Faraday Rotation of Microwave Background Polarization by a Primordial Magnetic Field

Abraham Loeb; Arthur Kosowsky (Harvard University)

REVIEW

Faraday Rotation of Microwave Background Polarization by a Primordial Magnetic Field

Abraham Loeb, Arthur Kosowsky (Harvard University)

Astrophysics · Submitted 11 Jan 1996 · 2 references

Pith's verdict: A clean, correctly conditional calculation that gives the field its standard reference number; the real gap is that nobody quantifies what happens when the field is tangled.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 13, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 2 major objections · 7 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDastro-ph/9601055 (version 1)

Pith IDDWBWW5MG, Pith's permanent record of this paper and its review

CitationAbraham Loeb, Arthur Kosowsky (Harvard University). "Faraday Rotation of Microwave Background Polarization by a Primordial Magnetic Field." arXiv:astro-ph/9601055 (1996). https://pith.science/paper/DWBWW5MG

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Short version: this is the paper that put a number on Faraday rotation of CMB polarization, and the number has held up. Eq. (19) — about 1.1° rms for B0 = 10^-9 G at 30 GHz, scaling as B0/ν² — is the thing to take away, and it is worth citing in anything on CMB polarization or primordial fields. What is new is not the idea (they cite Milaneschi & Fabbri 1985 for rotation in anisotropic models) but the calculation: Q–U mixing added to the standard transport equations, solved perturbatively in the tight-coupling expansion, with the polarization source term taken from Hu & Sugiyama. The internal check is real. The order-of-magnitude estimate in Eq. (2) gives 1.6°, and the full calculation gives 1.1° after the 1/√2 orientation average. That is a genuine consistency check, not a restatement. Fig. 2 backs the claim that the answer barely moves with Ω0h² and Ωbh², which is the useful part: the signal is set by recombination physics, not cosmology. Soft spots, in order of size. The coherence-length assumption is the real one, and the stress-test note is right that it goes unquantified: §2 assumes B uniform across the last-scattering shell and offers only a plausibility argument about galaxies assembling from a few Mpc. I would push back a little on how bad that is. The Faraday weight is x_e n_e, confined to a narrow shell, so the coherence requirement is milder than “5 Mpc comoving” makes it sound. The paper does not make that argument, and it should have. What is missing is a curve of signal versus coherence length. Second, the abstract's “statistical detection is feasible” is an instrument projection (10^6 pixels, 10' beam), not a derived result, and it reads stronger than §4, which is appropriately hedged and even notes that foregrounds permit 10^-10 G. Third, minor: the Fig. 2 axis label and caption disagree on whether the plotted ratio is IU/IQ or IQ/IU. Who should read it: anyone working on CMB polarization or primordial magnetism; it is the reference number. It deserves referees — the derivation is complete enough to reimplement, and the coherence question is exactly what a referee should press on.

Referee report

Significance

If correct, this is a genuinely useful result: it converts a primordial field amplitude into a specific, frequency-dependent, falsifiable observable in CMB polarization, and it does so with a calculation whose answer is fixed by recombination physics rather than by cosmological parameters. The paper's strongest methodological feature is the internal cross-check between the analytic order-of-magnitude estimate of Eq. (2) (1.6°) and the full numerical radiative transfer result of Eq. (19) (1.1°), which agree to the accuracy expected of the estimate; this is a real consistency test, not a restatement. The demonstration in Fig. 2 that the rotation angle is nearly independent of Ω₀h² and Ω_bh² over a factor-of-several range is a nontrivial and valuable robustness statement. The prediction is falsifiable in a well-defined way: the ν⁻² scaling and the (1 − ν₁²/ν₂²) frequency-difference signature are distinctive. The paper is also appropriately explicit in §2 that the field is assumed coherent across the comoving width of the last-scattering surface, which is the condition under which the quoted number applies.

Major objections (2)

[§2, paragraph 2; §4; abstract] The central result is conditional on the field being coherent across the comoving thickness of the last-scattering surface (~5 Mpc), and the manuscript states this assumption clearly in §2. What it does not do is quantify the dependence. The rotation is a line-of-sight integral of x_e n_e (B·q̂), so a field that reverses on scales below the shell thickness partially cancels, and the signal in Eq. (19) degrades accordingly. The plausibility argument offered (galaxies assembled from a few Mpc comoving) is reasonable but is not a calculation. Please add an explicit estimate of the suppression factor as a function of coherence length l_c, even a simple analytic one such as the fractional variance of the line-of-sight integral for a tangled field with power on scales below the shell width, and state the resulting scaling in §4. Relatedly, the abstract's 'around 1°' and the detectability sentence (abstract:s3) are stated without the coherence caveat that §2 supplies; a clause in the abstract noting that the number assumes a field coherent on ~Mpc scales would prevent over-generalization to arbitrary primordial field configurations.
[§4, paragraph 3] The claim that foregrounds 'should allow the detection of a cosmological field as small as 10⁻¹⁰ G' needs an explicit arithmetic check against the foreground numbers the paper itself quotes. A Galactic rotation measure of 20 rad m⁻² at 30 GHz corresponds to a rotation of 20 × (0.01 m)² = 2 × 10⁻³ rad ≈ 0.1°, which is essentially the same angle as the cosmological signal from B₀ = 10⁻¹⁰ G (1.1° × 0.1 = 0.11°). The same coincidence applies to the cumulative intergalactic rotation measure of 'a few rad m⁻²' quoted from Vallee (1990) and Kronberg (1994). The statement may still be defensible, since the Galactic and intergalactic contributions are smooth, large-angle foregrounds distinguishable in character from the stochastic recombination signal, but the manuscript should say so and should show the comparison explicitly rather than asserting that the foregrounds are small enough. As written, a reader could conclude that the 10⁻¹⁰ G sensitivity follows from the foregrounds being negligible, which the quoted numbers do not support.

Minor objections (7)

[Eqs. (15), (18), (19)] The bookkeeping of the factor of √2 deserves one clarifying sentence. A direct small-angle expansion of Eq. (15) using Eq. (17) gives ⟨φ₁₂²⟩^{1/2} ≈ (1 − f)√(I_U/I_Q)/(2√2), whereas Eq. (18) as written carries a prefactor of 1/2, i.e., it is larger by √2. The text then applies a further factor 1/√2 in passing to Eq. (19), attributed to 'an average over all orientations of the magnetic field.' The net coefficient in Eq. (19) is consistent with the expansion of Eq. (15), so this appears to be a labeling issue rather than an error, but the stated origin of the 1/√2 should be corrected or explained, since the sky average in Eq. (15) already includes the orientation average for a uniform field.
[Fig. 2 caption] The caption reads 'The ratio I_Q/I_U' while the vertical axis is labeled 'I_U/I_Q' and the text of §3 says 'Figure 2 displays I_U/I_Q.' The caption should be corrected to match.
[§3, paragraph 2] The statement that the beam width 'only affects the signal-to-noise ratio of the polarization signal and has virtually no effect on the size of the rotation angle' is asserted rather than shown. Since the beam factor in Eq. (16) weights the (k, µ) integrand, a brief numerical demonstration (e.g., the value of I_U/I_Q for two beam widths) would substantiate the claim.
[Eq. (11)] Equation (11) writes the Faraday coefficient with an explicit factor of c in the denominator, while the rest of the paper uses natural units with c = 1 as stated in §1. Please make the unit convention uniform, or note explicitly why c is retained here.
[Fig. 1] Figure 1 plots only the real parts of Δ_Q and Δ_U. Since the integrals in Eq. (11) involve the full complex quantities, a sentence in the caption or text confirming that the imaginary parts are retained in the numerical evaluation would remove the ambiguity.
[References and citations] Kronberg (1994) appears twice in the reference list, and Mather et al. is cited as 1993 in §2 but listed as 1994. The ionization history used in §3 is taken from Hu et al. (1995), listed as 'Phys. Rev. D, submitted'; since the numerical results depend on that input, please note its status or cite the published version if available.
[§2, paragraph 2] The statement that a uniform field lets one 'extract mean results by averaging over the entire sky' could be sharpened: for a uniform field the rotation angle varies systematically as B·q̂ across the sky, so the signal is anisotropic rather than statistically isotropic, and the sky average is really an average over the angle between the field and the line of sight. One sentence making this explicit would help the reader interpret Eq. (15) and the 1/√2.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

A primordial magnetic field at the last scattering surface would twist the polarization of the microwave background by about one degree at 30 GHz, an effect the authors argue is large enough to detect statistically with future polarization-

The reading

The paper asks whether the magnetic field that may have seeded galactic magnetism can be seen directly, rather than inferred. Its answer is that a field present at the epoch when the microwave background was released would rotate the plane of polarization of that light by an amount that depends on frequency, and that this rotation is calculable from recombination physics alone. For a present-day field of $10^{-9}$ gauss — the amplitude that would explain observed galactic fields if the primordial flux were simply compressed as galaxies formed — the authors find a root-mean-square rotation near $1^circ$ at 30 GHz, falling as the inverse square of observing frequency. The practical interest is that the predicted angle barely depends on the matter or baryon density, so a measurement would convert almost directly into a field strength. The authors conclude that a statistical detection, averaged over many sky directions rather than in any single pixel, is within reach of future multi-frequency polarization maps.

What carries the argument

The load-bearing device is the Faraday mixing term in the radiative transfer equations for the Stokes parameters, $2 omega_B Delta U$ and $-2 omega_B Delta Q$, where $omega_B$ is the conformal rotation rate proportional to the electron density times the line-of-sight field component divided by frequency squared. This term couples the two linear-polarization states and converts an initially vanishing $U$ into a nonzero one proportional to the accumulated rotation. The authors solve the coupled system perturbatively to first order in small rotation, using the tight-coupling expansion for the polarization source $S_p = Delta I_2 + Delta Q_2 - Delta Q_0$ and analytic fits to the radiation dipole and the ionization history, then average $Q_1 Q_2 + U_1 U_2$ over directions and Fourier modes to get an observable rms angle.

Extended reading notes

Core claim

The central claim is quantitative: a cosmological magnetic field with present amplitude $B_0 = 10^{-9}$ gauss, coherent across the last-scattering surface, imprints an rms Faraday rotation on the microwave background polarization of $1.1^circ (1 - nu_1^2/nu_2^2)(B_0/10^{-9} {G})(30 {GHz}/nu_1)^2$ when the polarization is compared at two frequencies. The authors obtain this by adding the Faraday mixing terms between the Stokes parameters $Q$ and $U$ to the radiative transfer equations for the microwave background, then solving the polarization source through recombination semi-analytically. They show the rotation is generated in a narrow interval: polarization only appears once tight coupling begins to break, and the free-electron density that drives the rotation collapses shortly afterwards, so the rotation is essentially finished by redshift 1100 while polarization itself keeps growing to about 900. Scanning mass density and baryon density over plausible ranges changes the answer by only about ten percent, which is what makes the signal a clean measure of the field rather than of the cosmology.

Load-bearing premise

The calculation assumes the magnetic field is uniform and points the same way across the whole comoving thickness of the last-scattering surface, about 5 Mpc; if the field reverses on scales much smaller than that shell, the line-of-sight rotation cancels and the predicted angle shrinks accordingly.

Editorial extensions

If this is right

If the paper is right, the hypothesis that galactic magnetic fields are primordial rather than dynamo-amplified becomes directly testable: a $10^{-9}$ gauss seed leaves a rotation of about a degree on the microwave sky.
Because the rotation scales as $nu^{-2}$ while the polarization amplitude does not, comparing the polarization angle at two frequencies in the same direction separates the rotation from the polarization signal itself.
The predicted angle varies by only about ten percent across $Omega_b h^2 > 0.007$ and $Omega_0 h^2 < 0.3$, so a detection yields a field amplitude without strong priors on the cosmological densities.
Known foregrounds are small on this scale — the Milky Way contributes at most about $20$ rad m$^{-2}$ at high latitudes and the intergalactic medium out to $z approx 3$ only a few rad m$^{-2}$ — so the authors estimate a field as small as $10^{-10}$ gauss could still be seen.
The rotation is generated in the brief window after tight coupling ends but before the electrons disappear, so the signal is a probe of that window rather than of the whole reionization history.

Reading between the lines

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

Because the line-of-sight integral of the field cancels when the field reverses direction, the measured rotation is really a joint measurement of field amplitude and coherence length; the same data that fixes $B_0$ under a coherence assumption could instead be used to bound how tangled the field is.
A rotation generated by a primordial field scales as $nu^{-2}$, whereas a frequency-independent rotation of the polarization plane would point to a different, parity-violating mechanism; multi-frequency maps therefore discriminate between the two without extra modelling.
The paper notes that cluster fields already have measured rotation measures from radio sources, which suggests cross-correlating the microwave polarization rotation with known cluster positions as a way to subtract the local contribution and isolate any background component.
Since the signal is generated almost entirely by the residual free electrons after recombination, an early reionization episode would add a second, later rotation layer whose size depends on the optical depth — so a measured rotation in excess of the prediction would itself constrain reionization.

Original abstract

The existence of a primordial magnetic field at the last scattering surface may induce a measurable Faraday rotation in the polarization of the cosmic microwave background. We calculate the magnitude of this effect by evolving the radiative transfer equations for the microwave background polarization through the epoch of last scatter, in the presence of a magnetic field. For a primordial field amplitude corresponding to a present value of $10^{-9}{\rm G}$ (which would account for the observed galactic field if it were frozen in the pre-galactic plasma), we find a rotation angle of around $1^\circ$ at a frequency of 30 GHz. The statistical detection of this signal is feasible with future maps of the microwave background.

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, 3,665 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.07 · 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.

The existence of a primordial magnetic field at the last scattering surface may induce a measurable Faraday rotation in the polarization of the cosmic microwave background. We calculate the magnitude of this effect by evolving the radiative transfer equations for the microwave background polarization through the epoch of last scatter, in the presence of a magnetic field. For a primordial field amplitude corresponding to a present value of $10^{-9}{\rm G}$ (which would account for the observed galactic field if it were frozen in the pre-galactic plasma), we find a rotation angle of around $1^\circ$ at a frequency of 30 GHz. The statistical detection of this signal is feasible with future maps of the microwave background.

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	The existence of a primordial magnetic field at the last scattering surface may induce a measurable Faraday rotation in the polarization of the cosmic microwave background.	background 0.97	0.07	0.21	hedged possibility 1.00
s1	We calculate the magnitude of this effect by evolving the radiative transfer equations for the microwave background polarization through the epoch of last scatter, in the presence of a magnetic field.	method 0.96	0.95	0.05	asserted 0.98
s2	For a primordial field amplitude corresponding to a present value of $10^{-9}{\rm G}$ (which would account for the observed galactic field if it were frozen in the pre-galactic plasma), we find a rotation angle of around $1^\circ$ at a frequency of 30 GHz.	result 1.00	0.95	0.63	asserted 1.00
s3	The statistical detection of this signal is feasible with future maps of the microwave background.	interpretation 0.86	0.42	0.31	hedged possibility 0.70

What kind of paper the classifier reports this is: theoretical result 0.88 · evidence from simulation or computation 0.91.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

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

Figures

**Figure 1.** — The evolution of the polarization brightnesses, for

**Figure 2.** — The ratio IQ/IU as a function of Ω0h 2 and Ωbh 2 , for a magnetic field B0 = 10−9 G and an observed frequency of 30 GHz. The dotted lines from bottom to top are for Ωbh 2 = 0.005, 0.0075, and 0.01. The solid lines from top to bottom are for Ωbh 2 = 0.0125, 0.015, 0.02, and 0.025. 4. Discussion We have calculated the rotation of the microwave background polarization vector due to a primordial magnetic field at the surface of last scatter. The magnetic field was assumed to be coherent on the width of the last scattering surface, corresponding to a comoving scale of a few Mpc, whic

Figures reproduced from arXiv:astro-ph/9601055 by the authors.

References

Works cited (2)

[1]

Bond, J. R. & Efstathiou, G. 1984, ApJ, 245, L87 Cattaneo, F. 1994, ApJ, 434, 200 Coulson, D., Crittenden, R. G., & Turok, N. G. 1995, Phys. Rev. Let t. 73,

View on Pith 1984
[2390]

Crittenden, R.G., David, R., & Steinhardt, P. 1993, ApJ, 417, L13 Dreher, J. W., Carilli, C. L., & Perley, R. A. 1987, ApJ, 316, 611 Field, G. B. 1994, in The Physics of the Interstellar and Intergalact ic Medium, eds. A Ferrara, C. Heiles, C. F. McKee, and P. Shapiro, (San Francisco: A stronomical Society of the Paciﬁc), 1-14 Frewin, R. A., Polnarev, A.G...

View on Pith Pith review arXiv 1993

Forward citations

Cited by 21 Pith papers

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

CMB anisotropies from primordial inhomogeneous magnetic fields
astro-ph 2004-06 conditional novelty 7.0 of 10

Neutrino anisotropic stress cancels magnetic stress on super-horizon scales after decoupling, so primordial magnetic fields mainly produce small-scale B-modes, with 10^-9 G fields potentially detectable.
3-form dark energy and cosmic birefringence
astro-ph.CO 2026-08 conditional novelty 6.0 of 10

3-form dark energy can explain cosmic birefringence with a dimension-4 photon coupling, yielding redshift profiles that can mimic or differ from axion dark energy, but the implied photon mass estimate is numerically shaky.
Simultaneous determination of the cosmic birefringence and miscalibrated polarisation angles from CMB experiments
astro-ph.CO 2019-04 conditional novelty 6.0 of 10

A CMB experiment can separate cosmic birefringence from polarisation-angle miscalibration by using the Galactic foreground as an alpha-only calibrator, yielding a projected beta uncertainty of about 11 arcmin for a Li...
POLARBEAR Constraints on Cosmic Birefringence and Primordial Magnetic Fields
astro-ph.CO 2015-09 accept novelty 6.0 of 10

POLARBEAR's first-season polarization data set 95% upper limits of 93 nanogauss on an equivalent primordial magnetic field from anisotropic cosmic birefringence and 3.9 nanogauss on primordial magnetic fields from the...
Planck 2013 results. XVI. Cosmological parameters
astro-ph.CO 2013-03 conditional novelty 6.0 of 10

Planck's first CMB temperature and lensing spectra fit a flat six-parameter LambdaCDM model at high multipoles and yield H0 = 67.3 +/- 1.2 km/s/Mpc, Omega_m = 0.315 +/- 0.017, and no evidence for extra relativistic sp...

Show 16 more citing papers

On the non-Gaussian correlation of the primordial curvature perturbation with vector fields
astro-ph.CO 2012-10 conditional novelty 6.0 of 10

The three-point cross-correlation of the curvature perturbation with two magnetic-field powers peaks at |b_NL| ~ 10^3 in the flattened limit and reduces to b_NL = n_B - 4 in the squeezed limit.
Correlation of inflation-produced magnetic fields with scalar fluctuations
astro-ph.CO 2011-09 conditional novelty 6.0 of 10

Coupling electromagnetism to a rolling scalar field during inflation produces magnetic fields whose cross-correlation with scalar perturbations can reach order unity for plausible parameters.
Sensitivity of gamma-ray telescopes for detection of magnetic fields in intergalactic medium
astro-ph.CO 2009-10 conditional novelty 6.0 of 10

Gamma-ray cascade imaging and timing with Fermi and Cherenkov telescopes can probe intergalactic magnetic fields down to roughly 10^-16 to 10^-12 G over a wide range of coherence lengths, reaching the parameter space ...
How to De-Rotate the Cosmic Microwave Background Polarization
astro-ph 2008-10 conditional novelty 6.0 of 10

A quadratic estimator built from rotation-induced EB and TB correlations reconstructs the position-dependent CMB polarization rotation angle, separating rotation-induced B modes from primordial ones.
Constraints on a Primordial Magnetic Field
astro-ph 1997-01 conditional novelty 6.0 of 10

Any homogeneous primordial magnetic field must be weaker than about 3.4 x 10^-9 Gauss today, roughly a hundred times below the older nucleosynthesis bound.
The Benefits of CMB Delensing
astro-ph.CO 2021-11 conditional novelty 5.0 of 10

Iterative delensing of all CMB spectra on the curved sky, implemented in released code, tightens cosmological parameter forecasts and shrinks lensing-induced non-Gaussian covariance relative to lensed-spectrum analyses.
The Atacama Cosmology Telescope: Constraints on Cosmic Birefringence
astro-ph.CO 2020-01 accept novelty 5.0 of 10

ACTPol polarization data over 456 square degrees give a birefringence power spectrum consistent with zero, improving upper limits on scale-invariant anisotropic birefringence by a factor of 2 to 3.
B-mode Power Spectrum of CMB via Polarized Compton Scattering
astro-ph.CO 2019-09 conditional novelty 5.0 of 10

Compton scattering off partially polarized electrons can generate B-mode polarization from scalar density perturbations, with an amplitude proportional to the square of the electron polarization asymmetry.
Future CMB constraints on cosmic birefringence and implications for fundamental physics
astro-ph.CO 2019-04 conditional novelty 5.0 of 10

Forecasts show that LiteBIRD, Simons Observatory, a CMB-S4-like experiment, and PICO will tighten bounds on cosmic polarization rotation by one to three orders of magnitude, with corresponding gains for axion, magneti...
Constraints on Primordial Magnetic Fields from Planck combined with the South Pole Telescope CMB B-mode polarization measurements
astro-ph.CO 2016-11 accept novelty 5.0 of 10

Adding South Pole Telescope B-mode data to Planck tightens the 95% upper bound on a primordial magnetic field smoothed over 1 Mpc from 3.3 to 1.5 nanogauss.
Planck 2015 results. XIX. Constraints on primordial magnetic fields
astro-ph.CO 2015-02 conditional novelty 5.0 of 10

Planck 2015 data bound the comoving primordial magnetic field at 1 Mpc to below about 4.4 nG (95% CL) for a generic non-helical field, and below 0.9 nG for a nearly scale-invariant field once magnetic heating of the p...
Probing polarization states of primordial gravitational waves with CMB anisotropies
astro-ph 2007-05 conditional novelty 5.0 of 10

A circularly polarized inflationary gravitational wave background produces TB and EB CMB spectra that reionization boosts at large angles, and a cosmic-variance-limited experiment could detect a polarization degree ab...
CMBPol Mission Concept Study: Gravitational Lensing
astro-ph 2008-11 conditional novelty 4.0 of 10

Lens reconstruction from small-scale CMB polarization can constrain neutrino mass to roughly 0.05 eV and cut lensing contamination of the primordial B-mode by up to a factor of about seven, if the beam is a few arcmin...
Snowmass2021 CMB-HD White Paper
astro-ph.CO 2022-03 unverdicted novelty 3.0 of 10

The paper proposes a 30-meter-class CMB survey and argues that its forecast sensitivity would probe dark matter, light relics, inflation, neutrino mass, and dark energy.
New physics from the polarised light of the cosmic microwave background
astro-ph.CO 2022-02 accept novelty 3.0 of 10

Planck polarisation data hint at cosmic birefringence at about 3 sigma, and future CMB experiments could distinguish primordial gravitational waves made by vacuum fluctuations from those made by matter fields.
Primordial magnetogenesis
astro-ph.CO 2010-07 accept novelty 2.0 of 10

Standard inflation dilutes magnetic seeds to roughly 10^-50 G, so viable primordial fields require modified electromagnetism, non-flat cosmology, or non-standard physics.

How the literature uses it

37 arXiv papers cite this in 48 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 30 sentences without a confident label

Uses its data or values 1 paper

In the epoch of recombination, magnetic field is estimated to be about $10^-3μ$ to $10^-1μ$ [ref] .

Generation of circular polarization of the CMB · Circular polarization and magnetic field · 0.88

Cites it as background 16 papers

When CMB radiation passes through ionized regions permeated by magnetic fields, its polarization is rotated by an angle [ref] [equation] where $n̂$ is the direction of the line of sight, $τ̇$ is the differential optical depth, $ν_0$ is the detector frequency, $B$ is the comoving magnetic field strength, and $dl$ is the comoving length element along the photon trajectory.

Searching for primordial magnetism with multi-frequency CMB experiments · Estimator of rotation measure from multiple maps · 0.84
The existence of PMFs at the last scattering surface and later epochs induces a Faraday rotation (hereafter FR) signal in the CMB polarization anisotropies [ref] .

LiteBIRD Science Goals and Forecasts: Primordial Magnetic Fields · Faraday rotation · 0.90
Cosmic birefringence can be caused by parity-violating physics in the early universe, such as axion-like particles coupling to photons through Chern-Simons interaction [ref] , more general Lorentz-violating physics beyond the Standard Model [ref] , and primordial magnetic fields through Faraday rotation which is frequency-dependent [ref] .

Impact of Anisotropic Birefringence on Measuring Cosmic Microwave Background Lensing · Cosmic Birefringence · 0.95

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]

Bond, J. R. & Efstathiou, G. 1984, ApJ, 245, L87 Cattaneo, F. 1994, ApJ, 434, 200 Coulson, D., Crittenden, R. G., & Turok, N. G. 1995, Phys. Rev. Let t. 73,

View on Pith 1984

[2] [2390]

Crittenden, R.G., David, R., & Steinhardt, P. 1993, ApJ, 417, L13 Dreher, J. W., Carilli, C. L., & Perley, R. A. 1987, ApJ, 316, 611 Field, G. B. 1994, in The Physics of the Interstellar and Intergalact ic Medium, eds. A Ferrara, C. Heiles, C. F. McKee, and P. Shapiro, (San Francisco: A stronomical Society of the Paciﬁc), 1-14 Frewin, R. A., Polnarev, A.G...

View on Pith Pith review arXiv 1993