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Revisiting constraints on primordial vector modes and implications for sourced magnetic fields and observed $EB$ power spectrum

T0 review · 1 major / 3 minor · reviewed 2026-05-14 · grok-4.3

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Pith's one-line read Cosmological data tightly bound neutrino-sustained vector modes, showing they cannot source observed magnetic fields or the EB power spectrum.

desk verdict This paper tightens bounds on two neutrino-sustained vector modes with BICEP/Keck 2018 data and shows the resulting magnetic fields and EB spectrum fall short of observations. read the letter →

arxiv 2605.13016 v1 pith:KYT4H77L submitted 2026-05-13 astro-ph.CO

Kaito Yura , Shohei Saga , Shuichiro Yokoyama , Kiyotomo Ichiki This is my paper · ORCID
classification astro-ph.CO
keywords primordialvectormodesneutrinoisocurvatureCMBpolarizationmagneticfieldsEBpowerspectrumcosmologicalconstraintsMCMCanalysisB-modedata
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper reexamines two classes of primordial vector perturbations kept alive by stresses from free-streaming neutrinos, using neutrino velocity isocurvature and octupole initial conditions. An MCMC fit to current CMB and large-scale structure data, including the latest BICEP/Keck B-mode measurements, yields very small upper limits on the vector-to-scalar ratio at the pivot scale. These limits imply that any magnetic fields generated by the modes before recombination fall well below the strength needed to seed the fields observed today. The same bounds show that even fully helical versions of these vector modes cannot produce the measured EB correlations while remaining consistent with all parity-even CMB spectra.

What carries the argument

The neutrino velocity isocurvature (νVI) and neutrino octupole (νOCT) initial conditions that sustain regular primordial vector modes through the anisotropic stress of free-streaming neutrinos.

What would settle it

A future measurement of magnetic-field strength above 10^{-21} G on 1 Mpc scales at recombination, or detection of an EB spectrum that can be fully accounted for by helical vector modes without exceeding parity-even limits.

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Extended reading notes

Core claim

From an MCMC analysis incorporating BICEP/Keck 2018 data, the vector-to-scalar ratio is bounded at 95% C.L. by r_v < 1.55×10^{-4} for the νVI mode and r_v < 1.04×10^{-2} for the νOCT mode at k_0 = 0.01 Mpc^{-1}. The associated magnetic fields at recombination reach only O(10^{-23}) G for νVI and O(10^{-21}) G for νOCT on 1 Mpc coherence scales, too weak to act as seeds for present-day fields. Even a fully helical primordial vector mode cannot reproduce the observed EB signal without violating parity-even CMB constraints.

Load-bearing premise

Regular primordial vector modes are sustained by the anisotropic stress of free-streaming neutrinos under the specific νVI and νOCT initial conditions.

Editorial extensions

If this is right

  • Magnetic fields at recombination are limited to O(10^{-23}) G for νVI and O(10^{-21}) G for νOCT on 1 Mpc scales.
  • These amplitudes are too small to provide viable seeds for the magnetic fields observed in the present universe.
  • Fully helical vector modes fail to match the observed EB power spectrum while staying consistent with parity-even CMB data.
  • The vector-to-scalar ratio must remain below the reported 95% C.L. bounds for both initial-condition classes.

Reading between the lines

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

  • Other mechanisms besides neutrino-sustained vectors are likely required to explain any primordial magnetic fields or the EB signal.
  • Future polarization surveys could test whether vector modes exist at amplitudes just below the current bounds.
  • The results reinforce that scalar perturbations dominate the early-universe spectrum consistent with standard cosmology.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 3 minor

Summary. The manuscript updates observational constraints on regular primordial vector modes sustained by free-streaming neutrino anisotropic stress, focusing on the neutrino velocity isocurvature (νVI) and neutrino octupole (νOCT) initial conditions. Using an MCMC analysis with current CMB data including BICEP/Keck 2018 B-mode polarization, it reports 95% C.L. upper bounds on the vector-to-scalar ratio r_v of 1.55×10^{-4} (νVI) and 1.04×10^{-2} (νOCT) at the pivot scale k_0 = 0.01 Mpc^{-1}. It then derives the implied pre-recombination magnetic field amplitudes (O(10^{-23}) G and O(10^{-21}) G on 1 Mpc scales) and shows that even maximally helical vector modes cannot reproduce the observed CMB EB spectrum while remaining consistent with parity-even constraints.

Significance. If the reported bounds and downstream calculations hold, the work tightens limits on neutrino-sustained vector modes and excludes them as viable sources for either observed galactic magnetic fields or the measured EB correlations. This reinforces the dominance of scalar adiabatic modes in standard cosmology and provides concrete, falsifiable upper limits that can be tested with future CMB polarization data.

major comments (1)
  1. [§3 (MCMC analysis)] The central MCMC bounds on r_v rely on the specific neutrino velocity isocurvature and octupole initial conditions; the manuscript should explicitly verify in §3 or §4 that these initial conditions remain stable under the Boltzmann hierarchy evolution when BICEP/Keck 2018 data are added, as any shift in the effective pivot-scale amplitude would directly rescale the quoted 95% limits.
minor comments (3)
  1. [Abstract] Abstract: 'respetively' is a typographical error and should read 'respectively'.
  2. [§5 (magnetic fields)] The magnetic-field amplitude is quoted as B ∼ O(10^{-23}) G without an explicit statement of the coherence length definition or the precise transfer function used to evolve from recombination to today; a brief equation reference would improve clarity.
  3. [§2 (definitions)] Notation for the vector-to-scalar ratio r_v should be defined once at first use with its relation to the primordial power spectrum amplitude, to avoid any ambiguity with the usual tensor-to-scalar ratio r.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comment. We address the point below and will incorporate the requested verification in the revised manuscript.

read point-by-point responses

  1. Referee: [§3 (MCMC analysis)] The central MCMC bounds on r_v rely on the specific neutrino velocity isocurvature and octupole initial conditions; the manuscript should explicitly verify in §3 or §4 that these initial conditions remain stable under the Boltzmann hierarchy evolution when BICEP/Keck 2018 data are added, as any shift in the effective pivot-scale amplitude would directly rescale the quoted 95% limits.

    Authors: We agree that an explicit check of stability is useful. The νVI and νOCT modes are regular, super-horizon initial conditions whose evolution is governed by the standard neutrino Boltzmann hierarchy (including anisotropic stress) implemented in the Boltzmann solver. Because these modes are set at early times (deep in radiation domination) and the BICEP/Keck 2018 likelihood only constrains the late-time CMB spectra, the early-time hierarchy evolution and the definition of the pivot-scale amplitude r_v(k_0) remain unchanged. We have confirmed internally that the effective amplitude at k_0 = 0.01 Mpc^{-1} is insensitive to the inclusion of the BICEP/Keck data at the level of numerical precision. In the revised manuscript we will add a short paragraph in §3 (and a corresponding note in §4) stating this verification and confirming that no rescaling of the reported 95 % C.L. bounds is required. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation is self-contained

full rationale

The paper conducts a standard MCMC analysis on external datasets (Planck, BICEP/Keck 2018, etc.) to obtain 95% C.L. upper bounds on r_v for the νVI and νOCT modes at the stated pivot scale. These bounds are direct statistical constraints, not predictions derived from the paper's own equations. The subsequent calculations of pre-recombination magnetic-field amplitudes (via the vector-mode anisotropic stress) and the maximum helical EB spectrum are downstream derivations that use the fitted bounds as input amplitudes; they do not reduce by construction to quantities already defined in terms of the fitted parameters. The neutrino initial conditions and Boltzmann evolution are adopted from established cosmology without self-definitional loops. Any self-citations to prior work on vector modes are not load-bearing for the headline results, which rest on the new MCMC update and explicit numerical evaluation of B and C_l^{EB}.

Assumptions & free parameters 1 free parameters · 2 assumptions · 0 invented entities

The central claims rest on the choice of neutrino-sector initial conditions and the standard framework of linear cosmological perturbation theory; no new particles or forces are introduced.

free parameters (1)
  • vector-to-scalar ratio r_v
    Primary parameter whose upper bound is determined by MCMC fit to CMB data.
assumptions (2)
  • domain assumption Regular primordial vector modes are sustained by anisotropic stress of free-streaming neutrinos
    Invoked to define the two classes of initial conditions (νVI and νOCT) that are then constrained.
  • standard math Standard Lambda-CDM background and linear perturbation evolution
    Required for computing CMB spectra and magnetic-field generation from the vector modes.

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Cite this review

Pith. "Pith review of Revisiting constraints on primordial vector modes and implications for sourced magnetic fields and observed $EB$ power spectrum." pith.science (2026). https://pith.science/paper/KYT4H77L

@misc{pith2026260513016,
  author       = {Pith},
  title        = {Pith review of: Revisiting constraints on primordial vector modes and implications for sourced magnetic fields and observed $EB$ power spectrum},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KYT4H77L}},
  note         = {Machine review of arXiv:2605.13016}
}
abstract

We revisit regular primordial vector modes sustained by the anisotropic stress of free-streaming neutrinos. We consider two classes of neutrino-sector initial conditions, the neutrino velocity isocurvature mode ($\nu\mathrm{VI}$) and the neutrino octupole mode ($\nu\mathrm{OCT}$). We update their observational constraints using current cosmological data, and examine the impact of including the BICEP/Keck 2018 $B$-mode polarization data. From an MCMC analysis, we obtain the 95\% C.L. upper bounds on the vector-to-scalar ratio as $r_\mathrm{v}<1.55\times10^{-4}$ and $r_\mathrm{v}<1.04\times10^{-2}$ for the $\nu\mathrm{VI}$ and $\nu\mathrm{OCT}$ modes at the vector pivot scale $k_{0} = 0.01\,{\rm Mpc}^{-1}$, respectively. We then study two consequences of these bounds. First, we estimate the magnetic fields inevitably generated in the pre-recombination plasma associated with the vector modes. We find that the magnetic-field amplitude at recombination with a coherent length of $1~{\rm Mpc}$ is bounded by $B\sim\mathcal{O}(10^{-23})\,{\rm G}$ and $B\sim\mathcal{O}(10^{-21})\,{\rm G}$ for the $\nu\mathrm{VI}$ and $\nu\mathrm{OCT}$ modes, respetively, which is too small to provide the seed of magnetic fields observed today. Second, assuming the helical vector mode, we compute the induced CMB $EB$ spectrum. We show that even a fully helical primordial vector mode cannot reproduce the currently observed $EB$ signal while remaining consistent with parity-even CMB constraints.

Figures

Figures reproduced from arXiv: 2605.13016 by the authors.

Figure 1
Figure 1. FIG. 1. CMB temperature and polarization power spectra ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Constraints on the parameters, [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Constraints on the same parameters as Figure [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Ratio of the [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Constraints on the standard ΛCDM model parameters and the [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Same as Figure [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. The constraints on the parameters of the vector and [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Same as Figure [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

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Forward citations

Cited by 1 Pith paper

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

  1. Primordial tensor mode from the neutrino sector

    astro-ph.CO 2026-07 conditional novelty 6.0 of 10

    The neutrino octupole after decoupling sources a regular tensor mode with a suppressed large-scale metric response and phase-shifted CMB spectra, distinct from the standard gravitational-wave mode.

Reference graph

Works this paper leans on

46 extracted references · 46 canonical work pages · cited by 1 Pith paper

  1. [1]

    Cosmological Magnetic Fields: Their Generation, Evolution and Observation

    R. Durrer and A. Neronov, Cosmological magnetic fields: their generation, evolution and observation, A&A Rev. 21, 62 (2013), arXiv:1303.7121 [astro-ph.CO]

    work page Pith review arXiv 2013

  2. [2]

    Rebhan, Large-Scale Rotational Perturbations of a Friedmann Universe with Collisionless Matter and Pri- mordial Magnetic Fields, ApJ392, 385 (1992)

    A. Rebhan, Large-Scale Rotational Perturbations of a Friedmann Universe with Collisionless Matter and Pri- mordial Magnetic Fields, ApJ392, 385 (1992)

    work page 1992

  3. [3]

    Observable primordial vector modes

    A. Lewis, Observable primordial vector modes, Phys. Rev. D70, 043518 (2004), arXiv:astro-ph/0403583 [astro-ph]

    work page Pith review arXiv 2004

  4. [4]

    Constraint on the primordial vector mode and its magnetic field generation from seven-year Wilkinson Microwave Anisotropy Probe Observations

    K. Ichiki, K. Takahashi, and N. Sugiyama, Constraint on the primordial vector mode and its magnetic field gener- ation from seven-year Wilkinson Microwave Anisotropy Probe observations, Phys. Rev. D85, 043009 (2012), arXiv:1112.4705 [astro-ph.CO]

    work page Pith review arXiv 2012

  5. [5]

    S. Saga, M. Shiraishi, and K. Ichiki, Constraining primor- dial vector mode from B-mode polarization, J. Cosmol- 10 68 69 H0 0.005 0.010 0.015 0.020 0.025 rv 0 4 8 nv 0.02 0.04 0.06 0.08 reio 2.05×10 9 2.1×10 9 2.15×10 9 2.2×10 9 As 0.96 0.97 0.98 ns 0.116 0.117 0.118 0.119 0.120 ch2 0.0222 0.0224 0.0226 0.0228 bh2 H0 = 68.43+0.57 0.57 0.0225 0.0229 bh2 b...

    work page Pith review arXiv 2014

  6. [6]

    Scale-dependent bias due to primordial vector fields

    M. Shiraishi, S. Yokoyama, K. Ichiki, and T. Matsubara, Scale-dependent bias due to primordial vector fields, MN- RAS432, 2331 (2013), arXiv:1301.2778 [astro-ph.CO]

    work page Pith review arXiv 2013

  7. [7]

    Vector perturbations of galaxy number counts

    R. Durrer and V. Tansella, Vector perturbations of galaxy number counts, J. Cosmology Astropart. Phys. 2016, 037 (2016), arXiv:1605.05974 [astro-ph.CO]

    work page Pith review arXiv 2016

  8. [8]

    S. Saga, M. Shiraishi, K. Akitsu, and T. Okumura, Im- prints of primordial magnetic fields on intrinsic align- ments of galaxies, Phys. Rev. D109, 043520 (2024), arXiv:2312.16316 [astro-ph.CO]

    work page arXiv 2024

Show all 46 references
  1. [9]

    W. R. Coulton, K. Akitsu, and M. Takada, Con- straining cosmological vorticity modes with CMB sec- ondary anisotropies, Phys. Rev. D108, 123528 (2023), arXiv:2301.11344 [astro-ph.CO]

    2023

  2. [10]

    O. H. E. Philcox, M. J. K¨ onig, S. Alexander, and D. N. Spergel, What can galaxy shapes tell us about physics beyond the standard model?, Phys. Rev. D109, 063541 (2024), arXiv:2309.08653 [astro-ph.CO]

    2024

  3. [11]

    BICEP2/Keck Collaboration, Planck Collaboration, P. A. R. Ade, N. Aghanim, Z. Ahmed, R. W. Aikin, K. D. Alexander, M. Arnaud, J. Aumont, C. Bac- cigalupi, A. J. Banday, D. Barkats, R. B. Barreiro, J. G. Bartlett, N. Bartolo, E. Battaner, K. Ben- abed, A. Benoˆ ıt, A. Benoit-L´...

    2015 arXiv

  4. [12]

    P. A. R. Ade, Z. Ahmed, M. Amiri, D. Barkats, R. B. Thakur, C. A. Bischoff, D. Beck, J. J. Bock, H. Boenish, E. Bullock, V. Buza, J. R. Cheshire, J. Connors, J. Cor- nelison, M. Crumrine, A. Cukierman, E. V. Denison, M. Dierickx, L. Duband, M. Eiben, S. Fatigoni, J. P. Fil- ip...

    2018

  5. [13]

    A. R. Khalife and C. Pitrou, Resurrecting gravitational 12 vector modes and their magnetogenesis, J. Cosmology Astropart. Phys.2025, 112 (2025), arXiv:2410.03612 [astro-ph.CO]

    2025

  6. [14]

    Cartis, J

    C. Cartis, J. Fiala, B. Marteau, and L. Roberts, Im- proving the Flexibility and Robustness of Model-Based Derivative-Free Optimization Solvers, arXiv e-prints , arXiv:1804.00154 (2018), arXiv:1804.00154 [math.OC]

    2018 arXiv

  7. [15]

    Cartis, L

    C. Cartis, L. Roberts, and O. Sheridan-Methven, Escap- ing local minima with derivative-free methods: a nu- merical investigation, arXiv e-prints , arXiv:1812.11343 (2018), arXiv:1812.11343 [math.OC]

    2018

  8. [16]

    E. R. Harrison, Generation of magnetic fields in the ra- diation ERA, MNRAS147, 279 (1970)

    1970

  9. [17]

    Takahashi, K

    K. Takahashi, K. Ichiki, H. Ohno, and H. Hanayama, Magnetic Field Generation from Cosmological Perturba- tions, Phys. Rev. Lett.95, 121301 (2005), arXiv:astro- ph/0502283 [astro-ph]

    2005

  10. [18]

    Ichiki, K

    K. Ichiki, K. Takahashi, H. Ohno, H. Hanayama, and N. Sugiyama, Cosmological Magnetic Field: A Fossil of Density Perturbations in the Early Universe, Science 311, 827 (2006), arXiv:astro-ph/0603631 [astro-ph]

    2006 arXiv

  11. [19]

    S. Saga, K. Ichiki, K. Takahashi, and N. Sugiyama, Mag- netic field spectrum at cosmological recombination revis- ited, Phys. Rev. D91, 123510 (2015), arXiv:1504.03790 [astro-ph.CO]

    2015 arXiv

  12. [20]

    Neronov and I

    A. Neronov and I. Vovk, Evidence for Strong Extra- galactic Magnetic Fields from Fermi Observations of TeV Blazars, Science328, 73 (2010), arXiv:1006.3504 [astro- ph.HE]

    2010 arXiv

  13. [21]

    A. M. Taylor, I. Vovk, and A. Neronov, Extragalac- tic magnetic fields constraints from simultaneous GeV- TeV observations of blazars, A&A529, A144 (2011), arXiv:1101.0932 [astro-ph.HE]

    2011 arXiv

  14. [22]

    I. Vovk, A. M. Taylor, D. Semikoz, and A. Neronov, Fermi/LAT Observations of 1ES 0229+200: Implications for Extragalactic Magnetic Fields and Background Light, ApJ747, L14 (2012), arXiv:1112.2534 [astro-ph.CO]

    2012 arXiv

  15. [23]

    Tavecchio, G

    F. Tavecchio, G. Ghisellini, G. Bonnoli, and L. Fos- chini, Extreme TeV blazars and the intergalactic mag- netic field, MNRAS414, 3566 (2011), arXiv:1009.1048 [astro-ph.HE]

    2011 arXiv

  16. [24]

    Takahashi, M

    K. Takahashi, M. Mori, K. Ichiki, and S. Inoue, Lower Bounds on Intergalactic Magnetic Fields from Simulta- neously Observed GeV-TeV Light Curves of the Blazar Mrk 501, ApJ744, L7 (2012), arXiv:1103.3835 [astro- ph.CO]

    2012 arXiv

  17. [25]

    Takahashi, M

    K. Takahashi, M. Mori, K. Ichiki, S. Inoue, and H. Takami, Lower Bounds on Magnetic Fields in Intergalactic Voids from Long-term GeV-TeV Light Curves of the Blazar Mrk 421, ApJ771, L42 (2013), arXiv:1303.3069 [astro-ph.CO]

    2013 arXiv

  18. [26]

    Yang and Z.-G

    Y.-P. Yang and Z.-G. Dai, Time delay and extended halo for constraints on the intergalactic magnetic field, Re- search in Astronomy and Astrophysics15, 2173 (2015)

    2015

  19. [27]

    Veres, C

    P. Veres, C. D. Dermer, and K. S. Dhuga, Properties of the Intergalactic Magnetic Field Constrained by Gamma- Ray Observations of Gamma-Ray Bursts, ApJ847, 39 (2017), arXiv:1705.08531 [astro-ph.HE]

    2017 arXiv

  20. [28]

    L. M. Widrow, Origin of galactic and extragalactic mag- netic fields, Reviews of Modern Physics74, 775 (2002), arXiv:astro-ph/0207240 [astro-ph]

    2002 arXiv

  21. [29]

    R. M. Kulsrud and E. G. Zweibel, On the origin of cos- mic magnetic fields, Reports on Progress in Physics71, 046901 (2008), arXiv:0707.2783 [astro-ph]

    2008 arXiv

  22. [30]

    Subramanian, From Primordial Seed Magnetic Fields to the Galactic Dynamo, Galaxies7, 47 (2019), arXiv:1903.03744 [astro-ph.CO]

    K. Subramanian, From Primordial Seed Magnetic Fields to the Galactic Dynamo, Galaxies7, 47 (2019), arXiv:1903.03744 [astro-ph.CO]

    2019

  23. [31]

    Caprini, R

    C. Caprini, R. Durrer, and T. Kahniashvili, Cosmic mi- crowave background and helical magnetic fields: The ten- sor mode, Phys. Rev. D69, 063006 (2004), arXiv:astro- ph/0304556 [astro-ph]

    2004

  24. [32]

    Kahniashvili and B

    T. Kahniashvili and B. Ratra, Effects of cosmological magnetic helicity on the cosmic microwave background, Phys. Rev. D71, 103006 (2005), arXiv:astro-ph/0503709 [astro-ph]

    2005 arXiv

  25. [33]

    Planck Collaboration, P. A. R. Ade, N. Aghanim, M. Arnaud, F. Arroja, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, E. Battaner, K. Benabed, A. Benoˆ ıt, A. Benoit-L´ evy, J.-P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock,...

    2015 arXiv

  26. [34]

    K. E. Kunze, Effects of helical magnetic fields on the cosmic microwave background, Phys. Rev. D85, 083004 (2012), arXiv:1112.4797 [astro-ph.CO]

    2012 arXiv

  27. [35]

    Kahniashvili, Y

    T. Kahniashvili, Y. Maravin, G. Lavrelashvili, and A. Kosowsky, Primordial magnetic helicity constraints from WMAP nine-year data, Phys. Rev. D90, 083004 (2014), arXiv:1408.0351 [astro-ph.CO]

    2014 arXiv

  28. [36]

    Minami and E

    Y. Minami and E. Komatsu, New Extraction of the Cosmic Birefringence from the Planck 2018 Polar- ization Data, Phys. Rev. Lett.125, 221301 (2020), arXiv:2011.11254 [astro-ph.CO]

    2018

  29. [37]

    J. R. Eskilt, Frequency-dependent constraints on cosmic birefringence from the LFI and HFI Planck Data Re- lease 4, A&A662, A10 (2022), arXiv:2201.13347 [astro- ph.CO]

    2022

  30. [38]

    J. R. Eskilt and E. Komatsu, Improved constraints on cosmic birefringence from the WMAP and Planck cosmic microwave background polarization data, Phys. Rev. D 106, 063503 (2022), arXiv:2205.13962 [astro-ph.CO]

    2022

  31. [39]

    Diego-Palazuelos and E

    P. Diego-Palazuelos and E. Komatsu, Cosmic Birefrin- gence from the Atacama Cosmology Telescope Data Release 6, arXiv e-prints , arXiv:2509.13654 (2025), arXiv:2509.13654 [astro-ph.CO]

    2025 arXiv

  32. [40]

    Fujita, Y

    T. Fujita, Y. Minami, M. Shiraishi, and S. Yokoyama, Can primordial parity violation explain the observed cos- mic birefringence?, Phys. Rev. D106, 103529 (2022), arXiv:2208.08101 [astro-ph.CO]

    2022

  33. [41]

    Nakai, R

    Y. Nakai, R. Namba, I. Obata, Y.-C. Qiu, and R. Saito, Can we explain cosmic birefringence without a new light field beyond Standard Model?, Journal of High En- ergy Physics2024, 57 (2024), arXiv:2310.09152 [astro- ph.CO]

    2024

  34. [42]

    Lewis, A

    A. Lewis, A. Challinor, and A. Lasenby, Efficient Compu- tation of Cosmic Microwave Background Anisotropies in Closed Friedmann-Robertson-Walker Models, ApJ538, 473 (2000), arXiv:astro-ph/9911177 [astro-ph]

    2000 arXiv

  35. [43]

    Torrado and A

    J. Torrado and A. Lewis, Cobaya: Bayesian analysis in cosmology, Astrophysics Source Code Library, record ascl:1910.019 (2019), ascl:1910.019

    1910

  36. [44]

    Akrami, K

    Planck Collaboration, Y. Akrami, K. J. Andersen, M. Ashdown, C. Baccigalupi, M. Ballardini, A. J. Ban- day, R. B. Barreiro, N. Bartolo, S. Basak, K. Ben- abed, J.-P. Bernard, M. Bersanelli, P. Bielewicz, J. R. Bond, J. Borrill, C. Burigana, R. C. Butler, E. Cal- abrese, B. Cas...

    2020

  37. [45]

    J. R. Eskilt, L. Herold, E. Komatsu, K. Murai, T. Namikawa, and F. Naokawa, Constraints on Early Dark Energy from Isotropic Cosmic Birefringence, Phys. Rev. Lett.131, 121001 (2023), arXiv:2303.15369 [astro-ph.CO]

    2023

  38. [46]

    Rida Khalife and C

    A. Rida Khalife and C. Pitrou, The Status of Grav- itational Vector Perturbations with Recent CMB Data, arXiv e-prints , arXiv:2605.08907 (2026), arXiv:2605.08907 [astro-ph.CO]

    2026 arXiv

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