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Constraints on Anisotropic Cosmic Birefringence from CMB B-mode Polarization

T0 review · 2 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Four CMB surveys combine to place the tightest B-mode bound on anisotropic cosmic birefringence.

desk verdict Useful multi-experiment null constraint on anisotropic cosmic birefringence, but the headline upper bound doesn't match the paper's own Table I and the isotropic-rotation template in Eq. (16) is missing a square; both need fixing before the abstract is accurate. read the letter →

arxiv 2504.13154 v3 pith:QJEROGJF submitted 2025-04-17 astro-ph.CO gr-qchep-ph

A. I. Lonappan , B. Keating , K. Arnold This is my paper · ORCID
classification astro-ph.COgr-qchep-ph
keywords cosmicbirefringenceanisotropicCMBB-modepolarizationaxion-likeparticlesparityviolationlast-scatteringsurfacerotationexperiments
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 asks whether the rotation of CMB polarization by an anisotropic pseudoscalar field—the anisotropic part of cosmic birefringence—can be seen in B-mode polarization, the curl component of the microwave sky, using a treatment that does not approximate the last-scattering surface as infinitely thin. Combining B-mode spectra from SPTpol, ACT, POLARBEAR, and BICEP, it finds a best-fit amplitude $A_{\rm CB} = 0.42^{+0.40}_{-0.34}\times 10^{-4}$, consistent with zero within $2\sigma$, and a 95% upper limit $A_{\rm CB} < 1\times 10^{-4}$. The SPTpol-only hint of a $1.8\sigma$ preference weakens as the other datasets are added, and allowing an isotropic rotation angle further pulls the anisotropic amplitude toward zero. If the result holds, it is the current tightest B-mode constraint on anisotropic cosmic birefringence under the exact, beyond-thin-LSS calculation.

What carries the argument

The central object is the dimensionless amplitude $A_{\rm CB} = (g_\phi/2)^2 (H_I/2\pi)^2$, defined so that the rotation-angle power spectrum is $C^{\alpha\alpha}_L \simeq 2\pi/[L(L+1)]\,A_{\rm CB}$ at large angular scales. The computation carries this amplitude through the exact B-mode formula of Ref. [53], which uses the total angular momentum method to integrate the polarized radiative-transfer equation over the finite visibility function rather than freezing the rotation at a single last-scattering epoch. The key intermediate is the distorted E-mode spectrum $C^{EE}_{\ell',L}$ built from the projected polarization source $s_\ell(q,\eta)$ and the birefringence kernel $u_L(k,\eta)=(g_\phi/2)\,j_L(k(\eta_0-\eta))T(k,\eta)$, whose product sets how much E-polarization is converted into B-modes. In this treatment the predicted B-mode spectrum is suppressed by roughly an order of magnitude at $\ell\lesssim10$ and a factor of two at $\ell\gtrsim100$ relative to the thin-LSS approximation, which is why the exact template matters for the quoted bound.

What would settle it

A future high-sensitivity CMB experiment that pushes the 95% upper limit below roughly $3\times10^{-5}$ would test the point directly: if the best-fit $A_{\rm CB}$ rises above $1\times10^{-4}$ with $5\sigma$ significance, the paper's null-consistent conclusion is wrong. Alternatively, a direct quadratic-estimator measurement of the rotation-angle power spectrum whose shape departs from $1/[L(L+1)]$ would falsify the scale-invariant model under which the bound is derived.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central claim is that the anisotropic-birefringence B-mode signal, computed with the finite thickness of the last-scattering surface included, is not detected in the combined data: the joint likelihood prefers $A_{\rm CB} = 0.42^{+0.40}_{-0.34}\times 10^{-4}$ (about $1.1\sigma$), and the 95% confidence interval excludes amplitudes above $1\times 10^{-4}$. Two robustness results accompany the main bound: no single experiment drives the constraint, and marginalizing over an isotropic rotation angle $\alpha$ broadens the posterior and moves the best fit from about $4.6\times 10^{-5}$ to $1.9\times 10^{-5}$, so the anisotropic signal does not survive as a significant detection. The authors present the bound as the leading constraint of its kind, derived under a massless, scale-invariant pseudoscalar model.

Load-bearing premise

Everything rests on assuming the anisotropic rotation is produced by a massless pseudoscalar field whose primordial fluctuations are scale-invariant, so the rotation-angle power spectrum has the shape $C^{\alpha\alpha}_L\propto 1/[L(L+1)]$; if the true signal has a different multipole dependence, the quoted $A_{\rm CB}$ bound does not directly apply.

Editorial extensions

If this is right

  • The 95% upper limit $A_{\rm CB} < 1\times 10^{-4}$ becomes the reference B-mode bound for anisotropic cosmic birefringence under the exact finite-LSS treatment, replacing earlier estimates made with the thin-LSS approximation.
  • The SPTpol-only $1.8\sigma$ preference weakens when ACT, POLARBEAR, and BICEP are added, so the combined result is the one to use in future model comparisons.
  • Marginalizing over an isotropic rotation angle shifts the anisotropic best fit from about $4.6\times10^{-5}$ to $1.9\times10^{-5}$, showing that future analyses must fit both components jointly to avoid overestimating the anisotropic signal.
  • Because the exact treatment suppresses the B-mode signal at low multipoles by roughly an order of magnitude, large-angle B-mode surveys face a higher bar for detecting this effect than thin-LSS templates suggested.

Reading between the lines

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

  • The quoted bound is tied to a massless, scale-invariant pseudoscalar model; a massive axion or a defect network would imprint a different $L$-dependence in $C^{\alpha\alpha}_L$, so the same data would need a separate spectral-shape analysis before any limit is quoted.
  • A direct tomographic reconstruction of the rotation-angle power spectrum from EB correlations, rather than a template fit to the B-mode auto-spectrum, could break the $A_{\rm CB}$–$\alpha$ degeneracy and test the assumed spectral shape.
  • Because the exact treatment suppresses large-scale B-modes, the quickest route to beating the $1\times10^{-4}$ bound may be small-scale surveys with aggressive delensing rather than low-multipole observations alone.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. This paper constrains the amplitude A_CB of anisotropic cosmic birefringence using B-mode polarization bandpowers from SPTpol, ACT, POLARBEAR, and BICEP, adopting the exact treatment of Namikawa (TN24) that goes beyond the thin last-scattering-surface approximation. The model assumes a massless pseudoscalar field with a scale-invariant primordial power spectrum, with the rotation-angle power spectrum scaling as C_αα ∝ A_CB/[L(L+1)]. The main results are a best-fit amplitude A_CB = 0.42^{+0.40}_{-0.34} × 10^{-4} for the full dataset combination, a 95% confidence-level upper limit quoted as A_CB < 1 × 10^{-4} in the abstract, and a robustness study that includes an isotropic rotation angle α. The paper concludes that the joint data show no significant detection of anisotropic cosmic birefringence and that the bounds are not dominated by a single experiment.

Significance. If the reported constraints are correct, this would be one of the leading CMB B-mode limits on anisotropic cosmic birefringence under the exact beyond-thin-LSS treatment, and the combination of four independent experiments is a useful step beyond previous single-experiment analyses. The paper also makes its analysis code publicly available at https://github.com/antolonappan/bbCAB, which is a clear strength. The main scientific conclusion—that current B-mode data do not prefer a nonzero anisotropic birefringence amplitude—is plausible and consistent with previous upper limits. However, the numerical discrepancies between the abstract, the text, and Table I directly affect the headline bound, and the isotropic-rotation template in Eq. (16) is missing a square, both of which must be corrected before the quoted limits can be considered reliable.

major comments (2)
  1. [Abstract; Sec. III; Table I] The abstract's headline 95% upper limit A_CB < 1 × 10^{-4} is not supported by Table I, where the full-dataset (SPTpol+ACT+POLARBEAR+BICEP) row reports a 95% upper limit of 1.08 × 10^{-4}. Similarly, Sec. III states that the dataset combination excluding SPTpol gives A_CB < 1.00 × 10^{-4}, but Table I lists 0.85 × 10^{-4} for the ACT+POLARBEAR+BICEP row. Because the paper's central claim is a numerical constraint on A_CB, this internal inconsistency is load-bearing and must be resolved—either by correcting the abstract and text to match Table I, or by recomputing the limits if the table is wrong.
  2. [Sec. III, Eq. (16)] The isotropic rotation template is written as D^{iso,CB}_ℓ(α) = sin(2α) C^{EE}_ℓ, but the standard relation for rotation of Stokes parameters is C^{BB} = sin^2(2α) C^{EE} (for a pure E-mode input), so the equation is missing a square on the sine factor. This template is used in Sec. III.A and Fig. 3 for the joint fit with α, and the robustness claim 'A_CB < 1.0 × 10^{-4}' from that analysis is reported in the figure caption. The quoted joint-fit bound should not be trusted until Eq. (16) is corrected and the fit is repeated.
minor comments (4)
  1. [Sec. III; Sec. IV] The abstract says the result is 'consistent with zero within 2σ', but Table I reports 1.10σ for the full combination; this is technically true but vague, and the text should state the actual significance.
  2. [Sec. III, Eq. (15)] Equation (15) includes the isotropic term D^{iso,CB}_ℓ, but the next paragraph says 'we did not include the isotropic term... in our model' for the main constraints; please clarify that Eq. (15) is the general model and that the baseline analysis is a restricted version with α fixed to zero.
  3. [Sec. III.A; Fig. 3] The joint-fit 95% upper limit A_CB < 1.0 × 10^{-4} is quoted in the text and figure caption, but no corresponding row is given in Table I; the relationship between the joint-fit bound and the Table I bounds (e.g., why the joint limit is below the Table I full-dataset limit of 1.08 × 10^{-4}) should be explained.
  4. [References] Several references are incomplete, lacking volume/page numbers (e.g., refs. [13], [16]-[18], [23], [44]); these should be completed before publication.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the A_CB constraint is an external-data fit to a fixed theory template; neither the template nor the posterior reduces to the fitted input.

full rationale

The paper's central result is a likelihood constraint on A_CB, not a prediction from a fitted parameter. The amplitude enters linearly as the coefficient of a fixed template, D_ell^{aniso,CB} = A_CB D_ell^{aniso,CB,template}, in Eq. (15), with the template computed from Eqs. (10)-(14) using TN24's biref-aniso-bb code. A_CB is then sampled against external SPTpol/ACT/POLARBEAR/BICEP B-mode bandpowers through the Gaussian likelihood in Eq. (18). No equation defines A_CB in terms of the data or defines the reported upper bound in terms of the inputs; the posterior is data-conditioned and the amplitude is a fitted parameter, not a renamed prediction. The citations to TN24 are to an external prior work by T. Namikawa, not by the present authors, and the 'exact treatment' is used with stated assumptions (massless pseudoscalar, scale-invariant P_phi); none of those assumptions assert the target constraint. The paper's self-identified scope limitation, namely that only this spectral shape is tested while alternative mechanisms such as Faraday rotation and mass-dependent axions are deferred, is a model-dependence caveat rather than circularity. There is one passing self-citation [52] in the introduction, but it is not load-bearing. I also note, for completeness, a non-circular numerical inconsistency: the abstract quotes A_CB < 1e-4 while Table I gives 1.08e-4 for the full-dataset combination, and Sec. III's text says the SPTpol-excluded combination gives A_CB < 1.00e-4 while Table I gives 0.85e-4; this affects the accuracy of the headline figure but does not involve reducing a claim to its own input. Overall, no circular step was found.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on one fitted amplitude ACB (plus nuisance parameters) and on TN24's theoretical template. No new entities are introduced. The key axioms are the massless pseudoscalar model, the matter-domination transfer function, and the neglect of higher-order terms.

free parameters (5)
  • ACB = 0.42^{+0.40}_{-0.34} × 10^{-4} (full combination)
    Amplitude of anisotropic birefringence, fitted to CMB B-mode bandpowers.
  • alpha = 0.58^{+0.19}_{-0.35} degrees (marginalized from joint fit)
    Isotropic rotation angle, fitted jointly with ACB; absorbs part of the signal.
  • r
    Tensor-to-scalar ratio, marginalized with flat prior; nuisance parameter.
  • Alens
    Lensing amplitude, marginalized with Gaussian prior; nuisance parameter.
  • Adust = 0.0094 ± 0.0021 uK^2 (prior mean)
    Galactic dust amplitude at 150 GHz, ℓ=80; Gaussian prior from BICEP2/Keck.
assumptions (6)
  • domain assumption Massless pseudoscalar field with no correlation between δϕ and curvature perturbations.
    Stated in Sec. II.C as a condition for the TN24 formalism; simplifies the power spectrum calculation.
  • domain assumption Transfer function T(k,η) = 3 j1(kη)/(kη) during matter domination.
    Eq. (4) in Sec. II.A; needed to compute the rotation angle evolution.
  • domain assumption Primordial power spectrum Pϕ(k) = (H_I/2π)^2, scale-invariant from vacuum fluctuations during inflation.
    Eq. (5); fixes the spectral shape of the rotation angle power spectrum.
  • domain assumption Negligible lensing effects on the birefringence angle and higher-order terms O[(Cαα)^2] are minor for ℓ ≲ 1000.
    Stated in Sec. II.C; required for Eq. (10) to be valid.
  • domain assumption The external datasets (ACT, POLARBEAR, BICEP) enter only through foreground-marginalized combined spectra, and a Gaussian likelihood in bandpowers is adequate.
    Sec. III; assumes the published combined spectra and covariances are sufficient without re-fitting calibration and beam parameters for those experiments.
  • standard math Standard CMB theory (total angular momentum method, visibility function, scalar perturbation sources) as implemented in CAMB/CLASS.
    Background used in Eqs. (8)-(13); accepted prior literature.

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Cite this review

Pith. "Pith review of Constraints on Anisotropic Cosmic Birefringence from CMB B-mode Polarization." pith.science (2026). https://pith.science/paper/QJEROGJF

@misc{pith2026250413154,
  author       = {Pith},
  title        = {Pith review of: Constraints on Anisotropic Cosmic Birefringence from CMB B-mode Polarization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QJEROGJF}},
  note         = {Machine review of arXiv:2504.13154}
}
abstract

Cosmic birefringence$-$the rotation of the polarization plane of light as it traverses the universe$-$offers a direct observational window into parity-violating physics beyond the Standard Model. In this work, we revisit the anisotropic component of cosmic birefringence, which leads to the generation of $B$-mode polarization in the cosmic microwave background (CMB). Using an exact theoretical treatment beyond the thin last-scattering surface approximation, we constrain the amplitude of anisotropic birefringence with combined polarization data from SPTpol, ACT, POLARBEAR, and BICEP. The joint analysis yields a best-fit amplitude of $A_{\rm CB} = 0.42^{+0.40}_{-0.34} \times 10^{-4}$, consistent with zero within $2\sigma$, and we place a 95\% confidence-level upper bound of $A_{\rm CB} < 1 \times 10^{-4}$. The constraint is not dominated by any single experiment and remains robust under the inclusion of a possible isotropic rotation angle. These results provide leading constraints on anisotropic cosmic birefringence from CMB $B$-mode polarization and illustrate the potential of upcoming experiments to improve sensitivity to parity-violating effects in the early universe.

Figures

Figures reproduced from arXiv: 2504.13154 by the authors.

Figure 1
Figure 1. FIG. 1. Theoretical B-mode spectra are shown for tensor [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Posterior probability distributions for the amplitude [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Corner plot showing the marginalized and joint pos [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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Forward citations

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Reference graph

Works this paper leans on

71 extracted references · 17 canonical work pages · cited by 2 Pith papers

  1. [1]

    Ni, From Equivalence Principles to Cosmol- ogy: Cosmic Polarization Rotation, CMB Observa- tion, Neutrino Number Asymmetry, Lorentz Invariance and CPT, Prog

    W.-T. Ni, From Equivalence Principles to Cosmol- ogy: Cosmic Polarization Rotation, CMB Observa- tion, Neutrino Number Asymmetry, Lorentz Invariance and CPT, Prog. Theor. Phys. Suppl. 172, 49 (2008), arXiv:0712.4082 [astro-ph]

    arXiv 2008

  2. [2]

    Komatsu, New physics from the polarized light of the cosmic microwave background, Nature Rev

    E. Komatsu, New physics from the polarized light of the cosmic microwave background, Nature Rev. Phys. 4, 452 (2022), arXiv:2202.13919 [astro-ph.CO]

    arXiv 2022

  3. [3]

    Finelli and M

    F. Finelli and M. Galaverni, Rotation of Linear Polariza- tion Plane and Circular Polarization from Cosmological Pseudo-Scalar Fields, Phys. Rev. D 79, 063002 (2009), arXiv:0802.4210 [astro-ph]

    arXiv 2009

  4. [4]

    Liu and K.-W

    G.-C. Liu and K.-W. Ng, Axion Dark Matter Induced Cosmic Microwave Background B-modes, Phys. Dark Univ. 16, 22 (2017), arXiv:1612.02104 [astro-ph.CO]

    arXiv 2017

  5. [5]

    M. A. Fedderke, P. W. Graham, and S. Rajendran, Ax- ion Dark Matter Detection with CMB Polarization, Phys. Rev. D 100, 015040 (2019), arXiv:1903.02666 [astro- ph.CO]

    arXiv 2019

  6. [6]

    Murai, F

    K. Murai, F. Naokawa, T. Namikawa, and E. Komatsu, Isotropic cosmic birefringence from early dark energy, Phys. Rev. D 107, L041302 (2023), arXiv:2209.07804 [astro-ph.CO]

    arXiv 2023

  7. [7]

    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]

    arXiv 2023

  8. [8]

    Fujita, K

    T. Fujita, K. Murai, H. Nakatsuka, and S. Tsujikawa, De- tection of isotropic cosmic birefringence and its implica- tions for axionlike particles including dark energy, Phys. Rev. D 103, 043509 (2021), arXiv:2011.11894 [astro- ph.CO]

    arXiv 2021

Show all 71 references
  1. [9]

    S. M. Carroll, Quintessence and the rest of the world, Phys. Rev. Lett. 81, 3067 (1998), arXiv:astro- ph/9806099

    1998

  2. [10]

    Fujita, Y

    T. Fujita, Y. Minami, K. Murai, and H. Nakatsuka, Probing axionlike particles via cosmic microwave back- ground polarization, Phys. Rev. D 103, 063508 (2021), arXiv:2008.02473 [astro-ph.CO]

    2021 arXiv

  3. [11]

    Panda, Y

    S. Panda, Y. Sumitomo, and S. P. Trivedi, Axions as Quintessence in String Theory, Phys. Rev. D 83, 083506 (2011), arXiv:1011.5877 [hep-th]

    2011 arXiv

  4. [12]

    G. Choi, W. Lin, L. Visinelli, and T. T. Yanagida, Cosmic birefringence and electroweak axion dark energy, Phys. Rev. D 104, L101302 (2021), arXiv:2106.12602 [hep-ph]

    2021 arXiv

  5. [13]

    Obata, Implications of the cosmic birefringence mea- surement for the axion dark matter search, JCAP 09, 062, arXiv:2108.02150 [astro-ph.CO]

    I. Obata, Implications of the cosmic birefringence mea- surement for the axion dark matter search, JCAP 09, 062, arXiv:2108.02150 [astro-ph.CO]

    arXiv

  6. [14]

    Gasparotto and I

    S. Gasparotto and I. Obata, Cosmic birefringence from monodromic axion dark energy, JCAP 08 (08), 025, arXiv:2203.09409 [astro-ph.CO]

    arXiv

  7. [15]

    Galaverni, F

    M. Galaverni, F. Finelli, and D. Paoletti, Redshift evolu- tion of cosmic birefringence in CMB anisotropies, Phys. Rev. D 107, 083529 (2023), arXiv:2301.07971 [astro- ph.CO]

    2023 arXiv

  8. [16]

    Takahashi and W

    F. Takahashi and W. Yin, Kilobyte Cosmic Bire- fringence from ALP Domain Walls, JCAP 04, 007, arXiv:2012.11576 [hep-ph]

    2012 arXiv

  9. [17]

    Kitajima, F

    N. Kitajima, F. Kozai, F. Takahashi, and W. Yin, Power spectrum of domain-wall network, and its implications for isotropic and anisotropic cosmic birefringence, JCAP 10, 043, arXiv:2205.05083 [astro-ph.CO]

    arXiv

  10. [18]

    M. Jain, R. Hagimoto, A. J. Long, and M. A. Amin, Searching for axion-like particles through CMB bire- fringence from string-wall networks, JCAP 10, 090, arXiv:2208.08391 [astro-ph.CO]

    arXiv

  11. [19]

    Gonzalez, N

    D. Gonzalez, N. Kitajima, F. Takahashi, and W. Yin, Stability of domain wall network with initial inflationary fluctuations and its implications for cosmic birefringence, Phys. Lett. B 843, 137990 (2023), arXiv:2211.06849 [hep- ph]

    2023 arXiv

  12. [20]

    R. C. Myers and M. Pospelov, Ultraviolet modifications of dispersion relations in effective field theory, Phys. Rev. Lett. 90, 211601 (2003), arXiv:hep-ph/0301124

    2003 arXiv

  13. [21]

    K. R. S. Balaji, R. H. Brandenberger, and D. A. Eas- son, Spectral dependence of CMB polarization and par- ity, JCAP 12, 008, arXiv:hep-ph/0310368

    arXiv

  14. [22]

    Arvanitaki, S

    A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, and J. March-Russell, String Axiverse, Phys. Rev. D 81, 123530 (2010), arXiv:0905.4720 [hep-th]

    2010 arXiv

  15. [23]

    Louis et al

    T. Louis et al. (ACT), The Atacama Cosmology Tele- scope: DR6 Power Spectra, Likelihoods and LCDM Pa- rameters, (2025), arXiv:2503.14452 [astro-ph.CO]

    2025 arXiv

  16. [24]

    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]

    2020 arXiv

  17. [25]

    Diego-Palazuelos et al., Cosmic Birefringence from the Planck Data Release 4, Phys

    P. Diego-Palazuelos et al., Cosmic Birefringence from the Planck Data Release 4, Phys. Rev. Lett. 128, 091302 (2022), arXiv:2201.07682 [astro-ph.CO]

    2022 arXiv

  18. [26]

    J. R. Eskilt and E. Komatsu, Improved constraints on cosmic birefringence from the WMAP and Planck cosmic microwave background polarization data, Phys. Rev. D 7 106, 063503 (2022), arXiv:2205.13962 [astro-ph.CO]

    2022 arXiv

  19. [27]

    J. R. Eskilt et al. (Cosmoglobe), COSMOGLOBE DR1 results - II. Constraints on isotropic cosmic birefringence from reprocessed WMAP and Planck LFI data, Astron. Astrophys. 679, A144 (2023), arXiv:2305.02268 [astro- ph.CO]

    2023 arXiv

  20. [28]

    Sigl and P

    G. Sigl and P. Trivedi, Axion-like Dark Mat- ter Constraints from CMB Birefringence, (2018), arXiv:1811.07873 [astro-ph.CO]

    2018 arXiv

  21. [29]

    B. D. Sherwin and T. Namikawa, Cosmic birefringence tomography and calibration independence with reioniza- tion signals in the CMB, Mon. Not. Roy. Astron. Soc. 520, 3298 (2023), arXiv:2108.09287 [astro-ph.CO]

    2023 arXiv

  22. [30]

    Nakatsuka, T

    H. Nakatsuka, T. Namikawa, and E. Komatsu, Is cosmic birefringence due to dark energy or dark matter? A to- mographic approach, Phys. Rev. D 105, 123509 (2022), arXiv:2203.08560 [astro-ph.CO]

    2022 arXiv

  23. [31]

    G.-C. Liu, S. Lee, and K.-W. Ng, Effect on cos- mic microwave background polarization of coupling of quintessence to pseudoscalar formed from the electro- magnetic field and its dual, Phys. Rev. Lett. 97, 161303 (2006), arXiv:astro-ph/0606248

    2006 arXiv

  24. [32]

    Lee, G.-C

    S. Lee, G.-C. Liu, and K.-W. Ng, Imprint of Scalar Dark Energy on Cosmic Microwave Background Polarization, Phys. Rev. D 89, 063010 (2014), arXiv:1307.6298 [astro- ph.CO]

    2014 arXiv

  25. [33]

    Gubitosi, M

    G. Gubitosi, M. Martinelli, and L. Pagano, Including birefringence into time evolution of CMB: current and fu- ture constraints, JCAP 12, 020, arXiv:1410.1799 [astro- ph.CO]

    arXiv

  26. [34]

    E. Y. S. Wu et al. (QUaD), Parity Violation Con- straints Using Cosmic Microwave Background Polariza- tion Spectra from 2006 and 2007 Observations by the QUaD Polarimeter, Phys. Rev. Lett. 102, 161302 (2009), arXiv:0811.0618 [astro-ph]

    2009 arXiv

  27. [35]

    Komatsu, K

    E. Komatsu, K. M. Smith, J. Dunkley, C. L. Bennett, B. Gold, G. Hinshaw, N. Jarosik, D. Larson, M. R. Nolta, L. Page, D. N. Spergel, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. Weiland, E. Wollack, and E. L. Wright, Seven- year Wilk...

    2011 arXiv

  28. [36]

    J. P. Kaufman et al. (BICEP1), Self-Calibration of BI- CEP1 Three-Year Data and Constraints on Astrophysical Polarization Rotation, Phys. Rev. D 89, 062006 (2014), arXiv:1312.7877 [astro-ph.IM]

    2014 arXiv

  29. [37]

    Aghanim et al

    N. Aghanim et al. (Planck), Planck intermediate re- sults. XLIX. Parity-violation constraints from polar- ization data, Astron. Astrophys. 596, A110 (2016), arXiv:1605.08633 [astro-ph.CO]

    2016 arXiv

  30. [38]

    Monelli, E

    M. Monelli, E. Komatsu, A. E. Adler, M. Billi, P. Campeti, N. Dachlythra, A. J. Duivenvoorden, J. E. Gudmundsson, and M. Reinecke, Impact of half- wave plate systematics on the measurement of cosmic birefringence from CMB polarization, JCAP 03, 034, arXiv:2211.05685 [astro-ph.CO]

    arXiv

  31. [39]

    Lue, L.-M

    A. Lue, L.-M. Wang, and M. Kamionkowski, Cosmolog- ical signature of new parity violating interactions, Phys. Rev. Lett. 83, 1506 (1999), arXiv:astro-ph/9812088

    1999 arXiv

  32. [41]

    Lee, G.-C

    S. Lee, G.-C. Liu, and K.-W. Ng, Cosmic Birefrin- gence Fluctuations and Cosmic Microwave Background B-mode Polarization, Phys. Lett. B 746, 406 (2015), arXiv:1403.5585 [astro-ph.CO]

    2015 arXiv

  33. [42]

    D. Leon, J. Kaufman, B. Keating, and M. Mewes, The cosmic microwave background and pseudo- Nambu–Goldstone bosons: Searching for Lorentz violations in the cosmos, Mod. Phys. Lett. A 32, 1730002 (2016), arXiv:1611.00418 [astro-ph.CO]

    2016 arXiv

  34. [43]

    L. Yin, J. Kochappan, T. Ghosh, and B.-H. Lee, Is cosmic birefringence model-dependent?, JCAP 10, 007, arXiv:2305.07937 [astro-ph.CO]

    arXiv

  35. [44]

    R. Z. Ferreira, S. Gasparotto, T. Hiramatsu, I. Obata, and O. Pujolas, Axionic defects in the CMB: bire- fringence and gravitational waves, JCAP 05, 066, arXiv:2312.14104 [hep-ph]

    arXiv

  36. [45]

    Gluscevic, M

    V. Gluscevic, M. Kamionkowski, and A. Cooray, De- Rotation of the Cosmic Microwave Background Polar- ization: Full-Sky Formalism, Phys. Rev. D 80, 023510 (2009), arXiv:0905.1687 [astro-ph.CO]

    2009 arXiv

  37. [46]

    P. A. R. Ade et al. (BICEP2, Keck Arrary), BICEP2 / Keck Array IX: New bounds on anisotropies of CMB polarization rotation and implications for axionlike par- ticles and primordial magnetic fields, Phys. Rev. D 96, 102003 (2017), arXiv:1705.02523 [astro-ph.CO]

    2017 arXiv

  38. [47]

    Namikawa et al., Atacama Cosmology Telescope: Con- straints on cosmic birefringence, Phys

    T. Namikawa et al., Atacama Cosmology Telescope: Con- straints on cosmic birefringence, Phys. Rev. D 101, 083527 (2020), arXiv:2001.10465 [astro-ph.CO]

    2020 arXiv

  39. [48]

    Moncelsi et al

    L. Moncelsi et al. , Receiver development for BICEP Ar- ray, a next-generation CMB polarimeter at the South Pole, Proc. SPIE Int. Soc. Opt. Eng. 11453, 1145314 (2020), arXiv:2012.04047 [astro-ph.IM]

    2020 arXiv

  40. [49]

    Ade et al

    P. Ade et al. (Simons Observatory), The Simons Ob- servatory: Science goals and forecasts, JCAP 02, 056, arXiv:1808.07445 [astro-ph.CO]

    arXiv

  41. [50]

    Abazajian et al

    K. Abazajian et al. (CMB-S4), CMB-S4: Forecasting Constraints on Primordial Gravitational Waves, Astro- phys. J. 926, 54 (2022), arXiv:2008.12619 [astro-ph.CO]

    2022 arXiv

  42. [51]

    Allys et al

    E. Allys et al. (LiteBIRD), Probing Cosmic Infla- tion with the LiteBIRD Cosmic Microwave Back- ground Polarization Survey, PTEP2023, 042F01 (2023), arXiv:2202.02773 [astro-ph.IM]

    2023 arXiv

  43. [52]

    Idicherian Lonappan, Improving Cosmic Birefringence Constraints via Delensing, J

    A. Idicherian Lonappan, Improving Cosmic Birefringence Constraints via Delensing, J. Cosmol. Astropart. Phys. (2025), arXiv:2503.04708 [astro-ph.CO]

    2025 arXiv

  44. [53]

    Namikawa, Exact CMB B-mode power spectrum from anisotropic cosmic birefringence, Phys

    T. Namikawa, Exact CMB B-mode power spectrum from anisotropic cosmic birefringence, Phys. Rev. D 109, 123521 (2024), arXiv:2404.13771 [astro-ph.CO]

    2024 arXiv

  45. [54]

    Harari and P

    D. Harari and P. Sikivie, Effects of a Nambu-Goldstone boson on the polarization of radio galaxies and the cosmic microwave background, Phys. Lett. B 289, 67 (1992)

    1992

  46. [55]

    S. M. Carroll, G. B. Field, and R. Jackiw, Limits on a Lorentz and Parity Violating Modification of Electrody- namics, Phys. Rev. D 41, 1231 (1990)

    1990

  47. [56]

    S. M. Carroll and G. B. Field, Einstein equivalence prin- ciple and the polarization of radio galaxies, Phys. Rev. D 43, 3789 (1991)

    1991

  48. [57]

    Greco, N

    A. Greco, N. Bartolo, and A. Gruppuso, Probing Axions through Tomography of Anisotropic Cosmic Birefrin- gence, JCAP 05, 026, arXiv:2211.06380 [astro-ph.CO]

  49. [58]

    Li and X

    M. Li and X. Zhang, Cosmological CPT violating effect on CMB polarization, Phys. Rev. D 78, 103516 (2008), arXiv:0810.0403 [astro-ph]. 8

    2008 arXiv

  50. [59]

    Hu and M

    W. Hu and M. J. White, CMB anisotropies: Total an- gular momentum method, Phys. Rev. D 56, 596 (1997), arXiv:astro-ph/9702170

    1997 arXiv

  51. [60]

    Pogosian, A

    L. Pogosian, A. P. S. Yadav, Y.-F. Ng, and T. Vachas- pati, Primordial Magnetism in the CMB: Exact Treat- ment of Faraday Rotation and WMAP7 Bounds, Phys. Rev. D 84, 043530 (2011), [Erratum: Phys.Rev.D 84, 089903 (2011)], arXiv:1106.1438 [astro-ph.CO]

    2011 arXiv

  52. [61]

    R. R. Caldwell, V. Gluscevic, and M. Kamionkowski, Cross-correlation of cosmological birefringence with CMB temperature, Phys. Rev. D 84, 043504 (2011), arXiv:1104.1634 [astro-ph.CO]

    2011 arXiv

  53. [62]

    D. Blas, J. Lesgourgues, and T. Tram, The cosmic linear anisotropy solving system (class). part ii: Approximation schemes, Journal of Cosmology and Astroparticle Physics 2011 (07), 034–034

    2011

  54. [63]

    Https://github.com/toshiyan/biref-aniso-bb

  55. [64]

    P. A. R. Ade et al. (BICEP, Keck), Improved Con- straints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season, Phys. Rev. Lett. 127, 151301 (2021), arXiv:2110.00483 [astro-ph.CO]

    2021

  56. [65]

    Adachi et al

    S. Adachi et al. (POLARBEAR), Improved Upper Limit on Degree-scale CMB B-mode Polarization Power from the 670 Square-degree POLARBEAR Survey, Astrophys. J. 931, 101 (2022), arXiv:2203.02495 [astro-ph.CO]

    2022 arXiv

  57. [66]

    J. T. Sayre et al. (SPT), Measurements of B-mode Po- larization of the Cosmic Microwave Background from 500 Square Degrees of SPTpol Data, Phys. Rev. D 101, 122003 (2020), arXiv:1910.05748 [astro-ph.CO]

    2020 arXiv

  58. [67]

    https://github.com/cmbant/CAMB

  59. [68]

    https://github.com/toshiyan/biref-aniso-bb

  60. [69]

    Foreman-Mackey, D

    D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Good- man, emcee: The mcmc hammer, Publications of the As- tronomical Society of the Pacific 125, 306–312 (2013), arXiv:1202.3665 [astro-ph.IM]

    2013 arXiv

  61. [70]

    Kosowsky, T

    A. Kosowsky, T. Kahniashvili, G. Lavrelashvili, and B. Ratra, Faraday rotation of the Cosmic Microwave Background polarization by a stochastic magnetic field, Phys. Rev. D71, 043006 (2005), arXiv:astro-ph/0409767

    2005 arXiv

  62. [71]

    V. A. Kostelecky and M. Mewes, Lorentz-violating elec- trodynamics and the cosmic microwave background, Phys. Rev. Lett. 99, 011601 (2007), arXiv:astro- ph/0702379

    2007

  63. [72]

    Greco, N

    A. Greco, N. Bartolo, and A. Gruppuso, Probing axions through tomography of anisotropic cosmic birefringence, Journal of Cosmology and Astroparticle Physics 2023

    2023

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