|^2 << 1
    Used to relate scale factor, temperature, and source; the authors cite a correction from Ref. [54] in footnote 2.
  • domain assumption Chiral feedback parameter λ = λ⋆ = (ℏc/kB^2)(12α^2/(π^2 T^2))
    The theoretically preferred value from Eq. (10), used in Eqs. (29) and (38).
invented entities (1)
  • Metastable scalar ϕ with chirality-asymmetric decay no independent evidence
    purpose: Provides the chirality source S5(t) that counteracts washout; necessary for the CPI to operate below 80 TeV.
    A toy model; no collider or cosmological signature is tied to this paper, and the hM prediction scales with its unknown abundance and CP-violating parameter.

pith-pipeline@v1.3.0-alltime-deepseek · 21291 in / 16478 out tokens · 158559 ms · 2026-08-03T17:28:06.167546+00:00 · methodology

0 comments
read the original abstract

In an electron-positron plasma, an imbalance in the number of right- and left-chiral particles can lead to the growth of a helical magnetic field through a phenomenon called the chiral plasma instability (CPI). In the early universe, scattering reactions that violate chirality come into thermal equilibrium when the plasma cools below a temperature of approximately $80 \, \mathrm{TeV}$. Since these reactions tend to relax any pre-existing chiral asymmetry to zero as the system approaches equilibrium, the standard lore is that primordial magnetogenesis via the CPI is not viable below $80 \, \mathrm{TeV}$. In this work, we propose that the presence of a source for chirality can allow the CPI to operate even below $80 \, \mathrm{TeV}$, we explore the implications of this scenario, and we derive predictions for the resultant magnetic field helicity using a combination of analytical methods and direct numerical simulation.

Figures

Figures reproduced from arXiv: 2512.09177 by Alberto Roper Pol, Andrew J. Long, Axel Brandenburg, Murman Gurgenidze, Tina Kahniashvili.

Figure 1
Figure 1. Figure 1: FIG. 1: Evolution of the chiral source [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Evolution of the volume averaged chiral asymmetry. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Evolution of the magnetic helicity. We show the mag [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Evolution of the magnetic spectra. We plot the co [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Magnetic (dashed), helicity (dashed-dotted), rms [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗

discussion (0)

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

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A charge-flow instability in plasmas with charge fluctuations

    astro-ph.CO 2026-07 conditional novelty 7.0

    The charge-flow instability grows magnetic fields in magnetized plasmas via a current proportional to μ v, with maximum growth rate C_flow kμ |μ| B0/8.

  2. Relativistic Chiral MHD with application to the early Universe

    astro-ph.CO 2026-07 conditional novelty 6.0

    The paper adds a charge-flow term proportional to μ v and charge-density corrections to the standard chiral MHD equations, with ready-to-use early-Universe estimates.

  3. Plasma heating during the chiral plasma instability

    hep-ph 2026-05 unverdicted novelty 5.0

    During chiral plasma instability, excess energy from chiral asymmetry heats the plasma with δT ~ μ5²/T instead of fully building the helical magnetic field.

  4. Inefficiency of chiral dynamos in protoneutron stars and the early universe

    astro-ph.HE 2026-03 unverdicted novelty 5.0

    Chiral dynamos grow too slowly and are suppressed by flipping when chirality is pumped gradually, rendering them inefficient in protoneutron stars and barely viable near the electroweak transition.

Reference graph

Works this paper leans on

69 extracted references · 1 canonical work pages · cited by 4 Pith papers

  1. [1]

    Fiducial

    The vector potential may be decomposed into Fourier modesA(x, t) = R d3k (2π)3 Ak(t) eik·x, and further decom- posed onto a basis of right- and left-handed circular po- larization modesA k(t) =A k,+(t)ˆϵk,+ +A k,−(t)ˆϵk,−. In terms of these variables, the equation of motion becomes ∂ ∂t Ak,± + η|k|2 ∓η˜µ5|k| Ak,± = 0.(12) If ˜µ5 = 0, thenA k,± ∝exp[−η|k| ...

  2. [2]

    Hearing beyond the standard model with cosmic sources of Gravitational Waves

    This is a factor of∼30 larger than the numerical result (35), which is partly due to neglecting the washout. At Eq. (27) we derived an approximation to the magnetic helicity that results from the CPI in the presence of source and washout. Evaluat- ing that expression givesh M ≈(1.6×10 −13 G)2 Mpca 3 0, which is in excellent agreement with the numerical re...

    2019

  3. [3]

    Sakharov,Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh

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

    1967

  4. [4]

    Pilaftsis,CP violation and baryogenesis due to heavy Majorana neutrinos,Phys

    A. Pilaftsis,CP violation and baryogenesis due to heavy Majorana neutrinos,Phys. Rev. D56(1997) 5431 [hep-ph/9707235]

    Pith/arXiv arXiv 1997

  5. [5]

    Shaposhnikov,Baryon Asymmetry of the Universe in Standard Electroweak Theory,Nucl

    M.E. Shaposhnikov,Baryon Asymmetry of the Universe in Standard Electroweak Theory,Nucl. Phys. B287 (1987) 757

    1987

  6. [6]

    Vilenkin,Equilibrium Parity Violating Current in a Magnetic Field,Phys

    A. Vilenkin,Equilibrium Parity Violating Current in a Magnetic Field,Phys. Rev. D22(1980) 3080

    1980

  7. [7]

    Joyce and M.E

    M. Joyce and M.E. Shaposhnikov,Primordial magnetic fields, right-handed electrons, and the Abelian anomaly, Phys.Rev.Lett.79(1997) 1193 [astro-ph/9703005]

    Pith/arXiv arXiv 1997

  8. [8]

    Boyarsky, J

    A. Boyarsky, J. Fr¨ ohlich and O. Ruchayskiy, Self-consistent evolution of magnetic fields and chiral asymmetry in the early Universe,Phys. Rev. Lett.108 (2012) 031301 [1109.3350]

    Pith/arXiv arXiv 2012

  9. [9]

    Boyarsky, O

    A. Boyarsky, O. Ruchayskiy and M. Shaposhnikov, Long-range magnetic fields in the ground state of the Standard Model plasma,Phys. Rev. Lett.109(2012) 111602 [1204.3604]

    Pith/arXiv arXiv 2012

  10. [10]

    Tashiro, T

    H. Tashiro, T. Vachaspati and A. Vilenkin,Chiral Effects and Cosmic Magnetic Fields,Phys. Rev. D86 (2012) 105033 [1206.5549]

    Pith/arXiv arXiv 2012

  11. [11]

    Akamatsu and N

    Y. Akamatsu and N. Yamamoto,Chiral Plasma Instabilities,Phys. Rev. Lett.111(2013) 052002 [1302.2125]

    Pith/arXiv arXiv 2013

  12. [12]

    Boyarsky, J

    A. Boyarsky, J. Fr¨ ohlich and O. Ruchayskiy, Magnetohydrodynamics of Chiral Relativistic Fluids, Phys. Rev. D92(2015) 043004 [1504.04854]

    Pith/arXiv arXiv 2015

  13. [13]

    Sigl and N

    G. Sigl and N. Leite,Chiral Magnetic Effect in Protoneutron Stars and Magnetic Field Spectral Evolution,JCAP01(2016) 025 [1507.04983]

    Pith/arXiv arXiv 2016

  14. [14]

    Long and E

    A.J. Long and E. Sabancilar,Chiral Charge Erasure via Thermal Fluctuations of Magnetic Helicity,JCAP05 (2016) 029 [1601.03777]

    Pith/arXiv arXiv 2016

  15. [15]

    Pavlovi´ c, N

    P. Pavlovi´ c, N. Leite and G. Sigl,Chiral Magnetohydrodynamic Turbulence,Phys. Rev. D96 (2017) 023504 [1612.07382]

    Pith/arXiv arXiv 2017

  16. [16]

    Rogachevskii, O

    I. Rogachevskii, O. Ruchayskiy, A. Boyarsky, J. Fr¨ ohlich, N. Kleeorin, A. Brandenburg et al., Laminar and turbulent dynamos in chiral magnetohydrodynamics-I: Theory,Astrophys. J.846 (2017) 153 [1705.00378]

    Pith/arXiv arXiv 2017

  17. [17]

    Brandenburg, J

    A. Brandenburg, J. Schober, I. Rogachevskii, T. Kahniashvili, A. Boyarsky, J. Fr¨ ohlich et al.,The turbulent chiral-magnetic cascade in the early universe, Astrophys. J. Lett.845(2017) L21 [1707.03385]

    Pith/arXiv arXiv 2017

  18. [18]

    Schober, I

    J. Schober, I. Rogachevskii, A. Brandenburg, A. Boyarsky, J. Fr¨ ohlich, O. Ruchayskiy et al.,Laminar and turbulent dynamos in chiral magnetohydrodynamics. II. Simulations,Astrophys. J. 858(2018) 124 [1711.09733]

    Pith/arXiv arXiv 2018

  19. [19]

    Pavlovi´ c and G

    P. Pavlovi´ c and G. Sigl,On minimal energy states of chiral MHD turbulence,JCAP04(2019) 055 [1806.06447]

    Pith/arXiv arXiv 2019

  20. [20]

    Schober, I

    J. Schober, I. Rogachevskii and A. Brandenburg, Dynamo instabilities in plasmas with inhomogeneous chiral chemical potential,Phys. Rev. D105(2022) 043507 [2107.13028]

    Pith/arXiv arXiv 2022

  21. [21]

    Schober, I

    J. Schober, I. Rogachevskii and A. Brandenburg,Chiral Anomaly and Dynamos from Inhomogeneous Chemical Potential Fluctuations,Phys. Rev. Lett.132(2024) 065101 [2307.15118]

    Pith/arXiv arXiv 2024

  22. [22]

    Giovannini,Anomalous Magnetohydrodynamics, Phys

    M. Giovannini,Anomalous Magnetohydrodynamics, Phys. Rev. D88(2013) 063536 [1307.2454]

    Pith/arXiv arXiv 2013

  23. [23]

    Yamamoto,Scaling laws in chiral hydrodynamic turbulence,Phys

    N. Yamamoto,Scaling laws in chiral hydrodynamic turbulence,Phys. Rev. D93(2016) 125016 [1603.08864]

    Pith/arXiv arXiv 2016

  24. [24]

    Hattori, Y

    K. Hattori, Y. Hirono, H.-U. Yee and Y. Yin, MagnetoHydrodynamics with chiral anomaly: phases of collective excitations and instabilities,Phys. Rev. D100 (2019) 065023 [1711.08450]

    Pith/arXiv arXiv 2019

  25. [25]

    Fukushima, D.E

    K. Fukushima, D.E. Kharzeev and H.J. Warringa,The Chiral Magnetic Effect,Phys. Rev. D78(2008) 074033 [0808.3382]

    Pith/arXiv arXiv 2008

  26. [26]

    Kharzeev,The Chiral Magnetic Effect and Anomaly-Induced Transport,Prog

    D.E. Kharzeev,The Chiral Magnetic Effect and Anomaly-Induced Transport,Prog. Part. Nucl. Phys.75 (2014) 133 [1312.3348]

    Pith/arXiv arXiv 2014

  27. [27]

    Liao,Anomalous transport effects and possible environmental symmetry ‘violation’ in heavy-ion collisions,Pramana84(2015) 901 [1401.2500]

    J. Liao,Anomalous transport effects and possible environmental symmetry ‘violation’ in heavy-ion collisions,Pramana84(2015) 901 [1401.2500]

    Pith/arXiv arXiv 2015

  28. [28]

    Kharzeev, J

    D.E. Kharzeev, J. Liao, S.A. Voloshin and G. Wang, Chiral magnetic and vortical effects in high-energy nuclear collisions—A status report,Prog. Part. Nucl. Phys.88(2016) 1 [1511.04050]

    Pith/arXiv arXiv 2016

  29. [29]

    Kamada, N

    K. Kamada, N. Yamamoto and D.-L. Yang,Chiral effects in astrophysics and cosmology,Prog. Part. Nucl. Phys.129(2023) 104016 [2207.09184]

    Pith/arXiv arXiv 2023

  30. [30]

    Kharzeev,Chiral Magnetic Effect: A Brief Introduction, inHandbook of Nuclear Physics, I

    D.E. Kharzeev,Chiral Magnetic Effect: A Brief Introduction, inHandbook of Nuclear Physics, I. Tanihata, H. Toki and T. Kajino, eds., pp. 1–14 (2023), DOI

    2023

  31. [31]

    W. Li, Q. Shou and F. Wang,Experimental review on the chiral magnetic effect in relativistic heavy ion collisions,2511.07358

    arXiv

  32. [32]

    Neronov and I

    A. Neronov and I. Vovk,Evidence for strong extragalactic magnetic fields from Fermi observations of TeV blazars,Science328(2010) 73 [1006.3504]

    Pith/arXiv arXiv 2010

  33. [33]

    Durrer and A

    R. Durrer and A. Neronov,Cosmological Magnetic Fields: Their Generation, Evolution and Observation, Astron. Astrophys. Rev.21(2013) 62 [1303.7121]

    Pith/arXiv arXiv 2013

  34. [34]

    Jedamzik and A

    K. Jedamzik and A. Saveliev,Stringent Limit on Primordial Magnetic Fields from the Cosmic Microwave Background Radiation,Phys. Rev. Lett.123(2019) 021301 [1804.06115]

    Pith/arXiv arXiv 2019

  35. [35]

    Subramanian,From primordial seed magnetic fields to the galactic dynamo,Galaxies7(2019) 47 [1903.03744]

    K. Subramanian,From primordial seed magnetic fields to the galactic dynamo,Galaxies7(2019) 47 [1903.03744]

    Pith/arXiv arXiv 2019

  36. [36]

    Vachaspati,Progress on cosmological magnetic fields, Rept

    T. Vachaspati,Progress on cosmological magnetic fields, Rept. Prog. Phys.84(2021) 074901 [2010.10525]

    Pith/arXiv arXiv 2021

  37. [37]

    Jedamzik and T

    K. Jedamzik and T. Abel,Weak Primordial Magnetic Fields and Anisotropies in the Cosmic Microwave Background Radiation,1108.2517

    Pith/arXiv arXiv

  38. [38]

    Jedamzik and L

    K. Jedamzik and L. Pogosian,Relieving the Hubble tension with primordial magnetic fields,Phys. Rev. Lett. 125(2020) 181302 [2004.09487]

    Pith/arXiv arXiv 2020

  39. [39]

    Galli, L

    S. Galli, L. Pogosian, K. Jedamzik and L. Balkenhol, Consistency of Planck, ACT, and SPT constraints on magnetically assisted recombination and forecasts for future experiments,Phys. Rev. D105(2022) 023513 13 [2109.03816]

    Pith/arXiv arXiv 2022

  40. [40]

    Mirpoorian, K

    S.H. Mirpoorian, K. Jedamzik and L. Pogosian, Modified recombination and the Hubble tension,Phys. Rev. D111(2025) 083519 [2411.16678]

    Pith/arXiv arXiv 2025

  41. [41]

    Jedamzik, L

    K. Jedamzik, L. Pogosian and T. Abel,Hints of Primordial Magnetic Fields at Recombination and Implications for the Hubble Tension,2503.09599

    arXiv

  42. [42]

    Campbell, S

    B.A. Campbell, S. Davidson, J.R. Ellis and K.A. Olive, Cosmological baryon asymmetry constraints on extensions of the standard model,Phys.Lett.B256 (1991) 484

    1991

  43. [43]

    B¨ odeker and D

    D. B¨ odeker and D. Schr¨ oder,Equilibration of right-handed electrons,JCAP05(2019) 010 [1902.07220]

    Pith/arXiv arXiv 2019

  44. [44]

    Schober, A

    J. Schober, A. Brandenburg and I. Rogachevskii,Chiral fermion asymmetry in high-energy plasma simulations, Geophys. Astrophys. Fluid Dynamics114(2020) 106 [1808.06624]

    Pith/arXiv arXiv 2020

  45. [45]

    Schober, J

    J. Schober, J. Schober, T. Fujita, T. Fujita, R. Durrer and R. Durrer,Generation of chiral asymmetry via helical magnetic fields,Phys. Rev. D101(2020) 103028 [2002.09501]

    Pith/arXiv arXiv 2020

  46. [46]

    Brandenburg, Y

    A. Brandenburg, Y. He, T. Kahniashvili, M. Rheinhardt and J. Schober,Relic gravitational waves from the chiral magnetic effect,Astrophys. J.911(2021) 110 [2101.08178]

    Pith/arXiv arXiv 2021

  47. [47]

    Schober, I

    J. Schober, I. Rogachevskii and A. Brandenburg, Production of a Chiral Magnetic Anomaly with Emerging Turbulence and Mean-Field Dynamo Action, Phys. Rev. Lett.128(2022) 065002 [2107.12945]

    Pith/arXiv arXiv 2022

  48. [48]

    Schober, I

    J. Schober, I. Rogachevskii and A. Brandenburg, Efficiency of dynamos from an autonomous generation of chiral asymmetry,Phys. Rev. D110(2024) 043515 [2404.07845]

    Pith/arXiv arXiv 2024

  49. [49]

    Akhmedov, V.A

    E.K. Akhmedov, V.A. Rubakov and A.Y. Smirnov, Baryogenesis via neutrino oscillations,Phys. Rev. Lett. 81(1998) 1359 [hep-ph/9803255]

    Pith/arXiv arXiv 1998

  50. [50]

    Trodden,Electroweak baryogenesis,Rev

    M. Trodden,Electroweak baryogenesis,Rev. Mod. Phys. 71(1999) 1463 [hep-ph/9803479]

    Pith/arXiv arXiv 1999

  51. [51]

    Cline,Baryogenesis, inLes Houches Summer School - Session 86: Particle Physics and Cosmology: The Fabric of Spacetime, 9, 2006 [hep-ph/0609145]

    J.M. Cline,Baryogenesis, inLes Houches Summer School - Session 86: Particle Physics and Cosmology: The Fabric of Spacetime, 9, 2006 [hep-ph/0609145]

    Pith/arXiv arXiv 2006

  52. [52]

    G. Elor, M. Escudero and A. Nelson,Baryogenesis and Dark Matter fromBMesons,Phys. Rev. D99(2019) 035031 [1810.00880]

    Pith/arXiv arXiv 2019

  53. [53]

    Nelson and H

    A.E. Nelson and H. Xiao,Baryogenesis from B Meson Oscillations,Phys. Rev. D100(2019) 075002 [1901.08141]

    Pith/arXiv arXiv 2019

  54. [54]

    Klari´ c, M

    J. Klari´ c, M. Shaposhnikov and I. Timiryasov, Reconciling resonant leptogenesis and baryogenesis via neutrino oscillations,Phys. Rev. D104(2021) 055010 [2103.16545]

    Pith/arXiv arXiv 2021

  55. [55]

    Brandenburg, K

    A. Brandenburg, K. Enqvist and P. Olesen,Large scale magnetic fields from hydromagnetic turbulence in the very early universe,Phys. Rev. D54(1996) 1291 [astro-ph/9602031]

    Pith/arXiv arXiv 1996

  56. [56]

    Roper Pol and A.S

    A. Roper Pol and A.S. Midiri,Relativistic magnetohydrodynamics in the early Universe, 2501.05732

    Pith/arXiv arXiv

  57. [57]

    Peskin and D.V

    M.E. Peskin and D.V. Schroeder,An Introduction to Quantum Field Theory, Westview Press, Boulder, Colorado (1995)

    1995

  58. [58]

    Brandenburg, K

    A. Brandenburg, K. Kamada, K. Mukaida, K. Schmitz and J. Schober,Chiral magnetohydrodynamics with zero total chirality,Phys. Rev. D108(2023) 063529 [2304.06612]. [57]MAGICcollaboration,A lower bound on intergalactic magnetic fields from time variability of 1ES 0229+200 from MAGIC and Fermi/LAT observations,Astron. Astrophys.670(2023) A145 [2210.03321]

    Pith/arXiv arXiv 2023

  59. [59]

    Fujita and K

    T. Fujita and K. Kamada,Large-scale magnetic fields can explain the baryon asymmetry of the Universe, Phys. Rev. D93(2016) 083520 [1602.02109]

    Pith/arXiv arXiv 2016

  60. [60]

    Kamada and A.J

    K. Kamada and A.J. Long,Baryogenesis from decaying magnetic helicity,Phys. Rev. D94(2016) 063501 [1606.08891]

    Pith/arXiv arXiv 2016

  61. [61]

    Kamada and A.J

    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. D94 (2016) 123509 [1610.03074]

    Pith/arXiv arXiv 2016

  62. [62]

    Hamada, K

    Y. Hamada, K. Mukaida and F. Uchida,Symmetries of Hot SM, Magnetic Flux & Baryogenesis from Helicity Decay,2507.01576

    arXiv

  63. [63]

    Fukuda, Y

    H. Fukuda, Y. Hamada, K. Kamada, K. Mukaida and F. Uchida,Magnetic Helicity, Magnetic Monopoles, and Higgs Winding,2509.25734

    arXiv

  64. [64]

    Brandenburg, E

    A. Brandenburg, E. Clarke, T. Kahniashvili, A.J. Long and G. Sun,Relic gravitational waves from the chiral plasma instability in the standard cosmological model, Phys. Rev. D109(2024) 043534 [2307.09385]

    Pith/arXiv arXiv 2024

  65. [65]

    Arnold, G.D

    P.B. Arnold, G.D. Moore and L.G. Yaffe,Transport coefficients in high temperature gauge theories. 1. Leading log results,JHEP11(2000) 001 [hep-ph/0010177]. [65]Pencil Code Collaborationcollaboration,The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained,J. Open Source Softw.6(2021) 2807 ...

    Pith/arXiv arXiv 2000

  66. [66]

    Brandenburg, T

    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. D96(2017) 123528 [1711.03804]

    Pith/arXiv arXiv 2017

  67. [67]

    The pencil code. doi:10.5281/zenodo.2315093. https://github.com/pencil-code

    “The pencil code. doi:10.5281/zenodo.2315093. https://github.com/pencil-code.”

    doi:10.5281/zenodo.2315093

  68. [68]

    Datasets for “Primordial magnetic field from chiral plasma instability with sourcing

    “Datasets for “Primordial magnetic field from chiral plasma instability with sourcing” v.2025.08.12, doi.org/10.5281/zenodo.17852669; seehttp://norlx65. nordita.org/~brandenb/proj/Source-CME/.”

    work page doi:10.5281/zenodo.17852669 2025

  69. [69]

    Public code for reproducing results of this work

    “Public code for reproducing results of this work.” https://github.com/cosmoGW/cosmoGW