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Searching for primordial magnetism with multi-frequency CMB experiments
Cosmology and Nongalactic Astrophysics · Submitted 12 Nov 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that a recently proposed space-based experiment PRISM can detect magnetic fields of 0.1 nano-Gauss strength at a 2 sigma level.
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The abstract, sentence by sentence
Bounds on the amplitude of a scale-invariant stochastic primordial magnetic field (PMF) can be significantly improved by measurements of the Faraday Rotation (FR) of CMB polarization. The mode-coupling correlations induced by FR make it possible to extract it from cross-correlations of the B-mode polarization with the E-mode and the temperature anisotropy. In this paper, we construct an estimator of the rotation measure that appropriately combines measurements of the FR from multiple frequency channels. We study the dependence of the signal-to-noise in the PMF detection on the resolution and the noise of the detectors, as well as the removal of the weak lensing contribution and the galactic FR. We show that a recently proposed space-based experiment PRISM can detect magnetic fields of 0.1 nano-Gauss strength at a 2 sigma level. Higher detection levels can be achieved by reducing the detector noise and improving the resolution or increasing the number of channels in the 30-70 GHz frequency range.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Bounds on the amplitude of a scale-invariant stochastic primordial magnetic field (PMF) can be significantly improved by measurements of the Faraday Rotation (FR) of CMB polarization. | background 1.00 | 0.08 | 0.15 | asserted 0.57 |
| s1 | The mode-coupling correlations induced by FR make it possible to extract it from cross-correlations of the B-mode polarization with the E-mode and the temperature anisotropy. | background 0.55 | 0.13 | 0.05 | asserted 0.72 |
| s2 | In this paper, we construct an estimator of the rotation measure that appropriately combines measurements of the FR from multiple frequency channels. | method 0.71 | 0.94 | 0.05 | asserted 0.99 |
| s3 | We study the dependence of the signal-to-noise in the PMF detection on the resolution and the noise of the detectors, as well as the removal of the weak lensing contribution and the galactic FR. | contribution 0.73 | 0.80 | 0.04 | asserted 0.70 |
| s4 | We show that a recently proposed space-based experiment PRISM can detect magnetic fields of 0.1 nano-Gauss strength at a 2 sigma level. | result 1.00 | 0.83 | 0.62 | asserted 0.99 |
| s5 | Higher detection levels can be achieved by reducing the detector noise and improving the resolution or increasing the number of channels in the 30-70 GHz frequency range. | interpretation 0.46 | 0.73 | 0.16 | hedged possibility 0.70 |
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The paper
Original abstract
Bounds on the amplitude of a scale-invariant stochastic primordial magnetic field (PMF) can be significantly improved by measurements of the Faraday Rotation (FR) of CMB polarization. The mode-coupling correlations induced by FR make it possible to extract it from cross-correlations of the B-mode polarization with the E-mode and the temperature anisotropy. In this paper, we construct an estimator of the rotation measure that appropriately combines measurements of the FR from multiple frequency channels. We study the dependence of the signal-to-noise in the PMF detection on the resolution and the noise of the detectors, as well as the removal of the weak lensing contribution and the galactic FR. We show that a recently proposed space-based experiment PRISM can detect magnetic fields of 0.1 nano-Gauss strength at a 2 sigma level. Higher detection levels can be achieved by reducing the detector noise and improving the resolution or increasing the number of channels in the 30-70 GHz frequency range.
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References
How the literature uses it
14 arXiv papers cite this in 22 sentences
Papers citing it · 13 sentences without a confident label
Uses its method or tool 2 papers
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In such a case, one works with the estimator of RM defined, in the case of EB, as [ref] [r̂_B^iE^j,LM]_ll' = c^-2 ν^2_i [α̂_B^iE^j,LM]_ll' , where $i$ and $j$ label different frequency channels.
Searching for Primordial Magnetic Fields with CMB B-modes · Mode-coupling correlations induced by Faraday rotation · 0.91
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The details of constructing the multi-frequency RM estimator can be found in [ref] .
Future CMB constraints on cosmic birefringence and implications for fundamental physics · Faraday Rotation by a Primordial Magnetic Field · 0.91
Cites it as support 1 paper
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Going below $0.1$ nG would only be possible [ref] if there was an independent measurement of the galactic RM.
Searching for Primordial Magnetic Fields with CMB B-modes · Forecasted bounds from SPT-3G, the Simons Observatory, CMB-S4 and Space Probe · 0.97
Cites it as background 4 papers
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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
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The occurrence of cosmic birefringence can be attributed potentially to parity-violating phenomena in the early universe, such as the interaction between axionlike particles and photons through the Chern-Simons mechanism, [ref] , more general Lorentz-violating physics beyond the Standard Model [ref] , and primordial magnetic fields through Faraday rotation which is frequency-dependent [ref] .
Efficient estimation of rotation-induced bias to reconstructed CMB lensing power spectrum · Cosmic Birefringence · 0.97
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Various phenomena may generate $B$-modes in polarization measurements of the microwave sky: primordial tensor perturbations (gravitational waves) [ref] ; weak gravitational lensing of $E$-modes induced by the potentials of intervening large scale structures; Milky Way foregrounds (especially Galactic synchrotron and dust emission) [ref] ; uncorrected systematic problems in the data [ref] ; and unknown, exotic phenemena like cosmic birefringence or primordial magnetic fields [ref] .
Real-space computation of $E$/$B$-mode maps I: Formalism, Compact Kernels, and Polarized Filaments · Introduction · 0.93
What it cites · 31 sentences without a confident label
Builds on 2 papers
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In this work, we generalize the estimator of the FR angle at a single frequency used in [ref] to that of a rotation measure that appropriately accounts for the covariance of measurements of the FR at multiple frequencies.
Probing Primordial Magnetism with Off-Diagonal Correlators of CMB Polarization · Introduction · 0.99
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In this work, we generalize the estimator of the FR angle at a single frequency used in [ref] to that of a rotation measure that appropriately accounts for the covariance of measurements of the FR at multiple frequencies.
CMB Faraday rotation as seen through the Milky Way · Introduction · 0.99
Uses the method or tool of 6 papers
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Given measurements of B- and E-modes at frequencies $i$ and $j$, respectively, the quantity [ref] [α̂_B^iE^j,LM]_ll' = 2π∑_mm' B^i_lmE_l'm'^j* ξ_lml'm'^LM (2l+1)(2l'+1)C_l^EEH_ll'^L
Revealing Cosmic Rotation · Estimator of rotation measure from multiple maps · 0.93
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Given measurements of B- and E-modes at frequencies $i$ and $j$, respectively, the quantity [ref] [α̂_B^iE^j,LM]_ll' = 2π∑_mm' B^i_lmE_l'm'^j* ξ_lml'm'^LM (2l+1)(2l'+1)C_l^EEH_ll'^L
How to De-Rotate the Cosmic Microwave Background Polarization · Estimator of rotation measure from multiple maps · 0.93
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Given measurements of B- and E-modes at frequencies $i$ and $j$, respectively, the quantity [ref] [α̂_B^iE^j,LM]_ll' = 2π∑_mm' B^i_lmE_l'm'^j* ξ_lml'm'^LM (2l+1)(2l'+1)C_l^EEH_ll'^L
Cosmic Microwave Background Statistics for a Direction-Dependent Primordial Power Spectrum · Estimator of rotation measure from multiple maps · 0.93
Uses data or values from 3 papers
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We show the RM spectra for $B_SI=0.1$ and $0.01$ nG in Fig. [ref], along with the galactic RM spectrum based on the map of [ref] with $f_sky=0.6$ [ref] .
An improved map of the Galactic Faraday sky · Detection prospects · 0.84
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We show the RM spectra for $B_SI=0.1$ and $0.01$ nG in Fig. [ref], along with the galactic RM spectrum based on the map of [ref] with $f_sky=0.6$ [ref] .
CMB Faraday rotation as seen through the Milky Way · Detection prospects · 0.84
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Recently released Planck data limits $B_SI$ to a few nano-Gauss (nG) [ref] , although these results assume initial conditions in which the magnetic stress-energy is compensated by that of the surrounding fluid.
Planck 2013 results. XVI. Cosmological parameters · Introduction · 0.91
Compares with 2 papers
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Similar, i. e. a few nG, level constraints on $B_SI$ were obtained by [ref] from Lyman-$α$ spectra [ref] .
Constraining primordial magnetic fields through large scale structure · Introduction · 0.95
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Similar, i. e. a few nG, level constraints on $B_SI$ were obtained by [ref] from Lyman-$α$ spectra [ref] .
Towards a Precise Measurement of Matter Clustering: Lyman-alpha Forest Data at Redshifts 2-4 · Introduction · 0.95
Cites as support 1 paper
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Giving additional impetus to the PMF hypothesis is the claimed detection of a magnetic field in the intergalactic space [ref] based on non-observation of GeV $γ$-rays expected to accompany TeV blazars.
Evidence for strong extragalactic magnetic fields from Fermi observations of TeV blazars · Introduction · 0.97
Cites as background 14 papers
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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.
Depolarization of the cosmic microwave background by a primordial magnetic field and its effect upon temperature anisotropy · Estimator of rotation measure from multiple maps · 0.84
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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.
Faraday Rotation of Microwave Background Polarization by a Primordial Magnetic Field · Estimator of rotation measure from multiple maps · 0.84
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There are additional modes, such as the “passive mode” [ref] generated prior to neutrino decoupling, and the so-called “inflationary magnetic mode” [ref] produced during the inflation.
Magnetic fields from inflation: the transition to the radiation era · Introduction · 0.85
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