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Astrophysics · arXiv:astro-ph/0405413 v2 · submitted 21 May 2004 · 62 references

Primordial Magnetic Fields in the Post-recombination Era and Early Reionization

Shiv K. Sethi, Kandaswamy Subramanian

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The paper says

“We explore the ways in which primordial magnetic fields influence the thermal and ionization history of the post-recombination universe. After recombination the universe becomes mostly neutral resulting also in a sharp drop in the radiative viscosity.”

more of the abstract

Primordial magnetic fields can then dissipate their energy into the intergalactic medium (IGM) via ambipolar diffusion and, for small enough scales, by generating decaying MHD turbulence. These processes can significantly modify the thermal and ionization history of the post-recombination universe. We show that the dissipation effects of magnetic fields which redshifts to a present value B0 = 3 × 10−9 Gauss smoothed on the magnetic Jeans scale and below, can give rise to Thomson scattering optical depths $\tau \ga 0.1$, although not in the range of redshifts needed to explain the recent WMAP polarization observations. We also study the possibility that primordial fields could induce the formation of subgalactic structures for $z \ga 15$. We show that early structure formation induced by nano-Gauss magnetic fields is potentially capable of producing the early re-ionization implied by the WMAP data. Future CMB observations will be very useful to probe the modified ionization histories produced by primordial magnetic field evolution and constrain their strength.

from the abstract

Pith says

Machine review · deepseek-v4.1-flash · 13 Nov 2026 · what was read was not recorded · not checked by a person

Reviewed in 2026 with later literature in view.

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Holds up, with conditions. A solid forward calculation of magnetic dissipation heating the post-recombination IGM, undercut by an abstract claim about structure-induced reionization that the body never computes. This line is wrong

4 major objections · 8 minor

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The paper says, at Abstract, sentence s6, versus §6.2

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Pith says: Objection 1 of 4 · major

The abstract states 'We show that early structure formation induced by nano-Gauss magnetic fields is potentially capable of producing the early re-ionization implied by the WMAP data,' but §6.2 delivers no such demonstration. What is computed is σ(R,z) and the collapse redshift (Figs. 6–7); the collapsed mass fraction, the ionizing emissivity per collapsed baryon, and the resulting reionization history are …

more of objection 1

… all deferred, and the authors state plainly that this is 'generally a difficult question to address' and that they 'hope to return to this issue in a later work.' The qualitative argument that the density field goes as B² and therefore follows modified χ² statistics, giving more weight to high-density regions than a Gaussian, is plausible but never quantified. Either compute the collapsed fraction from the χ² density PDF at z ≈ 15–20 together with a photon budget, or reword the abstract so that the structure-formation branch is presented as a plausibility argument rather than a result. As written, the abstract's 'We show' outruns the body.

The paper says, at §6.1, Eq. (22)

The review did not quote this passage.

Pith says: Objection 2 of 4 · major

As printed, the second term of Eq. (22) is (t_i/t)^{-5/2}, which equals (t/t_i)^{5/2} and grows faster than the first term (t/t_i)^{2/3}. That contradicts the sentence immediately following, which states that the fastest growing solution of Eq. (23) is ∝ t^{2/3}, and it would make the second term dominate at late times.

more of objection 2

Either the exponent or the parenthesization is wrong. This matters because D(t) in Eq. (24), and hence σ(R,z) in Figs. 6 and 7, is read off this growth factor; the quoted collapse redshifts of z ≈ 50–60 (delta-function spectrum) and z ≈ 10–30 (n ≈ −3) should be re-verified once the mode structure of Eq. (22) is corrected. Please also show the intermediate steps from Eq. (21) to Eq. (22), since the Green's-function integral with a source S ∝ a^{-3} is the load-bearing step of the whole section.

The paper says, at §3.2 and §5.2, Eqs. (12)–(15)

The review did not quote this passage.

Pith says: Objection 3 of 4 · major

The decaying-turbulence channel rests on three chained approximations: the flat-space-to-FRW variable transformation of Eq. (13), the flat-space decay law of Eq. (12) with m = 2(n+3)/(n+5), and the hand estimate t_d/t_i ≃ (k_J/k_max)^{(n+5)/2}. The transformation in Eq. (13) is attributed to 'Banerjee, R. 2003, talk at COSMO 2003', which is an unpublished conference talk, and the validity condition stated (p ≪ ρ) is asserted rather than checked for the modes of interest.

more of objection 3

Because the dissipation rate in Eq. (15) depends on ln(1+t_d/t_i) raised to the power m, and t_d/t_i is estimated rather than computed, the turbulent contribution to τ_ion is sensitive to a quantity that is not independently determined. Please provide a sensitivity analysis: vary t_d/t_i by a factor of a few and m over its plausible range, and report how much τ_turb changes for the n = −2.8, B0 = 3×10⁻⁹ G case that gives the combined τ_ion ≈ 0.15. If the combined number moves substantially, the claim in conclusion (1) that the two mechanisms 'add' should be softened. A published derivation or a demonstration of insensitivity would resolve this.

The paper says, at §5.1, Eq. (18)

The review did not quote this passage.

Pith says: Objection 4 of 4 · major

τ_ion is defined with a step function Θ(n_e − n_es), which makes it a non-standard quantity that is not directly comparable to the τ ≈ 0.17 ± 0.08 inferred by WMAP. The authors acknowledge this in §5.1 and are right that the visibility function, not τ alone, is what CMB data constrain.

more of objection 4

Nevertheless the headline number 'τ_ion ≳ 0.1' is the paper's main quantitative selling point, and a reader cannot tell how much of it would survive under the standard cumulative definition. Please report both: the excess optical depth of Eq. (18) and the standard cumulative τ to last scattering, for each model in Figs. 1 and 4. A small table of (B0, spectral index, τ_ion, cumulative τ, y) for the model grid would make the comparison to WMAP unambiguous and would also let readers check the y-parameter statements in §5.1 and §5.2.

8 minor objections

The paper says, at §3.2, Eq. (14)

Pith says: minor objection 1 of 8

The second term on the right-hand side reads '3mH(t)E_B2[...]', which appears to be a typographical corruption of E_B/2; the factor 3m/2 in Eq. (15) is consistent with the latter. Please correct the displayed equation.

The paper says, at §3.1, footnote 1

Pith says: minor objection 2 of 8

The footnote states that Eq. (9) does not agree with Shu (1992) Eq. (27.19) but is correct for an arbitrary ionized medium per Cowling (1956) Eq. (27). Since the ambipolar heating rate is the backbone of the τ result, it would help to write the general expression explicitly and show how it reduces to the two limiting forms, so that a reader can check the normalization without consulting both sources.

show 6 more

The paper says, at §3.1

Pith says: minor objection 3 of 8

The energy from ambipolar diffusion is deposited in the neutral component, and the electron heating rate is then taken as Γ_e = x_e Γ_in on the grounds of rapid collisional thermalization. This equipartition assumption deserves one sentence of justification or a citation, since the collisional ionization that drives the ionization history depends on the electron temperature specifically.

The paper says, at §5.1

Pith says: minor objection 4 of 8

The statement that 'less than 40 percent of the energy is dissipated by decaying turbulence for n = −2.9 even by z = 10' is not supported by any figure or calculation in the paper. Please show the dissipated fraction as a function of redshift, or cite where it comes from.

The paper says, at §5.2

Pith says: minor objection 5 of 8

The phrase 'a negligibly small y parameter as comparable to observational bounds on y' is ambiguous, since 'comparable to the bound' would suggest y near 1.5×10⁻⁵ rather than negligible. Please state the computed value.

The paper says, at §2, Eq. (5)

Pith says: minor objection 6 of 8

The Alfvén velocity expression mixes B, a, and c in a way that is hard to parse dimensionally; please state the units of each factor and confirm the numerical coefficient.

The paper says, at References

Pith says: minor objection 7 of 8

Several citations do not match the reference list: Landau & Lifshitz 1959 in the text versus Landau & Lifshitz 1987 (Fluid Mechanics) in the list; Subramanian, Narasimha & Chitre 1995 in the text versus 1994 in the list; Biskamp & Müller 2000 in the text versus Müller & Biskamp 2000 in the list; 'Reiss et al. 2004' versus 'Riess et al. 2004'; 'Kleoorin et al 2000' versus 'Kleeorin'; 'Zeldovich, Ruzmaikin & Sokoloff' versus 'Sokolov'.

more of objection 7

'SB98' and 'SB98a' are used interchangeably in §1 and §2 and should be disambiguated.

The paper says, at §5.1

Pith says: minor objection 8 of 8

The statement that a preliminary study shows the models cannot explain the WMAP results is a substantive claim that is not displayed anywhere. Either show the relevant anisotropy calculation or restrict the statement to what Fig. 3 supports, namely that the visibility function is broad in redshift.

What would settle it

Compute the collapsed mass fraction at z = 15-20 from the χ² density PDF (or a Press-Schechter analog for χ² statistics) for the n ≈ -3 spectrum with B0 = 3e-9 G, and estimate the ionizing photon budget per collapsed baryon using a reasonable escape fraction and ionizing efficiency. If the collapsed fraction times the escape fraction times the ionizing efficiency falls below the ~10^-3-10^-2 needed to reionize the universe at that epoch, the abstract's claim fails. A simpler check: recompute σ(R, z) with the full χ² PDF rather than the Gaussian window used in Eq. (26), and see whether the collapse redshift shifts by more than Δz ~ 5.

from the skeptic's reading

How the review went

4 readings by deepseek-v4.1-flash · 13 Nov 2026

  1. Reader holds up, with conditions confidence high
  2. Skeptic partly agrees 4 min 21 s · 21,939 tokens read, 15,007 written
  3. Editor wrote the verdict above 13 s · 22,857 tokens read, 797 written
  4. Referee major revision: 4 major objections, 8 minor 1 min 45 s · 22,202 tokens read, 6,168 written

Not run on this paper: the simulated authors' defence.

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The review in full

The review in brief, machine-written

The part worth your time is the τ calculation. Sethi and Subramanian take a tangled field with present-day value around 3e-9 G, run ambipolar diffusion (Cowling's heating rate) and decaying MHD turbulence into the standard Peebles ionization and thermal equations, and read off the Thomson optical depth. Nothing is fitted to WMAP: B0 goes in, heating rates follow from Eqs. (9) and (15), τ comes out. They get τ ≳ 0.1 and then say plainly that the resulting visibility function is too broad in redshift to explain the WMAP polarization result. Reporting a negative that cleanly is worth something, and the ambipolar half is careful — they check the back-reaction on the field and show under 10 percent of the field energy is drained, so B ∝ 1/a² is fine there. The Eq. (17) collisional-ionization term looks like a transcription slip in a load-bearing equation; worth a check, but it is a typo-level concern, not a structural one. The decaying-turbulence channel is the soft spot. The flat-space to FRW mapping in Eq. (13) is asserted with a citation, m = 2(n+3)/(n+5) is imported from flat-space simulations, and td/ti is estimated by hand from Alfvén crossing times at kJ and kmax. No error propagation. If that ratio is off by a large factor, the turbulent contribution to the combined τ ≈ 0.15 for n = −2.8 loses its footing. A sensitivity check would settle it. The bigger issue is the abstract. [abstract:s6] says they show nano-Gauss fields can produce the WMAP reionization. Section 6.2 does not show this. It computes σ(R, z) and collapse redshifts, then says the ionizing flux from a collapsed structure is 'generally a difficult question' and defers the collapsed mass fraction to later work. The χ²-statistics argument is plausible but never quantified — no collapsed fraction, no emissivity, no reionization history. The authors flag the gap themselves, so it is not hidden, but 'We show' in the abstract still outruns the body. This is a paper for people working on magnetic fields and reionization who want the τ–B0 relation and will use it as a constraint handle. The ambipolar result is citable; the turbulence number I would quote with a caveat. Send it out. The core calculation deserves a referee, and the fix is editorial — either derive the structure-formation claim or soften the abstract to match Section 6.2.

The strongest objection

The paper's own headline (abstract:s6) is that early structure formation from nano-Gauss fields is 'potentially capable of producing the early re-ionization implied by the WMAP data.' Section 6.2 does not deliver this. It computes σ(R, z) and collapse redshifts (Figures 6-7), then states: 'This is generally a difficult question to address given the uncertainties in understanding astrophysical processes that determine the hydrogen ionizing flux from a collapsed structure... We hope to return to this issue in a later work.' The qualitative argument that the density field ∝ B² satisfies modified χ² statistics, so 'high density regions get more weight than a Gaussian,' is plausible but never quantified. No collapsed mass fraction, no ionizing emissivity, no reionization history is computed. The authors acknowledge the gap, so it is not hidden, but the abstract still says 'We show.' What remains unresolved is whether the χ² density PDF actually yields a large enough collapsed fraction at z ~ 15-20 and whether the ionizing photon budget per collapsed baryon suffices. Without that, s6 is a plausibility argument, not a demonstration. By contrast, the τ claim (s4) is supported by ambipolar diffusion alone, so the s6 gap is the more load-bearing issue for the paper's framing.

The paper's demonstrated result (abstract:s4) is a forward computation: given B0, the ambipolar and turbulent heating rates feed standard ionization and thermal equations, and τ follows. It is supported by ambipolar diffusion alone (B0 >~ 3e-9 G gives τ >~ 0.1 for n ≈ -3), so the turbulence channel is not load-bearing for the headline τ claim. The reader's weakest_assumption — the conformal mapping in Eq. (13) and the hand-estimated td/ti in Section 5.2 — is a real soft spot: the matter-dominated mapping is cited to an unpublished conference talk (Banerjee 2003, COSMO), and td/ti is assumed, not derived. But it affects the combined τ ~ 0.15 and the visibility-function shape, not the headline τ >~ 0.1. The more load-bearing concern is the s6 gap: the paper's own headline claim about structure-formation-driven reionization is asserted, not computed, and Section 6.2 explicitly defers it. The authors acknowledge this, so the issue is not hidden, but the abstract's 'We show' still outruns the body. The reader's rationale lists this gap first, but the weakest_assumption field picks turbulence; I'd prioritize the s6 gap. One reader flag I would downgrade: the Eq. (17) collisional term γ_e n_b (1-x_e) x_e is the standard form for ẋ_e (the volume rate β_coll n_b² x_e(1-x_e) divided by n_b), so it is not a transcription slip. Overall, CONDITIONAL is the right verdict: the τ calculation stands, but the reionization claim needs derivation or removal from the abstract.

The referee's report

The τ–B0 mapping in §5 is a genuine forward computation: B0 is an input, the heating follows from stated microphysics, and τ is an output, so the result converts a reionization observable into a constraint on small-scale primordial fields. The paper deserves credit for reporting a negative result against its own motivating observation (the visibility function is too broad to explain WMAP), for explicitly justifying the neglect of back-reaction on the field (under 10% of the magnetic energy dissipated by ambipolar diffusion), and for supplying the visibility-function diagnostic in Fig. 3 that makes the negative result checkable rather than asserted. The prediction that Planck-scale data could detect the broad partial-reionization signature is falsifiable. The structure-formation branch of §6 is a different matter: it delivers collapse redshifts and masses but not a reionization history, and the abstract's claim for that branch is not matched by the body.

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

Right after recombination the universe went dark and mostly neutral, and the radiative viscosity that had been choking off fluid motions dropped sharply. Sethi and Subramanian ask what a tangled primordial magnetic field would do with that opening: the field's Lorentz force drags the few remaining ions through the neutral gas (ambipolar diffusion), and on scales below the magnetic Jeans length the field can stir decaying MHD turbulence, both of which turn magnetic energy into heat. The paper pushes that heat through the standard thermal and ionization equations and asks how much Thomson scattering optical depth it buys, then separately asks whether the same field's density perturbations could collapse into the first subgalactic objects. The payoff, if the numbers hold, is a second knob on reionization: small-scale magnetic fields become something CMB polarization can bound, and early structure formation gets a non-gravitational trigger.

Core claim. The paper's demonstrated result is a forward calculation: take a field with present-day value $B_0 = 3$-$10^{-9}$ G smoothed on the magnetic Jeans scale and below, let it dissipate through ambipolar diffusion and decaying turbulence, feed the resulting heating into the ionization and temperature equations, and the Thomson optical depth comes out at $B_0 = 3$-$10^{-9}$ G smoothed on the magnetic Jeans scale and below, let it dissipate through ambipolar diffusion and decaying turbulence, feed the resulting heating into the ionization and temperature equations, and the Thomson optical depth comes out at $B_0 = 3$-$10^{-9}$ G smoothed on the magnetic Jeans scale and below, let it dissipate through ambipolar diffusion and decaying turbulence, feed the resulting heating into the ionization and temperature equations, and the Thomson optical depth comes out at $B_0 = 3$-$10^{-9}$ G smoothed on the magnetic Jeans scale and below, let it dissipate through ambipolar diffusion and decaying turbulence, feed the resulting heating into the ionization and temperature equations, and the Thomson optical depth comes out at $B_0 = 3$-$10^{-9}$ G smoothed on the magnetic Jeans scale and below, let it dissipate through ambipolar diffusion and decaying turbulence, feed the resulting heating into the ionization and temperature equations, and the Thomson optical depth comes out at $B_0 = 3$-$10^{-9}$ G smoothed on the magnetic Jeans scale and below, let it dissipate through ambipolar diffusion and decaying turbulence, feed the resulting heating into the ionization and temperature equations, and the Thomson optical depth comes out at $B_0 = 3$-$10^{-9}$ G smoothed on the magnetic Jeans scale and below, let it dissipate through ambipolar diffusion and decaying turbulence, feed the resulting heating into the ionization and temperature equations, and the Thomson optical depth comes out at $B_0 = 3$-$10^{-9}$ G smoothed on the magnetic Jeans scale and below, let it dissipate through ambipolar diffusion and decaying turbulence, feed the resulting heating into the ionization and temperature equations, and the Thomson optical depth comes out at $B_0 = 3$-$10^{-9}$ G smoothed on the magnetic Jeans scale and below, let it dissipate through ambipolar diffusion and decaying turbulence, feed the resulting heating into the ionization and temperature equations, and the Thomson optical depth comes.

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The paper

Abstract

We explore the ways in which primordial magnetic fields influence the thermal and ionization history of the post-recombination universe. After recombination the universe becomes mostly neutral resulting also in a sharp drop in the radiative viscosity. Primordial magnetic fields can then dissipate their energy into the intergalactic medium (IGM) via ambipolar diffusion and, for small enough scales, by generating decaying MHD turbulence. These processes can significantly modify the thermal and ionization history of the post-recombination universe. We show that the dissipation effects of magnetic fields which redshifts to a present value B0 = 3 × 10−9 Gauss smoothed on the magnetic Jeans scale and below, can give rise to Thomson scattering optical depths $\tau \ga 0.1$, although not in the range of redshifts needed to explain the recent WMAP polarization observations. We also study the possibility that primordial fields could induce the formation of subgalactic structures for $z \ga 15$. We show that early structure formation induced by nano-Gauss magnetic fields is potentially capable of producing the early re-ionization implied by the WMAP data. Future CMB observations will be very useful to probe the modified ionization histories produced by primordial magnetic field evolution and constrain their strength.

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

abstract compiled · 2026-09-23

The authors' main claim, as the classifier picked it out 0.91

“We show that early structure formation induced by nano-Gauss magnetic fields is potentially capable of producing the early re-ionization implied by the WMAP data.”

How the main claim is stated: hedged possibility 0.86

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.93 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.29 · mentions code or data availability 0.02

The abstract, sentence by sentence

This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.

SentenceRoleThe authors' own workStates the main conclusionStrength
We explore the ways in which primordial magnetic fields influence the thermal and ionization history of the post-recombination universe. contribution 0.99 0.83 0.05 unclear 0.66
After recombination the universe becomes mostly neutral resulting also in a sharp drop in the radiative viscosity. background 1.00 0.07 0.02 asserted 1.00
Primordial magnetic fields can then dissipate their energy into the intergalactic medium (IGM) via ambipolar diffusion and, for small enough scales, by generating decaying MHD turbulence. background 0.90 0.09 0.06 hedged possibility 0.87
These processes can significantly modify the thermal and ionization history of the post-recombination universe. background 0.54 0.11 0.14 hedged possibility 0.83
We show that the dissipation effects of magnetic fields which redshifts to a present value $B_{0}=3\times 10^{-9}$ Gauss smoothed on the magnetic Jeans scale and below, can give rise to Thomson scattering optical depths $\tau \ga 0.1$, although not in the range of redshifts needed to explain the recent WMAP polarization observations. result 0.99 0.93 0.23 asserted 0.93
We also study the possibility that primordial fields could induce the formation of subgalactic structures for $z \ga 15$. contribution 1.00 0.77 0.05 hedged possibility 0.97
We show that early structure formation induced by nano-Gauss magnetic fields is potentially capable of producing the early re-ionization implied by the WMAP data. result 0.79 0.89 0.39 hedged possibility 0.86
Future CMB observations will be very useful to probe the modified ionization histories produced by primordial magnetic field evolution and constrain their strength. future work 0.99 0.08 0.16 hedged possibility 0.79

What kind of paper the classifier reports this is: theoretical result 0.77 · evidence from simulation or computation 0.78

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Figures (7)
Figure 1 of the paper
Figure 1. Evolution of the ionization state of the universe is shown for ambipolar dissipation. Different curves are: standard recombination (solid curve); the dotted and dashed curves correspond to nearly scale free magnetic field power spectra with n = −2.9 and n = −2.8 with B0 = 3 × 10−9 G; the dot-dashed curves correspond to the delta function magnetic field power spectrum with B0 = 3 × 10−9 G and k⋆ = kmax. c 0000 RAS, MNRAS 000, 000–000
Figure 2 of the paper
Figure 2. Evolution of the thermal state of the universe is shown for ambipolar dissipation. Curves are for the same parameters as in
Figure 3 of the paper
Figure 3. Visibility function, defined as dτ /dη exp(−τ)H −1 0 , is plotted for different models. The solid and the dotted curves are for the standard recombination and a model in which the universe reionizes at z = 17, respectively. Dashed curve corresponds to a decaying turbulence model with B0 = 3 × 10−9 G and m = 0.2 (Eq. (15)). Dot-dashed curve corresponds to the ambipolar diffusion case with B0 = 3 × 10−9 G and n = −2.8. c 0000 RAS, MNRAS 000, 000–000
Figure 4 of the paper
Figure 4. Evolution of the ionization state of the universe is shown for dissipation of magnetic field energy due to decaying turbulence. Different curves are: standard recombination (solid curve), the dot-dashed, and dashed curves correspond to B0 = 3 × 10−9 G, m = {0.2, 0.1}, respectively (Eq. (15)). c 0000 RAS, MNRAS 000, 000–000
Figure 5 of the paper
Figure 5. Evolution of the thermal state of the universe is shown for decaying turbulence. Curves are for the same parameters as in
Figure 6 of the paper
Figure 6. The mass dispersion σ(R, z) is shown for the delta function magnetic field power spectrum. Different curves, from top to bottom, correspond to redshifts z = {50, 60, 70, 80, 90}, respectively. The horizontal line corresponds to σ = 1.68. c 0000 RAS, MNRAS 000, 000–000
Figure 7 of the paper
Figure 7. The mass dispersion σ(R, z) is shown for two models with nearly scale free magnetic field power spectra. The solid and dashed curves correspond to n = −2.9 and n = −2.8, respectively. Different curves, from top to bottom, correspond to redshifts z = {10, 15, 20, 25, 30}, respectively. The horizontal line corresponds to σ = 1.68. c 0000 RAS, MNRAS 000, 000–000

Figures are the authors', reproduced from the paper.

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  12. Planck 2015 results. XIX. Constraints on primordial magnetic fields astro-ph.CO · Feb 2015
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  • In this work, we follow Sethi and Subramanian's calculation to account for ambipolar diffusion and turbulent decay [ref] .

    Primordial Magnetic Fields in Light of Dark Ages Global 21-cm Signal · Primordial magnetic fields · 1.00

  • This can be described by the energy injection rate [ref] [equation] where $< L^2>$, $ρ_b$ and $X_p$ are the Lorentz force, the baryon density and the coupling between the two components, neutral and ionized.[For the Lorentz force we use the same treatment as in [ref] , which is the one relative to the sharp cut off damping model for the fields.] In <ref> we show the effect of ambipolar diffusion on the CMB anisotropy angular power spectra in temperature and polarization.

    LiteBIRD Science Goals and Forecasts: Primordial Magnetic Fields · Ambipolar diffusion · 0.91

  • While computing the magnetic correction, we make use of the magnetic Jeans cut-off scale given by [ref] k_J=[14.8(Ω_m0.3)^0.5(h0.7)(B_01 nG)^-1]^2/n__B+5 Mpc^-1 , which appears as a hard cut-off to the magnetically induced matter power spectrum in our calculations.

    Revisiting primordial magnetic fields through 21-cm physics: Bounds and forecasts · Impact of PMF on star formation · 0.90

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