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BICEP/Keck XXI: Constraints on Early-Universe Parity Violation from Multipole-Dependent Birefringence

T0 review · 0 major / 5 minor · reviewed 2026-07-15 · grok-4.5

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Pith's one-line read BICEP/Keck finds no multipole-dependent cosmic birefringence: step sizes under 0.15° and EDE coupling consistent with zero.

desk verdict First solid BK limits on multipole-dependent birefringence via a clean step-function estimator; nulls are robust and the pipeline checks out. read the letter →

arxiv 2603.06812 v2 pith:JT3W5QFY submitted 2026-03-06 astro-ph.CO

BICEP/Keck Collaboration: P. A. R. Ade , Zeeshan Ahmed , Mandana Amiri , Denis Barkats , Ritoban Basu Thakur , Colin A. Bischoff , Dominic Beck , James J. Bock
show 88 more authors
Hans Boenish Victor Buza Brianna Cantrall James R. Cheshire IV Jake Connors James Cornelison Michael Crumrine Ari Jozef Cukierman Edward Denison Lionel Duband Michael Echter Miranda Eiben Brodi D. Elwood Sofia Fatigoni Jeffrey P. Filippini Antonio Fortes Min Gao Christos Giannakopoulos Neil Goeckner-Wald David C. Goldfinger Stephen Gratton James A. Grayson Annsley Greathouse Paul K. Grimes Grantland Hall George Halal Mark Halpern Emma Hand Sam A. Harrison Shawn Henderson Thuong Hoang Johannes Hubmayr Howard Hui Kent D. Irwin Jae Hwan Kang Kirit S. Karkare Sinan Kefeli J. M. Kovac Chao-Lin Kuo Kekoa Lasko King Lau Margaret Lautzenhiser Amber Lennox Tongtian Liu Scott Mackey Nolan Maher Koko G. Megerian Lorenzo Minutolo Lorenzo Moncelsi Yuka Nakato H. T. Nguyen Roger O'Brient Scott Paine Anika Patel Matthew A. Petroff Anna R. Polish Thomas Prouve Clement Pryke Carl D. Reintsema Steffen Richter Thibault Romand Maria Salatino Alessandro Schillaci Benjamin Schmitt Robert Schwarz Chris D. Sheehy Baibhav Singari Ahmed Soliman Tyler St Germaine Aaron Steiger Bryan Steinbach Rashmi Sudiwala Grant Teply Keith L. Thompson Carole Tucker Anthony D. Turner Clara Vergès Abigail G. Vieregg Albert Wandui Alexis C. Weber Justin Willmert Chin Lin Wong Wai Ling K. Wu Hung-I Yang Cyndia Yu Lingzhen Zeng Cheng Zhang Silvia Zhang
This is my paper
classification astro-ph.CO
keywords cosmicbirefringenceCMBpolarizationEarlyDarkEnergyaxion-photoncouplingEBspectrummultipoledependenceBICEP/Keckparityviolation
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

This paper reports the first search for multipole-dependent cosmic birefringence in BICEP/Keck BK18 polarization data. A time-evolving axion-like field during recombination would rotate CMB polarization by an angle that depends on multipole, producing a distinctive EB spectrum that cannot be faked by a simple detector miscalibration. The authors model that dependence as a step in rotation angle at several multipole breakpoints and also fit the amplitude of the rotation expected from Early Dark Energy models. Both analyses return results consistent with no rotation: the step sizes are consistent with zero at the 0.15° level, and the axion-photon coupling for the baseline EDE parameters is g = 0.11 ± 0.37. The result matters because a detection would have been direct evidence of new parity-violating physics operating at recombination, while a null result tightens the allowed range for such couplings without needing absolute polarization-angle calibration.

What carries the argument

A phenomenological multipole-dependent rotation angle β(ℓ) written as a Heaviside step of amplitude Δβ_ℓb at a chosen multipole breakpoint; the step is inserted into the standard rotation formulas for EE, BB and EB and then marginalized over per-band instrumental angles, allowing a search for ℓ-dependent parity violation that is independent of any particular Early Dark Energy template.

What would settle it

A statistically significant nonzero step Δβ_ℓb (greater than roughly 0.3°) at one or more of the tested multipole breakpoints, or a posterior on g for the baseline EDE parameters that excludes zero at high significance, would overturn the null result.

Watch

Extended reading notes

Core claim

Using multi-frequency EE, BB and EB spectra from the BK18 data set, a multipole-dependent polarization rotation modeled as a step function is consistent with zero at every tested breakpoint, with 68 % uncertainties less than or equal to 0.15°, and the axion-photon coupling amplitude for the baseline Early Dark Energy model (f_EDE = 0.087) is g = 0.11 ± 0.37 (68 % CL), consistent with earlier Planck limits.

Load-bearing premise

The Early Dark Energy background parameters are held fixed at published best-fit values while only the overall coupling amplitude is free to vary, so any mismatch between those fixed templates and the true cosmology is absorbed into the recovered coupling.

Editorial extensions

If this is right

  • The first model-independent limits on multipole-dependent birefringence from BICEP/Keck data are now available at the ~0.15° level.
  • Absolute polarization-angle calibration is not required to place useful bounds on time-evolving parity-violating fields during recombination.
  • The same step-function machinery can be re-run on future deeper maps or on other multipole-dependent templates without redesigning the likelihood.
  • Existing Planck limits on the EDE axion-photon coupling are corroborated by an independent data set with different sky coverage and foreground treatment.

Reading between the lines

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

  • Once absolute angle calibration becomes available, the same data can convert the present relative limits into absolute bounds on both isotropic and multipole-dependent birefringence simultaneously.
  • A linear or smoothly varying β(ℓ) parameterization would test a broader class of early-universe dynamics with only a modest increase in free parameters.
  • The limited multipole lever arm of BICEP/Keck relative to full-sky experiments remains the dominant statistical limitation; joint analyses with higher-ℓ data would tighten the step-function bounds further.
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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

0 major / 5 minor

Summary. The paper reports the first constraints on multipole-dependent cosmic birefringence from the BK18 multi-frequency (95/150/220 GHz) EE, BB and EB spectra. A phenomenological step-function model β(ℓ) = Δβ_ℓb H(ℓ−ℓb) yields Δβ_ℓb consistent with zero at every tested breakpoint (ℓb = 265–405) with 68 % uncertainties ≲ 0.15°. For an Early Dark Energy (EDE) Chern–Simons model the axion–photon coupling is constrained at fixed literature EDE parameters; the baseline (f_EDE = 0.087) result is g = 0.11 ± 0.37 (68 % CL). The analysis employs the standard BICEP/Keck foreground and likelihood framework, is validated on 499 baseline and EDE-injected simulations, and extends the multipole range to ℓ ≈ 520 after jackknife checks.

Significance. A null result on multipole-dependent birefringence at the 0.15° level is a useful, model-independent bound on time-varying parity violation during recombination. The step-function estimator cleanly separates ℓ-dependent physics from isotropic instrumental angles without absolute polarization calibration, and the multi-frequency EE+BB+EB pipeline with free A_lens and dust marginalization is thoroughly validated. The EDE constraints, while weaker than Planck, are complementary and demonstrate that the same data set can be used for both phenomenological and model-specific tests. The work therefore supplies a reusable framework for future absolute-angle-calibrated analyses.

minor comments (5)
  1. Section II D and Table I: the decision to freeze the full set of EDE background parameters (f_EDE, z_c, θ_i and the accompanying ΛCDM parameters) while floating only g is clearly stated, but a short quantitative statement of the residual bias expected from template mismatch (already quantified in Table S4) would help readers assess the robustness of the reported g uncertainties.
  2. Eqs. (5)–(7) and the subsequent step-function substitution: the text notes that more elaborate β(ℓ) forms are left for future work; a one-sentence remark on why a linear or piecewise-linear model was not already tried (given that only one extra parameter is involved) would strengthen the justification for the Heaviside choice.
  3. Figure 1 (right) and Eq. (2): the effective β(ℓ) is defined under the assumption that EB arises solely from rotated EE; a brief caveat that residual BB or foreground EB can bias this diagnostic would avoid over-interpretation by non-specialists.
  4. Section III A: the extension of jackknife tests to 14 bandpowers is welcome; stating the exact PTE thresholds or χ^{2} values for the highest multipole bin would make the claim of consistency fully self-contained.
  5. Typographical consistency: “BICEP/Keck” appears both with and without a space or slash in several places (abstract, Section I, figure captions); a uniform house style would improve readability.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: null constraints arise from free-amplitude MCMC fits of observed bandpowers to forward-modeled spectra, not from quantities that already encode the result.

full rationale

The paper is a standard observational constraint analysis. The model-independent step-function analysis introduces a free parameter Δβ_ℓb (Eq. 8) that multiplies a Heaviside step and is sampled jointly with the four per-band angles α_ν; the posterior is obtained by direct Gaussian likelihood comparison of the resulting binned EE/BB/EB spectra against BK18 data (Eq. 17). The EDE analysis likewise floats only the overall amplitude g that multiplies a fixed external template D_EB,EDE_ℓ (Eq. 4) generated by a modified CLASS code for literature values of (f_EDE, z_c, θ_i). Neither quantity is defined in terms of the other, nor is either obtained by fitting a subset of the same data and then re-predicting a related observable. Self-citations are exclusively to earlier BICEP/Keck pipeline papers (map-making, purification, band-power covariance, jackknife tests) whose performance is re-validated here on 499 end-to-end simulations (Tables S1–S6). No uniqueness theorem, ansatz, or renaming of a known empirical pattern is load-bearing. The only mild self-referential element is the reuse of the collaboration’s own foreground and likelihood framework, which is independently exercised by the simulation suite and does not force the reported null results. Hence the circularity score is 1.

Assumptions & free parameters 4 free parameters · 4 assumptions · 1 invented entities

The central null results rest on standard CMB power-spectrum modeling, a Chern–Simons interaction term taken from the literature, fixed EDE background parameters taken from external fits, and a set of free amplitudes (g, Δβ, α_ν, foregrounds) that are fitted to the BK18 bandpowers. No new dynamical entities are postulated; the step-function β(ℓ) is a purely phenomenological ansatz.

free parameters (4)
  • g (axion-photon coupling) = 0.11 ± 0.37 (f_EDE=0.087)
    Overall amplitude of the EDE-induced EB template; floated while all other EDE parameters are held fixed.
  • Δβ_ℓb (step amplitude) = consistent with 0, |Δβ| ≲ 0.15°
    Size of the multipole-dependent rotation jump at each chosen breakpoint; the sole free parameter of the model-independent analysis.
  • α_ν (per-band instrumental angles)
    Four free angles (95 large-field, 95, 150, 220 GHz) that absorb absolute polarization calibration uncertainty; marginalized in all results.
  • A_lens, A_d^{XY}, α_d^{XY}, β_d, A_s^{XY}, …
    Standard foreground and lensing amplitudes floated or fixed according to the analysis configuration; necessary to isolate the cosmological EB signal.
assumptions (4)
  • domain assumption CMB polarization is generated at recombination and can be decomposed into parity-even E and parity-odd B modes whose cross-spectrum vanishes in the absence of birefringence or systematics.
    Standard result used throughout Sections I–II to interpret a non-zero EB as a birefringence signature.
  • domain assumption A Chern–Simons interaction L ⊃ −(1/4)g ϕ F μν F̃ μν produces a polarization rotation angle proportional to the change in the pseudoscalar field ϕ.
    Taken from the axion-photon literature (Eq. 1) and used to generate the EDE EB templates.
  • ad hoc to paper The multipole dependence of the rotation can be adequately captured by a single Heaviside step at a chosen breakpoint ℓ_b.
    Explicit modeling choice (Eq. 8) adopted to keep the number of free parameters minimal; more flexible β(ℓ) forms are deferred to future work.
  • ad hoc to paper Background EDE parameters (f_EDE, z_c, θ_i) and standard ΛCDM parameters may be fixed at external best-fit values while only g is varied.
    Stated in Section II D to avoid volume effects; the recovered g therefore inherits any template mismatch.
invented entities (1)
  • phenomenological step-function β(ℓ)
    purpose: Provides a model-independent probe of multipole-dependent rotation without committing to a specific EDE trajectory.
    Introduced in Section II and validated on simulations; it is an analysis tool rather than a new physical field.

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Cite this review

Pith. "Pith review of BICEP/Keck XXI: Constraints on Early-Universe Parity Violation from Multipole-Dependent Birefringence." pith.science (2026). https://pith.science/paper/JT3W5QFY

@misc{pith2026260306812,
  author       = {Pith},
  title        = {Pith review of: BICEP/Keck XXI: Constraints on Early-Universe Parity Violation from Multipole-Dependent Birefringence},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JT3W5QFY}},
  note         = {Machine review of arXiv:2603.06812}
}
read the original abstract

We present the first constraints on multipole-dependent cosmic birefringence using CMB polarization data from the BK18 dataset, which combines observations from BICEP2, Keck Array, and BICEP3 at frequencies of 95, 150, and 220 GHz. Photon coupling to an axion-like field leads to the rotation of CMB polarization, inducing non-zero EB cross-correlations. We show that a multipole-dependent rotation beta(l) imprints a distinct signature in the polarization spectra that can be constrained. Specifically, we consider an Early Dark Energy (EDE) scenario in which a pseudoscalar field couples to photons through a Chern-Simons interaction, generating a polarization rotation with multipole dependence. We introduce a phenomenological beta(l) as a step function, obtaining constraints on the step function size consistent with zero, with uncertainties less than 0.15 degrees (68% CL). In addition, using multi-frequency EE, BB, and EB cross-spectra, along with robust BICEP/Keck foreground treatment and likelihood framework, we derive constraints on the axion-photon coupling amplitude g for several choices of EDE parameters. For the baseline best-fit value f_{EDE} = 0.087 from the Planck 2018 analysis, we obtain g = 0.11 +/- 0.37 (68% CL), consistent with previous limits.

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Works this paper leans on

60 extracted references

  1. [1]

    We then compile the best-fit values from 9 TABLE I:Best-fit cosmological parameters for Early Dark Energy (EDE) modelsbased on ACT and Planckdatasets, compiled from [36, 39]

    Impact of Different Polarization Cross-Spectra Our MCMC likelihood supports fitting to different combinations of polarization spectra: •Marginalizing over foregrounds, freeA s andA d: –EE+EB –EE+EB+BB(A lens fixed to 1) –EE+EB+BB(freeA lens) •Without marginalizing over foregrounds,A s and Ad set to zero: –EB-only For each test configuration, we run the pi...

  2. [2]

    We use a modified version ofCLASS[44] developed by Murai et al.[29] to generate four differentD EB,EDE ℓ curves us- ing the EDE parameters described in Table I

    Impact of EDE Parameters Used in Generating the EB Curve We also examine how the recovered polarization ro- tation anglesα ν and couplinggvary as a function of theEBtemplateD EB,EDE ℓ used in the likelihood, un- der bothg= 0 andg= 1 simulation scenarios. We use a modified version ofCLASS[44] developed by Murai et al.[29] to generate four differentD EB,EDE...

  3. [3]

    The baselinedataset uses a Gaussian dust model for fore- 10 grounds in the BICEP/Keckpatch

    Impact of Different Dust Models We run the MCMC pipeline on multiple datasets us- ing a variety of dust models to assess the impact of fore- ground modeling on the estimator’s recovery ofg. The baselinedataset uses a Gaussian dust model for fore- 10 grounds in the BICEP/Keckpatch. To test robustness, we repeat the analysis using several alternative dust r...

  4. [4]

    This test evaluates whether the estima- tor can recover rotation angles correctly without biasing the inference of the photon-axion coupling parameterg

    Impact of Injected Per-Band Rotation To validate the robustness of our estimator against isotropic per-band rotation from instrumental sources, we inject known polarization rotation angles directly into theEBspectra. This test evaluates whether the estima- tor can recover rotation angles correctly without biasing the inference of the photon-axion coupling...

    2018

  5. [5]

    Finelli and M

    F. Finelli and M. Galaverni, Rotation of Linear Polariza- tion Plane and Circular Polarization from Cosmological Pseudoscalar Fields, Phys. Rev. D79, 063002 (2009)

    2009

  6. [6]

    Minami and E

    Y. Minami and E. Komatsu, New Extraction of the Cosmic Birefringence from the Planck 2018 Polarization Data, Phys. Rev. Lett.125, 221301 (2020)

    2018

  7. [7]

    J. Q. Xia, H. Li, and X. Zhang, Probing CPT viola- tion with CMB polarization measurements, Phys. Lett. B687, 129 (2010)

    2010

  8. [8]

    Diego-Palazuelos, J

    P. Diego-Palazuelos, J. R. Eskilt, Y. Minami,et al., Cos- mic Birefringence from Planck Data Release 4, Phys. Rev. Lett.130, 141001 (2022)

    2022

Show all 60 references
  1. [9]

    J. R. Eskilt and E. Komatsu, Improved Constraints on Cosmic Birefringence from the WMAP and Planck Cosmic Microwave Background Polarization Data, Phys. Rev. D106, 063503 (2022)

    2022

  2. [10]

    G.-C. Liu, S. Lee, and K.-W. Ng, Effect on Cos- mic Microwave Background Polarization of Coupling of Quintessence to Pseudoscalar Fields, Phys. Rev. Lett.97, 161303 (2006)

    2006

  3. [11]

    S. M. Carroll, G. B. Field, and R. Jackiw, Limits on a Lorentz- and Parity-Violating Modification of Electrody- namics, Phys. Rev. D41, 1231 (1990)

    1990

  4. [12]

    Greco, N

    A. Greco, N. Bartolo, and A. Gruppuso, A New Solu- tion for the Observed Isotropic Cosmic Birefringence An- gle and its Implications for the Anisotropic Counterpart through a Boltzmann Approach, J. Cosmol. Astropart. Phys.10, 028

  5. [13]

    Fujita, K

    T. Fujita, K. Murai, H. Nakatsuka, and S. Tsujikawa, Detection of isotropic cosmic birefringence and its im- plications for axionlike particles including dark energy, Phys. Rev. D103, 043509 (2021)

    2021

  6. [14]

    Nakagawa, F

    S. Nakagawa, F. Takahashi, and W. Yin, Early dark en- ergy by dark Higgs, and axion-induced non-thermal trap- ping, Phys. Rev. D107, 063016 (2023)

    2023

  7. [15]

    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. B289, 67 (1992)

    1992

  8. [16]

    Kamionkowski, A

    M. Kamionkowski, A. Kosowsky, and A. Stebbins, A Probe of Primordial Gravity Waves and Vorticity, Phys. Rev. Lett.78, 2058 (1997)

  9. [17]

    Zaldarriaga and U

    M. Zaldarriaga and U. Seljak, All-sky analysis of polar- ization in the microwave background, Phys. Rev. D55, 1830 (1997)

    1997

  10. [18]

    BICEP/Keck and Planck Collaborations, P. A. R. Ade, N. Aghanim,et al., A Joint Analysis of BICEP2/Keck Array and Planck Data, Phys. Rev. Lett.114, 101301 (2015)

    2015

  11. [19]

    A. Lue, L. Wang, and M. Kamionkowski, Cosmologi- cal Signature of New Parity-Violating Interactions, Phys. Rev. Lett.83, 1506 (1999)

    1999

  12. [20]

    Kamionkowski, How to De-Rotate the Cosmic Mi- crowave Background Polarization, Phys

    M. Kamionkowski, How to De-Rotate the Cosmic Mi- crowave Background Polarization, Phys. Rev. Lett.102, 111302 (2009)

    2009

  13. [21]

    E. Y. S. Wu, P. Ade, J. Bock,et al., Parity Violation Con- straints Using Cosmic Microwave Background Polariza- tion Spectra from QUaD, Phys. Rev. Lett.102, 161302 (2009)

    2009

  14. [22]

    BICEP/Keck Collaboration, P. A. R. Ade, Z. Ahmed, et al., BICEP/Keck XVIII: Measurement of BICEP3 po- larization angles and consequences for constraining cos- mic birefringence and inflation, Phys. Rev. D111, 063505 (2025)

    2025

  15. [23]

    Cornelison, C

    J. Cornelison, C. Verg` es, P. A. R. Ade, Z. Ahmed, M. Amiri,et al., Improved polarization calibration of the BICEP3 CMB polarimeter at the south pole, inSPIE Astronomical Telescopes + Instrumentation 2022(2022) p. 121901X

    2022

  16. [24]

    Bianchini, W

    F. Bianchini, W. L. K. Wu,et al., Searching for Anisotropic Cosmic Birefringence with Polarization Data from SPTpol, Phys. Rev. D102, 083504 (2020)

    2020

  17. [25]

    Contreras, P

    D. Contreras, P. Boubel, and D. Scott, Constraints on direction-dependent cosmic birefringence from planck po- larization data, Journal of Cosmology and Astroparticle Physics2017(12), 046

  18. [26]

    K. R. Ferguson, A. J. Anderson, N. Whitehorn,et al., 13 Searching for axion-like time-dependent cosmic birefrin- gence with data from SPT-3G, Phys. Rev. D106, 042011 (2022)

    2022

  19. [27]

    BICEP2 / Keck Array Collaboration, P. A. R. Ade, Z. Ahmed,et al., BICEP2 / Keck Array IX: New bounds on anisotropies of CMB polarization rotation and impli- cations for axionlike particles and primordial magnetic fields, Phys. Rev. D96, 102003 (2017)

    2017

  20. [28]

    BICEP / Keck Collaboration, P. A. R. Ade, Z. Ahmed, et al., BICEP / Keck XII: Constraints on axion-like polarization oscillations in the cosmic microwave back- ground, Phys. Rev. D103, 042002 (2021)

    2021

  21. [29]

    BICEP / Keck Collaboration, P. A. R. Ade, Z. Ahmed, et al., BICEP / Keck XIV: Improved constraints on axion-like polarization oscillations in the cosmic mi- crowave background, Phys. Rev. D105, 022006 (2022)

    2022

  22. [30]

    BICEP / Keck Collaboration, P. A. R. Ade, Z. Ahmed, et al., BICEP / Keck XVII: Line of Sight Distortion Anal- ysis: Estimates of Gravitational Lensing, Anisotropic Cosmic Birefringence, Patchy Reionization, and System- atic Errors, Astrophys. J.949, 43 (2023)

    2023

  23. [31]

    A. J. Cukierman, S. E. Clark, and G. Halal, Magnetic Misalignment of Interstellar Dust Filaments, Astrophys. J.946, 106 (2023)

    2023

  24. [32]

    J. R. Eskilt, L. Herold, E. Komatsu,et al., Constraint on Early Dark Energy from Isotropic Cosmic Birefringence, Astron. Astrophys.675, A89 (2023)

    2023

  25. [33]

    Murai, F

    K. Murai, F. Naokawa, T. Namikawa, and E. Komatsu, Isotropic cosmic birefringence from early dark energy, Phys. Rev. D107, L041302 (2023)

    2023

  26. [34]

    J. L. Bernal, L. Verde, and A. G. Riess, The trouble with H0, J. Cosmol. Astropart. Phys.10, 019

  27. [35]

    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)

    2023

  28. [36]

    Karwal and M

    T. Karwal and M. Kamionkowski, Dark energy at early times, the Hubble tension, and the string axiverse, Phys. Rev. D94, 103523 (2016)

    2016

  29. [37]

    Herold, E

    L. Herold, E. G. M. Ferreira, and E. Komatsu, New con- straint on Early Dark Energy from Planck and BOSS data using the profile likelihood, Astrophys. J. Lett.929, L16 (2022)

    2022

  30. [38]

    T. L. Smith, V. Poulin, J. L. Bernal,et al., Early dark energy is not excluded by current large-scale structure data, Phys. Rev. D103, 123542 (2021)

    2021

  31. [39]

    Reeves, L

    A. Reeves, L. Herold, S. Vagnozzi,et al., Restoring cos- mological concordance with early dark energy and mas- sive neutrinos?, Mon. Not. Roy. Astron. Soc.520, 3688 (2023)

    2023

  32. [40]

    Herold,Resolving the Hubble tension with Early Dark Energy, Ph.D

    L. Herold,Resolving the Hubble tension with Early Dark Energy, Ph.D. thesis, Ludwig-Maximilians-Universit¨ at M¨ unchen, Munich, Germany (2023)

    2023

  33. [41]

    Poulin, T

    V. Poulin, T. L. Smith, and T. Karwal, The Ups and Downs of Early Dark Energy solutions to the Hubble tension: a review of models, hints and constraints circa 2023, Phys. Rep.1032, 1 (2023)

    2023

  34. [42]

    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. D105, 123509 (2022)

    2022

  35. [43]

    J. C. Hill, E. Calabrese, S. Aiola,et al., The At- acama Cosmology Telescope: Constraints on Pre- Recombination Early Dark Energy, Phys. Rev. D105, 123536 (2022)

    2022

  36. [44]

    BICEP/Keck Collaboration, P. A. R. Ade, Z. Ahmed, et al., BICEP/Keck XIII: Improved Constraints on Pri- mordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season, Phys. Rev. Lett.127, 151301 (2021)

    2018

  37. [45]

    Planck Collaboration, P. A. R. Ade, N. Aghanim,et al., Planck 2015 results. XIX. Constraints on primordial mag- netic fields, Astron. Astrophys.594, A19 (2016)

    2015

  38. [46]

    Lewis, A

    A. Lewis, A. Challinor, and A. Lasenby, Efficient Com- putation of CMB anisotropies in closed FRW models, Astrophys. J.538, 473 (2000)

    2000

  39. [47]

    Planck Collaboration, P. Ade, N. Aghanim,et al., Planck 2013 results. XVI. Cosmological parameters, Astron. As- trophys.571, A16 (2014)

    2013

  40. [48]

    D. Blas, J. Lesgourgues, and T. Tram, The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes, J. Cosmol. Astropart. Phys.07, 034

  41. [49]

    B. Feng, H. Li, M. Li, and X. Zhang, Gravitational Lep- togenesis and Its Signatures in CMB, Phys. Lett. B620, 27 (2005)

    2005

  42. [50]

    Cai and Y

    H. Cai and Y. Guan, Computing microwave background polarization power spectra from cosmic birefringence, Phys. Rev. D105, 063536 (2022)

    2022

  43. [51]

    BICEP/Keck Collaboration, P. A. R. Ade, Z. Ahmed, et al., BICEP2 / Keck Array X: Constraints on Primor- dial Gravitational Waves Using Planck, WMAP, and New BICEP2/Keck Observations through the 2015 Season, Phys. Rev. Lett.121, 221301 (2018)

    2015

  44. [52]

    Poulin, T

    V. Poulin, T. L. Smith, T. Karwal, and M. Kamionkowski, Early Dark Energy Can Resolve The Hubble Tension, Phys. Rev. Lett.122, 221301 (2019)

    2019

  45. [53]

    Calabrese, J

    E. Calabrese, J. C. Hill, H. T. Jensen,et al., The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models, J. Cosmol. Astropart. Phys.10, 082

  46. [54]

    Torrado and A

    J. Torrado and A. Lewis, Cobaya: Code for Bayesian Analysis of hierarchical physical models, J. Cosmol. As- tropart. Phys.05, 057

  47. [55]

    Gelman and D

    A. Gelman and D. B. Rubin, Inference from Iterative Simulation Using Multiple Sequences, Statist. Sci.7, 457 (1992)

    1992

  48. [56]

    Dunkley, M

    J. Dunkley, M. Bucher, P. G. Ferreira, K. Moodley, and C. Skordis, Fast and reliable Markov chain Monte Carlo technique for cosmological parameter estimation, Mon. Not. Roy. Astron. Soc.356, 925 (2005), astro- ph/0405462

    2005

  49. [57]

    Planck Collaboration, Planck 2018 Results. III. High Frequency Instrument Data Processing and Frequency Maps, Astron. Astrophys.641, A3 (2020)

    2018

  50. [58]

    BICEP/Keck Collaboration, P. A. R. Ade, Z. Ahmed, et al., BICEP2 / Keck Array VII: Matrix Based E/B Separation Applied to BICEP2 and the Keck Array, As- trophys. J.825, 66 (2016)

    2016

  51. [59]

    BICEP2 Collaboration, P. A. R. Ade, R. W. Aikin,et al., BICEP2 I: Detection of B-mode Polarization at Degree Angular Scales, Phys. Rev. Lett.112, 241101 (2014)

    2014

  52. [60]

    G. E. Addison, C. L. Bennett, M. Halpern, G. Hinshaw, and J. L. Weiland, Revisiting theAL Lensing Anomaly in Planck 2018 Temperature Data, Astrophys. J.961, 161 (2024). 14 Appendix: Supplementary Figures and T able (a) Examples ofβ(ℓ) modeled as step functions at various break...

    2018

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