Braneworld Baryogenesis and QCD-Era Magnetogenesis: A Predictive Link

Micha\"el Sarrazin

REVIEW 4 major objections 6 minor 56 references

Braneworld Baryogenesis and QCD-Era Magnetogenesis: A Predictive Link

T0 review · 4 major / 6 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read A two-brane baryogenesis scenario, when combined with a stochastic primordial magnetic field, predicts that the observed matter–antimatter asymmetry forces the comoving magnetic field at the QCD epoch to be about 10^10 tesla.

desk verdict The stochastic treatment is new and the white-noise result is solid, but the B0 'prediction' is a fit, and the claimed agreement with QCD magnetogenesis is unquantified. read the letter →

arxiv 2601.04828 v3 pith:ZB7W5SMM submitted 2026-01-08 hep-ph astro-ph.CO

Michaël Sarrazin This is my paper · ORCID

classification hep-phastro-ph.CO

keywords baryogenesisbraneworldprimordialmagneticfieldsQCDphasetransitionbaryonisocurvatureCMBconstraintstwo-braneuniversemagnetogenesis

topics Matter-Antimatter Asymmetry

open problems Matter-Antimatter Asymmetry

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper seeks to settle whether the two-brane baryogenesis mechanism is compatible with realistic primordial magnetic fields and what strength that field must have had. Treating the magnetic field as a causal stochastic field with a broken power-law spectrum, the author finds that reproducing the observed baryon asymmetry can only be achieved for comoving field strengths in a narrow window around 10^10 T at the quark-hadron transition (T≈160 MeV), in agreement with independent estimates from QCD-era magnetogenesis. A second, more general result is that the baryon-density perturbations generated by the mechanism are universal white noise on large scales—independent of the magnetic spectral index—because the finite correlation length of the causal field passes through a strongly nonlinear local map. That produces a pure baryon isocurvature mode, statistically independent of the adiabatic mode and far below current CMB bounds. For a sympathetic reader, the outcome is that a previously ad hoc magnetic-field input becomes a quantitative, testable prediction.

What carries the argument

The mechanism runs on the pseudo-scalar phase θ = e∫(A+−A−)·dl, which encodes the difference of electromagnetic potentials between the visible and hidden branes. Through path-integral averaging the mean phase vanishes, but the nonlinear coupling functions g(θ) and ḡ(θ) average to different values (≈1.0507g and 1.1392g), breaking C/CP and allowing neutron↔hidden-neutron transitions to generate baryon number after the QGP–HG transition. The local baryon density is controlled by At=|A+−A−|, whose amplitude follows a Maxwellian distribution; the key mathematical step is a semi-analytical two-point Monte Carlo method that samples correlated Gaussian At fields with correlation function C(r), appl

What would settle it

Run the two-brane transport equations across the full range of temperature mismatches and stochastic field realizations: if no allowed |ΔT|/T window produces the observed baryon density while keeping the antibaryon density below 10^-16, the central claim collapses. Observationally, a CMB or gravitational-wave bound that excludes a QCD-epoch magnetic field above ~5×10^9 T would remove the required amplitude and falsify the predictive link.

Watch

Extended reading notes

Core claim

The central claim is that the two-brane baryogenesis mechanism becomes predictive once the magnetic field is treated stochastically: the baryon yield YB is a sharply nonlinear function of the local vector-potential difference At=|A+−A−|, and after averaging over the Maxwellian distribution of At, the observed baryon density (comoving YB ≈ 8.8×10^-11) is obtained only for a narrow interval of field amplitudes, roughly B0 ≈ (0.7–1.3)×10^10 T at T≈160 MeV. The same calculation shows that amplitudes in the upper part of the allowed window would overproduce antibaryons, so the requirement that the universe be matter-dominated narrows the range further. Independently of this amplitude, the density

Load-bearing premise

The fragile step is the assumed temperature mismatch between the two branes: the model produces the observed asymmetry only when |ΔT|/T lies between roughly 7×10^-3 and 10^-2, and the paper treats this window as a postulated initial condition with no dynamical derivation.

Editorial extensions

If this is right

The primordial magnetic field ceases to be a free parameter: matching the observed baryon density and the vanishing antibaryon density requires B0 ≈ 10^10 T at T≈160 MeV, with mild dependence on the spectral index n and the temperature mismatch κ.
The baryon-density power spectrum is white noise, Pδ(k) ∝ k^0, on scales larger than the magnetic injection scale, independent of whether the magnetic spectrum has n = 0, 2, or 4.
The generated fluctuations form a pure baryon isocurvature mode, uncorrelated with the adiabatic mode, with amplitude Pδ,0 between ~10^-19 and ~7×10^-18 R_H^3, far below the CMB upper limit of ~7×10^43 R_H^3.
Because the model decouples from the initial adiabatic perturbations at linear order (transfer coefficient C = 0), the standard ΛCDM matter power spectrum is preserved; the isocurvature addition is suppressed by f_b^2 ≈ 0.025.
The predicted field amplitude sits in the range that future CMB polarization and primordial-magnetic-field searches can probe, making the scenario falsifiable.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The white-noise universality argument is general: any Gaussian field with finite correlation length passed through a sufficiently local nonlinear function yields a flat large-scale spectrum. The same semi-analytical technique could be applied to other baryogenesis or particle-production mechanisms driven by a stochastic environmental field.
The required 10^10 T field, if it survives to later epochs on interesting scales, is close to the range often discussed for seeding galactic magnetic fields, which would tie braneworld baryogenesis to a concrete astrophysical observable.
The paper leaves the origin and persistence of the temperature mismatch |ΔT|/T ∈ [7×10^-3, 10^-2] open; a natural next step is to build a concrete brane-collision or thermal-history model that predicts this window rather than postulating it as an initial condition.
Because the two allowed field values for a uniform At bracket the stochastic results, a future extension could compute the full probability distribution of YB rather than only its mean, allowing direct comparison with primordial density statistics.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Tom—

I've read arXiv:2601.04828. The genuinely new part is the stochastic treatment of the braneworld baryogenesis model: modelling the PMF with a broken power-law spectrum, deriving the vector-potential statistics, and propagating these through the nonlinear baryon-production function to get a baryon-density power spectrum. The numerical method is careful, the code is on Zenodo, and the white-noise result is correctly derived and labelled as generic for local nonlinear maps of short-range Gaussian fields. They don't oversell the isocurvature part—they say it's unobservable and only a consistency check.

The problem is the framing of B0. In Section V A, they vary A0 until the Maxwellian average of YB(At) matches the observed asymmetry, then convert to B0 with Eq. (32). That's parameter determination, not a prediction. The only genuinely non-trivial test is whether the resulting B0 falls inside the QCD magnetogenesis range. They claim it does, but they never quote the numerical values from Refs [21–25], so the agreement can't be checked. That's the load-bearing gap.

A secondary issue: Eq. (46) states ∂Y*/∂Y_BB = 0 with only 'a numerical calculation' as support. This is what converts the white-noise baryon fluctuations into a pure isocurvature mode. It's a strong and non-obvious claim, and it needs either a derivation or a demonstration from the Boltzmann equations in Ref. [17].

The temperature mismatch is an effective initial condition, which they acknowledge. That's a limitation, but not a sleight. The paper is internally consistent and honestly written. I'd send it to a referee if I were the editor, but I'd expect a major revision asking for a quantified comparison with QCD magnetogenesis and a substantiation of Eq. (46). I wouldn't cite it in its current form.

This one is for the small community working on exotic baryogenesis and PMF effects. I'd bring it to a reading group if the discussion is about model-building and what counts as a prediction. Not a definitive paper, but an honest attempt.

Referee Report

4 major / 6 minor

Summary. The paper couples a stochastic primordial magnetic field (PMF) to the two-brane baryogenesis model of Ref. [17]. Assuming a broken power-law PMF spectrum and a Maxwellian distribution for the amplitude of the vector-potential difference, it determines the normalization A0 (hence B0 via Eq. (32)) that makes the averaged baryon density match the observed value. It finds B0 ~ 0.7–1.3×10^10 T for the parameter range considered, which it interprets as agreement with causal QCD-era magnetogenesis. It then computes the baryon-density power spectrum with a two-point Monte Carlo method, obtaining a white-noise spectrum for k<k*, and claims this is a pure baryon isocurvature mode far below CMB limits.

Significance. If the claims were fully established, the paper would provide an interesting link between a beyond-Standard-Model baryogenesis mechanism and QCD-era magnetic fields. The white-noise result is a generic consequence of applying a local non-linear map to a short-range correlated Gaussian field and is credible within the paper's assumptions. The release of code and the explicit admission that the temperature mismatch is an effective initial condition are positive features. However, the headline B0 is currently obtained by inverting the observed baryon density rather than predicted, and the claimed agreement with Refs [21–25] is not quantitative. The pure-isocurvature claim rests on an unproven derivative condition. These issues must be addressed before the paper's central claims can be accepted.

major comments (4)

[Sec. V.A, Table II, Eq. (32)] The quantity presented as the central prediction, B0 ≈ 10^10 T, is obtained by scanning A0 until the Maxwellian-averaged ⟨YB⟩ equals the observed (8.8±0.6)×10^-11, and then converting A0 to B0 with Eq. (32). This is a fit, not a prediction, and the paper's own description in Sec. V.A confirms it. The asserted agreement with Refs. [21–25] is therefore not a test: the manuscript nowhere quotes the B0 values (or ranges) predicted by those papers. Please quote those predictions with uncertainties and show the comparison explicitly, or reframe the B0 result as a consistency condition.
[Sec. V.C, Eq. (46)] The step that converts the white-noise spectrum into a pure baryon isocurvature mode is the assertion ∂Y*_B/∂Y^BB = 0 at ⟨At⟩, ⟨Y^BB⟩, said to follow from an unspecified numerical calculation. This is load-bearing: if this derivative is not exactly zero, the isocurvature mode is correlated with the adiabatic mode and the simple bound in Eq. (48) does not follow. Please provide the Boltzmann-equation derivation, a reproducible code, or an analytical argument; the current text gives the reader no way to check this.
[Sec. II.C and IV.B, Eq. (39)] The empirical mapping YB(At) is presented as a symbolic-regression fit with no validation: no residuals, fit error, or comparison to the numerical data of Fig. 1 are given, and the floor YB=10^-19 for At<At0 is asserted. Because Tables II and III and Fig. 2 all derive from this mapping, the paper should release the data behind Fig. 1 or a code that reproduces YB(At), and report the fit accuracy over the interval IA. The notation of Eq. (39) is also ambiguous as typeset.
[Sec. II.A, Eqs. (5)–(8)] The model produces the observed baryon asymmetry only for |ΔT|/T ≈ 7–10×10^-3, imposed as an effective initial condition with no dynamical mechanism, as the paper itself states. This parameter is as important as the PMF amplitude for the outcome. The predictive claim of the paper is conditional on this window being realized, and the paper provides no evidence that brane-collision scenarios (Refs. [33,34]) yield it. Please state clearly that the baryogenesis result is contingent on this input and discuss the plausibility of the window.

minor comments (6)

[Fig. 1] The axis labels in the manuscript text appear corrupted (sequences of /uni0000...); please ensure the final PDF renders them correctly.
[Eq. (26)] Check the placement of H and c; the derivation in Sec. III.A suggests k*^2 = 2π H sqrt(μ0ρ)/(α A0). Also, Eq. (27) should be re-derived to avoid the spurious c.
[Sec. V.A] 'Annexe' should be 'Appendix'.
[General notation] The notation YB and YB for baryon and antibaryon densities is easily confused; consider using Y_B and Y_{\bar B} consistently.
[Sec. V.C, Eq. (44)] The expansion in Eq. (44) assumes small fluctuations of Y^BB, but the magnetic-induced δb may not be small; state the regime of validity of this linearization.
[Appendix A] The statement that no transfer function is needed for the isocurvature mode between T=20 MeV and recombination should be justified; super-horizon isocurvature modes can evolve in multi-fluid systems.

Circularity Check

1 steps flagged · score 6.0 of 10

The headline B0 ~ 10^10 T is obtained by tuning A0 to reproduce the observed baryon asymmetry and then converting A0 to B0 via Eq. (32); the claimed agreement with QCD magnetogenesis is asserted but not quantified.

fitted input called prediction [Sec. V A, Eq. (32), Table II]
"We integrate the baryon density YB(At) generated over the statistical distribution f(At) (see Eq. 37) for various values of A0 of the magnetic vector potential in order to get the average baryon density <YB> = YB,obs in the visible universe, and then to determine the required typical magnetic field strength, B0 = sqrt<B^2> (using Eq. (32)), at the QGP-HG transition."

A0 is the free normalization of the stochastic PMF spectrum. The paper scans A0 until the Maxwellian average of the fitted function YB(At) equals the observed baryon density, YB,obs = (8.8 +/- 0.6) x 10^-11, and then obtains B0 from the same A0 through the algebraic relation Eq. (32), with k* itself tied to A0 by Eq. (26). Thus the headline quantity B0 ~ 10^10 T is a reparametrization of the fitted A0, i.e. of the observed baryon asymmetry, rather than an independent prediction of the brane model. The statement that the PMF amplitude 'is no longer an input parameter but becomes a required prediction' inverts the actual procedure: the amplitude is the fitted parameter, and B0 is its unit conversion. The asserted consistency with Refs [21-25] would require quoting their numerical B0 predicti

full rationale

The central advertised result is that matching the observed baryon asymmetry requires B0 ~ 10^10 T at the QCD epoch. But the derivation in Sec. V A varies A0 until the Maxwellian-averaged baryon yield equals YB,obs and then converts A0 to B0 via Eq. (32). Therefore the headline prediction reduces, by construction, to the observed input baryon density: this is the fitted-input-called-prediction pattern. This does not make every element of the paper worthless: the nonlinear YB(At) mapping, the Maxwellian averaging, and the white-noise spectrum are genuine computations. The white-noise and isocurvature conclusions are not circular—they follow from a finite correlation length combined with a local nonlinear map—and the paper itself concedes they are unobservable. The claimed numerical agreement with causal QCD magnetogenesis papers [21-25] is load-bearing for the 'predictive link', but the paper does not give the B0 values or uncertainties from those papers, so that external validation is unverified; this is a support gap rather than a circular step. Prior self-citations [17-20] supply the underlying brane model and are not separately scored as circular, though they do not cure the fitted-input construction at the center of the paper. Overall score 6: the central claim is statistically forced by fitting A0 to the observed baryon density, while the remaining content is internally consistent and generic.

Assumptions & free parameters 4 free parameters · 7 assumptions · 2 invented entities

The central result rests on the prior two-brane model (all dynamical equations), a uniform-phase ansatz, Gaussian zero-correlated brane potentials, passive field evolution, a hand-set temperature mismatch, an empirical fit to the code output, and an asserted vanishing transfer coefficient. The only numerically fitted quantity controlling the headline B0 is A0, which is tuned to the observed baryon density.

free parameters (4)

A0 (magnetic vector potential normalization; equivalently B0) = B0 ≈ (6.6×10^9 – 1.3×10^10) T depending on spectral index and κ (Table II)
A0 is chosen so that the Maxwellian-averaged baryon density ⟨YB⟩ equals the observed YB,obs = 8.8×10^-11; B0 is then derived via Eq. (32). The headline 'prediction' is therefore a fitted constraint.
κ = T/T′ (temperature mismatch) = κ = 0.991 (|ΔT|/T = 9×10^-3) for main results; allowed window 7–10×10^-3
No microscopic origin is provided; the model only reproduces the asymmetry in this narrow window (Sec. II.A, Eq. (8), Table I).
Symbolic-regression coefficients Y0, At0, S in Eq. (39) = Y0 = 1.07×10^-10, At0 = 1.01×10^6 Tm, S = 1.25×10^9 Tm
Eq. (39) is a PySR fit to the numerical code output for YB(At) in a restricted interval; outside the interval YB is set to 10^-19 by hand. No fit uncertainties are given.
PMF spectral indices n and m = n ∈ {0,2,4}; m = 11/3 or 7/2
Chosen by hand from turbulence models rather than derived in this paper; results depend on n through Tables II and III.

assumptions (7)

domain assumption The two-brane / M4×Z2 framework and the baryogenesis mechanism of Ref. [17] are correct, including Eqs. (13)–(14) and the Boltzmann equations of Ref. [17].
The entire calculation inherits the prior model without independent verification; the paper is self-contained only in summary (Sec. II.A).
ad hoc to paper The phase θ is uniformly distributed over [0,2π] and coupling constants are path-averaged via Eqs. (15)–(16).
Isotropy is invoked to set ⟨θ⟩=0 and uniform distribution; the path-integral average is replaced by a flat average, not derived from the action in Eq. (11).
domain assumption The magnetic vector potentials A± are statistically homogeneous, isotropic Gaussian random fields with zero inter-brane cross-correlation ρ(k)=0.
Standard in PMF literature, but the absence of inter-brane correlation is stated as 'absent or negligible' in Sec. III.B without a calculation.
domain assumption Magnetic fields evolve passively, |B|∝a^-2, with no dynamo or back-reaction between T=160 and 20 MeV.
Justified via large magnetic Reynolds number and baryon-poor plasma; standard but an assumption that fixes the mapping of A0 to later times.
ad hoc to paper The initial temperature mismatch |ΔT|/T ≈ 7–10×10^-3 is an effective initial condition.
Explicitly stated in Sec. II.A; no microphysical mechanism is supplied in this work.
ad hoc to paper The symbolic-regression formula Eq. (39) accurately represents YB(At), with YB=10^-19 for At<At0.
The form is empirical, not derived; the cutoff at At0 is an approximation said to cause 'no substantial error,' but no error estimate is given.
ad hoc to paper The transfer coefficient C of initial adiabatic perturbations vanishes, Eq. (46).
Stated as a numerical calculation from Ref. [17]'s Boltzmann equations; no derivation or plot is shown in this paper.

invented entities (2)

Hidden brane sector (hidden neutron n′, hidden electromagnetic potentials A−)
purpose: Provides C/CP-violating interbrane transitions through the pseudo-scalar phase; the asymmetry is generated by n↔n′ oscillations.
Introduced in prior works by the same author; this paper assumes their existence and gives no falsifiable handle beyond the baryon asymmetry, which is the quantity being fitted.
Interbrane pseudo-scalar field φ with phase θ
purpose: Mediates the coupling g → g + iqφ0, generating g ≠ ḡ for neutrons and antineutrons.
Inherited from Ref. [17]; no independent detection channel is proposed here.

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Cite this review

Pith. "Pith review of Braneworld Baryogenesis and QCD-Era Magnetogenesis: A Predictive Link." pith.science (2026). https://pith.science/paper/ZB7W5SMM

@misc{pith2026260104828,
  author       = {Pith},
  title        = {Pith review of: Braneworld Baryogenesis and QCD-Era Magnetogenesis: A Predictive Link},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZB7W5SMM}},
  note         = {Machine review of arXiv:2601.04828}
}

abstract

We demonstrate that primordial magnetic fields (PMF) play a decisive role in the braneworld baryogenesis scenario of [Phys. Rev. D $\textbf{110}$, 023520 (2024)], where C/CP violation arises from the coupling of visible and hidden matter-antimatter sectors through a pseudo-scalar field. Although this mechanism generates baryon number efficiently only after the quark-hadron transition, by incorporating a realistic stochastic PMF within a semi-analytical framework, we find that matching the observed baryon-antibaryon asymmetry robustly requires PMF strengths of order $10^{10}$ T right after the transition, in agreement with causal QCD-era magnetogenesis. We further reveal that magnetic fluctuations drive the baryon-density spectrum to white noise on large scales, yielding an isocurvature component compatible with Cosmic Microwave Background (CMB) bounds. This establishes a predictive link between the braneworld baryogenesis model and realistic early-Universe magnetic fields.

Figures

Figures reproduced from arXiv: 2601.04828 by the authors.

**Figure 2.** FIG. 2. The power spectrum of baryon density fluctuations, [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

56 extracted references · 1 linked inside Pith

[17]

Fujita and K

T. Fujita and K. Kamada, Baryogenesis from Helical Magnetic Fields and the Evolution of the Baryon Asym- metry, Phys. Rev. D 93, 083520 (2016)

2016
[1]

Bodeker and W

D. Bodeker and W. Buchmuller, Baryogenesis from the weak scale to the grand uniﬁcation scale, Rev. Mod. Phys. 93, 035004 (2021)

2021
[2]

Canetti, M

L. Canetti, M. Drewes, M. Shaposhnikov, Matter and Antimatter in the Universe, New J. Phys. 14, 095012 (2012)

2012
[3]

J. M. Cline, TASI lectures on early universe cosmol- ogy: Inﬂation, baryogenesis and dark matter, Proc. Sci., 13 TASI2018 001 (2019)

2019
[4]

Among the various ingredients po- tentially relevant for baryogenesis, primordial magnetic ﬁelds (PMF) occupy a particularly interesting position

while remaining compatible with the thermal history of the early Universe. Among the various ingredients po- tentially relevant for baryogenesis, primordial magnetic ﬁelds (PMF) occupy a particularly interesting position. They are generically expected across a wide range of sce- narios – from inﬂationary magnetogenesis [5, 6] to causal production during t...

arXiv 2026
[5]

M. S. Turner and L. M. Widrow, Inﬂation-produced, large-scale magnetic ﬁelds, Phys. Rev. D 37, 2743 (1988)

1988
[6]

Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe, JETP Lett

A. Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe, JETP Lett. 5, 24 (1967)

1967
[7]

Then, in this code, the magnetic ﬁelds, and thus At, were supposed to be constant in the whole universe, and ﬂuctuations were not considered

– but without detailed description of their features [17]. Then, in this code, the magnetic ﬁelds, and thus At, were supposed to be constant in the whole universe, and ﬂuctuations were not considered. /uni00000014/uni00000013 /uni00000014 /uni00000014/uni00000013 /uni00000016 /uni00000014/uni00000013 /uni00000018 /uni00000014/uni00000013 /uni0000001a /uni...

2018

Show all 56 references

[8]

Ratra, Cosmological magnetic ﬁelds from an inﬂation- ary universe, Astrophys

B. Ratra, Cosmological magnetic ﬁelds from an inﬂation- ary universe, Astrophys. J. Lett. 391, L1 (1992)

1992
[9]

Cheng and A

B. Cheng and A. Olinto, Primordial magnetic ﬁelds gen- erated in the quark-hadron transition, Phys. Rev. D 50, 2421 (1994)

1994
[10]

Grasso and H

D. Grasso and H. R. Rubinstein, Magnetic ﬁelds in the early universe, Phys. Rep. 348, 163 (2001)

2001
[11]

Subramanian, The origin, evolution and signatures of primordial magnetic ﬁelds, Rep

K. Subramanian, The origin, evolution and signatures of primordial magnetic ﬁelds, Rep. Prog. Phys. 79, 076901 (2016)

2016
[12]

L. M. Widrow, Origin of galactic and extragalactic mag- netic ﬁelds, Rev. Mod. Phys. 74, 775 (2002)

2002
[13]

L. M. Widrow, D. Ryu, D. R. G. Schleicher, K. Subra- manian, C. G. Tsagas, and R. A. Treumann, The ﬁrst magnetic ﬁelds, Space Sci. Rev. 166, 37 (2012)

2012
[14]

Joyce and M

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

1997
[15]

Grasso and A

D. Grasso and A. Riotto, On the nature of the elec- troweak phase transition in the presence of a primordial magnetic ﬁeld, Phys. Lett. B 418, 258 (1998)

1998
[16]

A. J. Long, E. Sabancilar, and T. Vachaspati, Leptogene - sis and primordial magnetic ﬁelds, J. Cosmol. Astropart. Phys. 02, 036 (2014)

2014
[18]

Ralegankar, E

P. Ralegankar, E. Garaldi, M. Viel, Matter power spec- trum induced by primordial magnetic ﬁelds: from the linear to the non-linear regime, JCAP 08, 011 (2025)

2025
[19]

Sarrazin and C

M. Sarrazin and C. Stasser, Violation of C/CP symme- try induced by a scalar ﬁeld emerging from a two-brane universe: A gateway to baryogenesis, Phys. Rev. D 110, 023520 (2024)

2024
[20]

Sarrazin, F

M. Sarrazin, F. Petit, Equivalence between domain-wal ls and ”noncommutative” two-sheeted spacetimes: Model- independent matter swapping between branes, Phys. Rev. D 81, 035014 (2010)

2010
[21]

Stasser, M

C. Stasser, M. Sarrazin, Sub-GeV-scale signatures of h id- den braneworlds up to the Planck scale in a SO(3, 1)- broken bulk, Int. J. Mod. Phys. A 34, 1950029 (2019)

2019
[22]

Stasser, M

C. Stasser, M. Sarrazin, Can neutron disappear- ance/reappearance experiments deﬁnitively rule out the existence of hidden braneworlds endowed with a copy of the Standard Model?, Int. J. Mod. Phys. A 35, 2050202 (2020)

2020
[23]

Brandenburg, K

A. Brandenburg, K. Enqvist, and P. Olesen, Large-scale magnetic ﬁelds from the quark-hadron phase transition, Phys. Rev. D 54, 1291 (1996)

1996
[24]

M. M. Forbes and A. R. Zhitnitsky, Primordial galac- tic magnetic ﬁelds from domain walls at the QCD phase transition, Phys. Rev. Lett. 85, 5268 (2000)

2000
[25]

Boyanovsky and H

D. Boyanovsky and H. J. de Vega, Magnetogenesis during phase transitions, Phys. Rev. D 70, 063508 (2004)

2004
[26]

Boeckel and J

T. Boeckel and J. Schaﬀner-Bielich, The cosmological QCD phase transition revisited, Prog. Part. Nucl. Phys. 67, 689 (2012)

2012
[27]

Tevzadze, L

A.G. Tevzadze, L. Kisslinger, A. Brandenburg, T. Kah- niashvili, Magnetic Fields from QCD Phase Transitions, Astrophys. J. 759, 54 (2012)

2012
[28]

Planck Collaboration, Planck 2018 results. VI. Cosmo- logical parameters, Astron. Astrophys. 641, A6 (2020)

2018
[29]

Connes, J

A. Connes, J. Lott, Particle Models and Concommutative Geometry, Nucl. Phys. B 18 (Proc.Suppl.), 29 (1990)

1990
[30]

Lizzi, G

F. Lizzi, G. Mangano, G. Miele, G. Sparano, Fermion Hilbert Space and Fermion Doubling in the Noncom- mutative Geometry Approach to Gauge Theories, Phys. Rev. D 55, 6357 (1997)

1997
[31]

H. Kase, K. Morita, Y. Okumura, Lagrangian Formula- tion of Connes’ Gauge Theory, Prog. Theor. Phys. 101, 1093 (1999)

1999
[32]

H. Kase, K. Morita, Y. Okumura, A Field-Theoretic Ap- proach to Connes’ Gauge Theory on M4 × Z2, Int. J. Mod. Phys. A 16, 3203 (2001)

2001
[33]

Mukhanov, Physical Foundations of Cosmology , Cam- bridge University Press, Cambridge (2005)

V. Mukhanov, Physical Foundations of Cosmology , Cam- bridge University Press, Cambridge (2005)

2005
[34]

Weinberg, Cosmology, Oxford University Press, Ox- ford (2008)

S. Weinberg, Cosmology, Oxford University Press, Ox- ford (2008)

2008
[35]

Khoury, B

J. Khoury, B. A. Ovrut, P.J. Steinhardt and N. Turok, The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang, Phys. Rev. D 64, 123522 (2001)

2001
[36]

Steinhardt and N

P.J. Steinhardt and N. Turok, A cyclic model of the uni- verse, Science 296, 1436 (2002)

2002
[37]

G. Baym, D. B¨ odeker, and L. McLerran, Magnetic ﬁelds produced by phase transition bubbles in the electroweak phase transition, Phys. Rev. D 53, 662 (1996)

1996
[38]

Banerjee and K

R. Banerjee and K. Jedamzik, The evolution of cosmic magnetic ﬁelds: From the very early universe, to recom- bination, to the present, Phys. Rev. D 70, 123003 (2004)

2004
[39]

Durrer and A

R. Durrer and A. Neronov, Cosmological magnetic ﬁelds: Their generation, evolution and observation, Astron. As- trophys. Rev. 21, 62 (2013)

2013
[40]

Planck Collaboration, Planck 2015 results. XIX. Con- straints on primordial magnetic ﬁelds, Astron. Astro- phys. 594, A19 (2016)

2015
[41]

Vachaspati, Progress on cosmological magnetic ﬁeld s, Rep

T. Vachaspati, Progress on cosmological magnetic ﬁeld s, Rep. Prog. Phys. 84, 074901 (2021)

2021
[42]

Kandus, K

A. Kandus, K. E. Kunze, and C. G. Tsagas, Primordial magnetogenesis, Phys. Rep. 505, 1 (2011)

2011
[43]

Brandenburg and K

A. Brandenburg and K. Subramanian, Astrophysical magnetic ﬁelds and nonlinear dynamo theory, Phys. Rep. 417, 1 (2005)

2005
[44]

Enqvist, Primordial magnetic ﬁelds, Int

K. Enqvist, Primordial magnetic ﬁelds, Int. J. Mod. Phys. D 7, 331 (1998)

1998
[45]

Durrer and C

R. Durrer and C. Caprini, Primordial magnetic ﬁelds and causality, JCAP 11, 010 (2003)

2003
[46]

Caprini, R

C. Caprini, R. Durrer, and G. Servant, The stochastic gravitational wave background from turbulence and mag- netic ﬁelds generated by a ﬁrst-order phase transition, JCAP 12, 024 (2009)

2009
[47]

Brandenburg, T

A. Brandenburg, T. Kahniashvili, S. Mandal, A. R. Pol, A. Tevzadze, and T. Vachaspati, Evolution of hydromag- netic turbulence from the electroweak phase transition, Phys. Rev. D 96, 123528 (2017)

2017
[48]

Kahniashvili, A

T. Kahniashvili, A. Brandenburg, A. G. Tevzadze, The evolution of the primordial magnetic ﬁeld since its gen- eration, Phys. Scr. 91, 104008 (2016)

2016
[49]

R. J. Adler, The Geometry of Random Fields (Wiley, Chichester, 1981)

1981
[50]

P. J. E. Peebles, The Large-Scale Structure of the Uni- verse (Princeton University Press, Princeton, 2020)

2020
[51]

J. M. Bardeen, J. R. Bond, N. Kaiser, and A. S. Sza- 14 lay, The statistics of peaks of Gaussian random ﬁelds, Astrophys. J. 304, 15 (1986)

1986
[52]

Caprini and R

C. Caprini and R. Durrer, Gravitational waves from stochastic magnetic ﬁelds, Phys. Rev. D 65, 023517 (2001)

2001
[53]

Coles and B

P. Coles and B. Jones, A lognormal model for the cos- mological mass distribution, Mon. Not. R. Astron. Soc. 248, 1 (1991)

1991
[54]

Gordon and A

C. Gordon and A. Lewis, Observational constraints on the curvaton model of inﬂation, Phys. Rev. D 67, 123513 (2003)

2003
[55]

Trotta, A

R. Trotta, A. Riazuelo, and R. Durrer, Cosmic microwave background anisotropies with mixed isocurvature pertur- bations, Phys. Rev. Lett. 87, 231301 (2001)

2001
[56]

Lewis, A

A. Lewis, A. Challinor, and A. Lasenby, Eﬃcient com- putation of CMB anisotropies in closed FR W models, Astrophys. J. 538, 473 (2000)

2000

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [17]

Fujita and K

T. Fujita and K. Kamada, Baryogenesis from Helical Magnetic Fields and the Evolution of the Baryon Asym- metry, Phys. Rev. D 93, 083520 (2016)

2016

[2] [1]

Bodeker and W

D. Bodeker and W. Buchmuller, Baryogenesis from the weak scale to the grand uniﬁcation scale, Rev. Mod. Phys. 93, 035004 (2021)

2021

[3] [2]

Canetti, M

L. Canetti, M. Drewes, M. Shaposhnikov, Matter and Antimatter in the Universe, New J. Phys. 14, 095012 (2012)

2012

[4] [3]

J. M. Cline, TASI lectures on early universe cosmol- ogy: Inﬂation, baryogenesis and dark matter, Proc. Sci., 13 TASI2018 001 (2019)

2019

[5] [4]

Among the various ingredients po- tentially relevant for baryogenesis, primordial magnetic ﬁelds (PMF) occupy a particularly interesting position

while remaining compatible with the thermal history of the early Universe. Among the various ingredients po- tentially relevant for baryogenesis, primordial magnetic ﬁelds (PMF) occupy a particularly interesting position. They are generically expected across a wide range of sce- narios – from inﬂationary magnetogenesis [5, 6] to causal production during t...

arXiv 2026

[6] [5]

M. S. Turner and L. M. Widrow, Inﬂation-produced, large-scale magnetic ﬁelds, Phys. Rev. D 37, 2743 (1988)

1988

[7] [6]

Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe, JETP Lett

A. Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe, JETP Lett. 5, 24 (1967)

1967

[8] [7]

Then, in this code, the magnetic ﬁelds, and thus At, were supposed to be constant in the whole universe, and ﬂuctuations were not considered

– but without detailed description of their features [17]. Then, in this code, the magnetic ﬁelds, and thus At, were supposed to be constant in the whole universe, and ﬂuctuations were not considered. /uni00000014/uni00000013 /uni00000014 /uni00000014/uni00000013 /uni00000016 /uni00000014/uni00000013 /uni00000018 /uni00000014/uni00000013 /uni0000001a /uni...

2018