Constraints on a Primordial Magnetic Field

John D. Barrow; Joseph Silk; Pedro G. Ferreira

REVIEW

Constraints on a Primordial Magnetic Field

John D. Barrow, Pedro G. Ferreira, Joseph Silk

Astrophysics · Submitted 13 Jan 1997 · 23 references

Pith's verdict: A durable result — the CMB bound on a homogeneous primordial field beats nucleosynthesis by two orders of magnitude — with a headline number that quietly picks the favorable end of its own fit.

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CitationJohn D. Barrow, Joseph Silk, Pedro G. Ferreira. "Constraints on a Primordial Magnetic Field." arXiv:astro-ph/9701063 (1997). https://pith.science/paper/RY7VCSAW

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Editor's note

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The thing to take away: the qualitative result is right and has held up. Magnetic anisotropic stress keeps the shear from decaying the way it does in a plain Bianchi I radiation universe, so rho_B/rho_r falls only logarithmically through the radiation era. That is why the CMB bound lands two orders of magnitude below the Grasso-Rubinstein nucleosynthesis number, and it is also why Adams et al.'s claim about observable acoustic-peak distortions does not survive. The statistical machinery — a deterministic type VII template, marginalized over sky orientation, against the 4-year DMR maps — is the right way to handle a non-Gaussian anisotropy pattern, and extending it from axisymmetric type I to general type VII with curvature anisotropy is a real step beyond Zeldovich's treatment. The chain through Eqs. (3) and (4) is traceable to published work and used correctly. Credit where it is due: this is the paper that made the CMB the binding constraint on a homogeneous primordial field, and it has stayed that way. Where it is soft: Eq. (7). f = 2.1 Omega_0^0.33 x^(-0.01/Omega_0) is a hand-fit to simulated eta distributions, and there are no residuals, no chi-square, no plot of the fit against the simulations. Since B0 goes as f^(1/2), the bound moves with f. The paper says 0.6 < f < 2.2; over the stated box the formula actually gives about 0.87 to 2.2, so the swing is a factor of roughly 1.6 rather than the factor of 2 the stress-test claims. The abstract's 3.4e-9 corresponds to f around 0.94, near the low end; the conservative end gives about 5.2e-9. That is a factor of 1.5 on an order-of-magnitude bound, not a threat to the physics, but the abstract should have said which (x, Omega_0) it assumed. The 3.4 versus 3.5 in Eq. (8) is rounding; ignore it. Eq. (9)'s tighter 2.3e-9 leans on Kogut et al., listed as in press, so treat that one as provisional until you have read the source. Who it is for: anyone working on primordial magnetism or on global anisotropy templates. The number is the standard citation. Recommendation: send it out. The physics is sound, and the soft spot is a calibration detail the referees can ask them to document.

Referee report

Significance

If the bound holds, it is a genuinely useful result: it closes off the window in which a homogeneous cosmological field could leave an observable imprint on microwave background structure, and it converts a detection of large-scale homogeneous anisotropy into a falsification test for standard inflation, since N e-folds suppress σ/H by exp(-3N) and ρB/ρ by exp(-4N). The analysis is built on published exact solutions (Thorne; Collins & Hawking; Lukash) rather than on new ansätze, and the statistical treatment correctly recognizes that a fixed global pattern is not a Gaussian random field, so the usual power-spectrum likelihood does not apply. The use of real 4-year DMR data with a properly defined frequentist statistic, and the explicit statement of the falsifiable prediction, are strengths. The qualitative conclusion that the microwave bound beats nucleosynthesis is robust to the details of the fit; the precise numerical coefficient is not, and that is where the report concentrates.

Major objections (2)

[Abstract vs. Eq. (8)] The abstract's headline number, B0 < 3.4e-9 (Ω0 h50²)^{1/2} G, is not the conservative bound that Eq. (8) actually delivers. Eq. (8) reads B0 < 3.5e-9 f^{1/2} (Ω0 h50²)^{1/2} G with 0.6 < f < 2.2, so the bound ranges from about 2.7e-9 to 5.2e-9 G across the stated (x, Ω0) box; the abstract's 3.4e-9 corresponds to f ≈ 0.94, i.e. near the low end of the allowed range. The paper is careful in the body to say that it has 'considered the largest possible contribution from the magnetic component', but that conservatism is applied to ρga and then undone by quoting a small f in the abstract. Either the abstract should quote the conservative value (f = 2.2, giving 5.2e-9) or it should state the fiducial (x, Ω0) at which 3.4e-9 applies. Relatedly, the abstract's phrase 'any primordial homogeneous magnetic field' is stronger than what is derived: the bound is for a homogeneous field whose stress produces the specific type VII pattern with a given curvature-anisotropy parameter x, and the x-dependence, though weak, is not absent.
[Eq. (7) and the statistical calibration] Eq. (7), f = 2.1 Ω0^{0.33} x^{-0.01/Ω0}, is the sole bridge from the simulated η distribution to the field bound, and it is presented without residuals, without a χ², and without a plot of the simulated quantiles against the fitted form. The authors describe it as 'a reasonable fit' and 'an approximate fit', which acknowledges the limitation, but the reader still cannot judge whether a power law in Ω0 and x is adequate over the full box x ∈ [0.01, 3], Ω0 ∈ [0.1, 1]. This matters quantitatively because B0 ∝ f^{1/2}: the factor 3.7 spread in f moves the bound by a factor of about 1.9. A second, independent source of uncertainty is not discussed at all: with 'approximately 200 to 500 random DMR sets' per parameter choice, the 95% quantile of η is estimated from the upper ~10-25 realizations, so the quantile itself carries a sampling error of order 20%, which propagates directly into f and into the quoted bound. Please supply a figure or table comparing the simulated quantiles with Eq. (7), state the number of realizations per (Ω0, x) point, and quote the sampling uncertainty on f.

Minor objections (8)

[Eqs. (7)-(8)] The numerical conversion from (ρB/ρ)0 in Eq. (7) to B0 in Eq. (8) is not shown, and it is not immediately reproducible. Taking ρ = ρcrit, γ = 4/3 so that (2-γ)^4 = 0.198, and ρcrit c² = 4.2e-9 h50² Ω0 erg/cm³, Eq. (7) at f = 1 implies B0 ≈ 4.6e-9 G rather than the 3.5e-9 G of Eq. (8). Please display the intermediate steps, including which density ρ refers to in Eq. (7) and the origin of the fourth power of (2-γ).
[Text following Eq. (9)] The text states that the bound 'can be improved by a factor of √3' using ref. [18], but Eq. (9) gives 2.3e-9 against Eq. (8)'s 3.5e-9, a factor of 1.52, not 1.73. Please reconcile the stated factor with the two equations.
[Abstract and Eq. (6)] The abstract says the anisotropy patterns are 'averaged over all possible sky orientations with respect to the COBE receiver', but Eq. (6) defines η as the minimum of η1 over σ, θ, φ, i.e. the statistic searches for the orientation that best fits the data rather than averaging over it. The distinction matters for the look-elsewhere interpretation of the bound, and the wording should match the method.
[Eq. (6)] The typeset definition 'η1 = Δ0² − Δ1²Δ0²' is ambiguous; presumably the intended expression is (Δ0² − Δ1²)/Δ0², consistent with the following sentence about dividing by Δ0². Please correct the typesetting.
[Ref. [18] and Eq. (9)] Eq. (9) rests on ref. [18], listed as 'Phys. Rev. D (in press)'. Since this is the improved bound and the only place where the covariance-weighted statistic is used, please confirm the publication status or supply the preprint number so the result can be checked.
[Reionization discussion, text after Eq. (5)] The bound's dependence on the last-scattering redshift is stated but not quantified. Since (ρB/ρ)0 scales roughly as 1/(1+zls), the bound on B0 scales as (1+zls)^{-1/2}; please state this scaling explicitly, and state the range of Ωb h50 for which the quoted formula 1+zls = 78(Ωb h50)^{-1} actually gives zls below 1100.
[Discussion of ref. [16]] The claim that the limit 'rules out any observable effect on the acoustic peaks' is argued qualitatively, via the (ln t)^{-1} decay making even the nucleosynthesis bound sufficient. A one-line numerical estimate of the fractional acoustic-peak distortion at the bound of Eq. (8) would make this conclusion checkable rather than asserted.
[Ref. [6]] The 4-year COBE DMR data are cited as 'K.M. Gorski et al., Report astro-ph/9601063'. Please give the published journal reference, since the entire numerical result depends on this data set.

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The paper

The paper claims

A uniform primordial magnetic field cannot exceed about $3.4$ nanogauss today, because a stronger one would have imprinted a large-scale pattern on the microwave sky that the four-year COBE data do not show.

The reading

The paper asks how strong a perfectly uniform magnetic field left over from the early universe could be without leaving a visible mark on the cosmic microwave background. The authors argue that such a field does not simply fade away: because it exerts a pressure that differs along different directions, it holds open a matching distortion in the expansion rate, and the two decay together only logarithmically during the radiation era rather than dying off quickly. That surviving distortion would tilt the microwave sky with a large-scale, non-Gaussian pattern whose orientation is arbitrary, so the authors build a statistical test that marginalises over all possible sky orientations and apply it to the four-year COBE maps. The result is an upper bound of roughly $3.4$ nanogauss, about two orders of magnitude tighter than what primordial nucleosynthesis allows, and tight enough that other magnetic effects on microwave background structure become unobservable.

What carries the argument

The load-bearing mechanism is the logarithmic, not power-law, decay of the ratio of magnetic energy density to blackbody radiation density during the radiation era, coupled to a shear distortion that tracks it. In an ordinary anisotropic universe with isotropic pressure the shear term dies away and any early anisotropy is erased; here the trace-free magnetic stress keeps $sigma/H$ pinned near $4(ho_B/ho)/(2-gamma)$, so an anisotropy present at nucleosynthesis is still present, diluted only by the slow logarithm, at last scattering. The second piece of machinery is the statistical treatment: the magnetic pattern is a fixed, non-Gaussian template on the sky up to an unknown rotation, so the authors define a goodness-of-fit statistic, take its minimum over orientation angles, and calibrate the resulting probability distribution with several hundred simulated COBE data sets per model.

Extended reading notes

Core claim

The central claim is an upper limit on the present strength of any homogeneous cosmological magnetic field, $B_0 < 3.5f^{1/2}(10^{-9})(10^{-9})^{1/2}$ — stated in the abstract as $B_0 < 3.4 imes 10^{-9}(10^{-9})^{1/2}$ — more precisely $B_0 < 3.5 imes 10^{-9} f^{1/2}(10^{-9})^{1/2}$ Gauss with $f$ a shape factor bounded roughly between $0.6$ and $2.2$ across the allowed range of curvature-anisotropy parameter $x$ and density parameter $Omega_0$. The bound comes from the joint evolution of the magnetic field density and the shear of the expansion in the most general flat and open anisotropic cosmologies of Bianchi type VII, which the authors argue can be represented by the simpler type I and type V models plus trace-free stresses. Because the magnetic pressure is anisotropic, the shear does not decay as it would in a purely isotropic universe; instead $ho_B/ho_r ightarrow Q/[1+4Qln(t/t_0)]$ during the radiation era, so the distortion persists at a level the microwave background can still see. Matching that predicted angular pattern against the COBE data, after allowing any sky orientation, gives the quoted limit; an alternative weighting scheme tightens it further to $2.3 imes 10^{-9}$ Gauss.

Load-bearing premise

The step from a 95 percent confidence bound on the goodness-of-fit statistic to a numerical field strength goes through an empirical power-law fit, $f = 2.1Omega_0^{0.33}x^{-0.01/Omega_0}$, whose exponents are chosen to match simulations rather than derived, and the final bound scales as the square root of that factor.

Editorial extensions

If this is right

Any homogeneous primordial magnetic field above a few nanogauss is excluded, so scenarios that generate large-scale uniform fields at or above $10^{-8}$ Gauss cannot be the origin of observed intergalactic fields.
The microwave background bound supersedes the nucleosynthesis bound by roughly two orders of magnitude, because the logarithmic decay keeps the anisotropy alive instead of diluting it away.
Proposed distortions of the acoustic peaks in the microwave background by cosmological magnetic fields are pushed below observability at the allowed field strengths.
A field near $10^{-9}$ Gauss, which the bound still permits, is large enough to produce measurable Faraday rotation in the polarisation of the microwave background.
Detecting a large-scale homogeneous anisotropy pattern in future microwave background data would rule out the standard inflationary picture, since inflation suppresses both the shear and the field by many e-folds.

Reading between the lines

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

The bound depends on the field being homogeneous and coherent on horizon scales; a tangled field with comparable total energy but no large-scale coherence would evade this constraint entirely, so the result is best read as a limit on the uniform component only.
Because the limit scales as $(Omega_0 h_{50}^2)^{1/2}$, independent measurements of the density parameter and Hubble constant from other probes directly move the numerical bound, which makes it a joint constraint rather than a standalone one.
The same shear-tracking argument applies to any trace-free stress that survives recombination, so the technique transfers to limits on long-wavelength gravitational waves and on anisotropic dark energy at last scattering.
The authors' own observation that the anisotropy decays only logarithmically cuts both ways: a future detection of a Bianchi-like pattern would not date the field, since the signal retains almost no memory of when the field was generated.

Original abstract

We derive an upper limit of $B_0<3.4\times 10^{-9}(\Omega_0h_{50}^2)^{1/2}$ Gauss on the present strength of any primordial homogeneous magnetic field. The microwave background anisotropy created by cosmological magnetic fields is calculated in the most general flat and open anisotropic cosmologies containing expansion-rate and 3-curvature anisotropies. Our limit is derived from a statistical analysis of the 4-year Cosmic Background Explorer data for anisotropy patterns characteristic of homogeneous anisotropy averaged over all possible sky orientations with respect to the COBE receiver. The limits we obtain are considerably stronger than those imposed by primordial nucleosynthesis and ensure that other magnetic field effects on the microwave background structure are unobservably small.

The compiled record

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. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,743 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.33 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We derive an upper limit of $B_0<3.4\times 10^{-9}(\Omega_0h_{50}^2)^{1/2}$ Gauss on the present strength of any primordial homogeneous magnetic field. The microwave background anisotropy created by cosmological magnetic fields is calculated in the most general flat and open anisotropic cosmologies containing expansion-rate and 3-curvature anisotropies. Our limit is derived from a statistical analysis of the 4-year Cosmic Background Explorer data for anisotropy patterns characteristic of homogeneous anisotropy averaged over all possible sky orientations with respect to the COBE receiver. The limits we obtain are considerably stronger than those imposed by primordial nucleosynthesis and ensure that other magnetic field effects on the microwave background structure are unobservably small.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We derive an upper limit of $B_0<3.4\times 10^{-9}(\Omega_0h_{50}^2)^{1/2}$ Gauss on the present strength of any primordial homogeneous magnetic field.	result 1.00	0.96	0.94	asserted 1.00
s1	The microwave background anisotropy created by cosmological magnetic fields is calculated in the most general flat and open anisotropic cosmologies containing expansion-rate and 3-curvature anisotropies.	method 0.71	0.89	0.03	asserted 0.99
s2	Our limit is derived from a statistical analysis of the 4-year Cosmic Background Explorer data for anisotropy patterns characteristic of homogeneous anisotropy averaged over all possible sky orientations with respect to the COBE receiver.	method 1.00	0.94	0.05	asserted 1.00
s3	The limits we obtain are considerably stronger than those imposed by primordial nucleosynthesis and ensure that other magnetic field effects on the microwave background structure are unobservably small.	interpretation 0.93	0.88	0.18	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.90 · evidence from analysis of existing data 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
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relations to other papers

levels run

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S sections
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (23)

[1]

R. Pudritz and J. Silk, Ap.J. 342, 650 (1989); R. Kul- srud, R. Cen, J. P. Ostriker, and D. Ryu, 1996, astro- ph/960714

View on Pith 1989
[2]

E. R. Harrison, Mon. Not. R. astron. Soc. 147, 279 (1970); ibid Mon. Not. R. astron. Soc. 165, 185 (1973); A. D. Dolgov, Phys. Rev. D 48, 2499 (1993); M. S. Turner and L. M. Widrow, Phys. Rev. D 30, 2743 (1988); K. Enqvist and P. Olensen, Phys. Lett. B329, 195 (1994); T. Vachaspati, Phys. Lett. B265, 258 (1991); A. D. Dol- gov and J. Silk, Phys. Rev. D 47...

View on Pith 1970
[3]

K. T. Kim, P. C. Tribble and P. P. Kronberg, Ap. J. 379, 80 (1991); R. Perley and G. Taylor, A. J. 101, 1623 (1991); P. P. Kronberg, Rep. Prog. Phys., 57, 325 (1994)

View on Pith 1991
[4]

P. P. Kronberg, J. J. Perry and E. L. Zukowski, Ap. J. 387, 528 (1992)

View on Pith 1992
[5]

A. M. Wolfe, K. Lanzetta and A. L. Oren, Ap. J. 388, 17 (1992)

View on Pith 1992
[6]

K.M. Gorski et al ., Report astro-ph/9601063

View on Pith Pith review arXiv
[7]

E. F. Bunn, P. G. Ferreira, and J. Silk, Phys. Rev. Lett. 77, 2883 (1996)

View on Pith 1996
[8]

K. S . Thorne, Ap. J. 148, 51 (1967); A. G. Doroshkevich, Astrophysics 1, 138 (1967); K. Jacobs, Ap. J. 155, 379 (1969)

View on Pith 1967
[9]

D. Grasso and H. R. Rubinstein, Astroparticle Phys . 3, 95 (1995), who disagree with the conclusions of B. Cheng, D.N. Schramm and J.W. Truran, Phys. Rev. D 49, 5006 (1994) and conﬁrm those of J. J. Matese and R. F. O’Connell, Ap. J. 160, 451 (1970) regarding the eﬀects of strong magnetic ﬁelds on the weak interaction and the electron density

View on Pith 1995
[10]

Y. B. Zeldovich, Sov. Astron . 13, 608 (1970); C. B. Collins, Comm. Math. Phys . 27, 37 (1972); I. S. Shikin, Sov. Phys. JETP 36, 811 (1972). If one linearizes the magnetic radiation universe Einstein equations about the isotropic Friedmann universe (magnetic ﬁeld = shear anisotropy = 0) then there is a zero eigenvalue associated with the evolution of the...

View on Pith 1970
[11]

V. N. Lukash, Nuovo Cimento B 35 , 269 (1976); A. G. Doroshkevich, V. N. Lukash, and I. D. Novikov, Sov. Phys. JETP 37, 739 (1973); C. B. Collins and S. W. Hawking, Ap. J .181, 317 (1972)

View on Pith 1976
[12]

J. D. Barrow, Phys. Rev. D 51, 3113 (1995)

View on Pith 1995
[13]

V. N. Lukash and A. A. Starobinskii, Sov. Phys. JETP 39, 742 (1974)

View on Pith 1974
[14]

E. Mart ´inez-Gonzalez and J.L. Sanz, Astron. Astrophys. 300, 346 (1995)

View on Pith 1995
[15]

R. Maartens, G.F.R. Ellis and W. R. Stoeger, Phys. Rev. D 51, 1525 (1995)

View on Pith 1995
[16]

J. Adams, U.H. Danielsson, D. Grasso and H. Rubinstein, Phys. Lett. B 388, 253 (1996)

View on Pith 1996
[17]

J. D. Barrow, R. Juszkiewicz, and D. H. Sonoda, Mon. Not. R. Astron. Soc . 213, 917 (1985). J.D. Barrow, Can. J. Phys. 164, 152 (1986); I. D. Novikov, Sov. Astron. 12, 427 (1968)

View on Pith 1985
[18]

A. Kogut, G. Hinshaw and A. Banday, Phys. Rev. D (in press)

View on Pith
[19]

J. D. Barrow, Mon. Not. R. astron. Soc . 175, 359 (1976)

View on Pith 1976
[20]

M. White, D. Scott, and J. Silk, Annu. Rev. Astron. Astrophys. 32, 319 (1994)

View on Pith 1994
[21]

A. Kosowsky and A. Loeb, astro-ph/9601055, Ap. J

View on Pith Pith review arXiv
[22]

A. Guth, Phys. Rev. D 23, 347 (1981)

View on Pith 1981
[23]

R. Wald, Phys. Rev. D 28, 2118 (1983), J.D. Barrow, Phys. Lett. B 180, 335 (1987). 4

View on Pith 1983

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How later papers used it

50 later papers cite it

Evidence: substantial. 49 of the citing papers share no author with it, and 8 of those carry a confident label from Pith's citation classifier.

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1 later paper by other authors is listed below: 1 used its data or values.

Uses its data or values 1 of 8 papers with this label

Took its upper bounds from this paper's limits on CMB anisotropies, scaled up to today.

TDiff-fuelled cosmic magnetic fields (2024) · 0.86 · paraphrased: the licence does not allow quoting

How the literature uses it

40 arXiv papers cite this in 48 sentences

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Papers citing it · 29 sentences without a confident label

Contests it 1 paper

The results for a constant magnetic field derived in the pioneering paper by [ref] are actually invalid, since there the compensation by neutrino anisotropic stresses (see [ref] ) which isotropize the Universe are not taken into account. * The energy momentum tensor of the magnetic field perturbs the geometry of the Universe which governs the geodesic motion of CMB photons.

Cosmological Magnetic Fields: Their Generation, Evolution and Observation · Limits from CMB observations · contest 0.92

Uses its data or values 8 papers

Then, we express the coupling term as in reference [ref] [equation] In reference [ref] , with measurements from the COBE experiment, a bound on the present value of the large-scale magnetic fields is found to be $B_T < 5·10^-9$ G.

Graviton-photon oscillation in a cosmic background for a general theory of gravity · Conversion probability in GR and beyond · 0.91
Early studies using CMB data set an upper limit $B ≲4 nG$ [ref] for intergalactic magnetic fields.

Implications of Strong Intergalactic Magnetic Fields for Ultra-High-Energy Cosmic-Ray Astronomy · The simulated cosmic web · 0.92
The observations of the CMB radiation imply that the upper limit on the magnetic field strength on $1$Mpc scale is $∼10^-9$G [ref] and that on the magnetic field strength on the scale larger than the present Hubble horizon is $4.8 ×10^-9 G$ [ref] .

Generation of large-scale magnetic fields, non-Gaussianity, and primordial gravitational waves in inflationary cosmology · Constraints on the strength of cosmic magnetic fields · 0.97

Cites it as background 10 papers

PMF are known to leave different imprints in the CMB inducing spectral distortions [ref] , anisotropic expansion [ref] , CMB polarization, non-gaussianities, inhomogeneous recombination [ref] and affecting CMB anisotropies [ref] and reionization [ref] .

Reionization, UV Luminosity and 21$\,$cm Sensitivity to Primordial Magnetic Fields: Impact of Energy Losses · Reionization observational constraints · 0.99
They considered anisotropic expansion [ref] , spectral $y$ and $μ$ distortions [ref] , anisotropies due to Alfven and slow magnetic waves [ref] , a changing ionization history due to plasma heating [ref] , extra polarization due to PMFs [ref] , as well as non-Gaussianity in bi- and tri-spectrum [ref] .

Cosmic Recombination in the Presence of Primordial Magnetic Fields · Introduction · 0.99
A magnetic field affects the CMB anisotropies and polarization in many ways, see [ref] .

Cosmological Magnetic Fields: Their Generation, Evolution and Observation · Limits from CMB observations · 0.93

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

R. Pudritz and J. Silk, Ap.J. 342, 650 (1989); R. Kul- srud, R. Cen, J. P. Ostriker, and D. Ryu, 1996, astro- ph/960714

View on Pith 1989

[2] [2]

E. R. Harrison, Mon. Not. R. astron. Soc. 147, 279 (1970); ibid Mon. Not. R. astron. Soc. 165, 185 (1973); A. D. Dolgov, Phys. Rev. D 48, 2499 (1993); M. S. Turner and L. M. Widrow, Phys. Rev. D 30, 2743 (1988); K. Enqvist and P. Olensen, Phys. Lett. B329, 195 (1994); T. Vachaspati, Phys. Lett. B265, 258 (1991); A. D. Dol- gov and J. Silk, Phys. Rev. D 47...

View on Pith 1970

[3] [3]

K. T. Kim, P. C. Tribble and P. P. Kronberg, Ap. J. 379, 80 (1991); R. Perley and G. Taylor, A. J. 101, 1623 (1991); P. P. Kronberg, Rep. Prog. Phys., 57, 325 (1994)

View on Pith 1991

[4] [4]

P. P. Kronberg, J. J. Perry and E. L. Zukowski, Ap. J. 387, 528 (1992)

View on Pith 1992

[5] [5]

A. M. Wolfe, K. Lanzetta and A. L. Oren, Ap. J. 388, 17 (1992)

View on Pith 1992

[6] [6]

K.M. Gorski et al ., Report astro-ph/9601063

View on Pith Pith review arXiv

[7] [7]

E. F. Bunn, P. G. Ferreira, and J. Silk, Phys. Rev. Lett. 77, 2883 (1996)

View on Pith 1996

[8] [8]

K. S . Thorne, Ap. J. 148, 51 (1967); A. G. Doroshkevich, Astrophysics 1, 138 (1967); K. Jacobs, Ap. J. 155, 379 (1969)

View on Pith 1967

[9] [9]

D. Grasso and H. R. Rubinstein, Astroparticle Phys . 3, 95 (1995), who disagree with the conclusions of B. Cheng, D.N. Schramm and J.W. Truran, Phys. Rev. D 49, 5006 (1994) and conﬁrm those of J. J. Matese and R. F. O’Connell, Ap. J. 160, 451 (1970) regarding the eﬀects of strong magnetic ﬁelds on the weak interaction and the electron density

View on Pith 1995

[10] [10]

Y. B. Zeldovich, Sov. Astron . 13, 608 (1970); C. B. Collins, Comm. Math. Phys . 27, 37 (1972); I. S. Shikin, Sov. Phys. JETP 36, 811 (1972). If one linearizes the magnetic radiation universe Einstein equations about the isotropic Friedmann universe (magnetic ﬁeld = shear anisotropy = 0) then there is a zero eigenvalue associated with the evolution of the...

View on Pith 1970

[11] [11]

V. N. Lukash, Nuovo Cimento B 35 , 269 (1976); A. G. Doroshkevich, V. N. Lukash, and I. D. Novikov, Sov. Phys. JETP 37, 739 (1973); C. B. Collins and S. W. Hawking, Ap. J .181, 317 (1972)

View on Pith 1976

[12] [12]

J. D. Barrow, Phys. Rev. D 51, 3113 (1995)

View on Pith 1995

[13] [13]

V. N. Lukash and A. A. Starobinskii, Sov. Phys. JETP 39, 742 (1974)

View on Pith 1974

[14] [14]

E. Mart ´inez-Gonzalez and J.L. Sanz, Astron. Astrophys. 300, 346 (1995)

View on Pith 1995

[15] [15]

R. Maartens, G.F.R. Ellis and W. R. Stoeger, Phys. Rev. D 51, 1525 (1995)

View on Pith 1995

[16] [16]

J. Adams, U.H. Danielsson, D. Grasso and H. Rubinstein, Phys. Lett. B 388, 253 (1996)

View on Pith 1996

[17] [17]

J. D. Barrow, R. Juszkiewicz, and D. H. Sonoda, Mon. Not. R. Astron. Soc . 213, 917 (1985). J.D. Barrow, Can. J. Phys. 164, 152 (1986); I. D. Novikov, Sov. Astron. 12, 427 (1968)

View on Pith 1985

[18] [18]

A. Kogut, G. Hinshaw and A. Banday, Phys. Rev. D (in press)

View on Pith

[19] [19]

J. D. Barrow, Mon. Not. R. astron. Soc . 175, 359 (1976)

View on Pith 1976

[20] [20]

M. White, D. Scott, and J. Silk, Annu. Rev. Astron. Astrophys. 32, 319 (1994)

View on Pith 1994

[21] [21]

A. Kosowsky and A. Loeb, astro-ph/9601055, Ap. J

View on Pith Pith review arXiv

[22] [22]

A. Guth, Phys. Rev. D 23, 347 (1981)

View on Pith 1981

[23] [23]

R. Wald, Phys. Rev. D 28, 2118 (1983), J.D. Barrow, Phys. Lett. B 180, 335 (1987). 4

View on Pith 1983