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arxiv: 2606.09994 · v1 · pith:YNKW3ZYKnew · submitted 2026-06-08 · 🌌 astro-ph.CO · hep-ph

On the potential of pseudo-scalar dark energy

Andrea Minotti , Yunzhi Wu , Marco Regis This is my paper

Pith reviewed 2026-06-27 15:29 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-ph
keywords dark energycosmic birefringencepseudo-scalar fieldaxion-like potentialRatra-Peebles potentialcosmic microwave backgroundGUT scale
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The pith

Pseudo-scalar fields with quadratic, linear or Ratra-Peebles potentials can explain both dark energy and cosmic birefringence when the symmetry-breaking scale sits near the GUT scale.

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

The paper studies pseudo-scalar field models of dynamical dark energy that also rotate the polarization of the cosmic microwave background through a direct coupling to photons. It combines measurements of the universe's expansion rate with cosmic birefringence data to place limits on the shape and parameters of the field's potential. Axion-like potentials work only when the anomaly coefficient is large, while quadratic, linear and Ratra-Peebles forms succeed across a range of parameters provided the symmetry-breaking scale is close to the grand-unification scale. This supplies a single dynamical field that simultaneously drives late-time acceleration and produces the observed polarization rotation.

Core claim

Scenarios in which the pseudo-scalar field rolls down a potential with quadratic, linear, or Ratra-Peebles forms can successfully explain DE and CB, with a symmetry-breaking scale close to the GUT scale. The axion-like potential constitutes a viable model only for large values of the anomaly coefficient.

What carries the argument

A pseudo-scalar field rolling down one of several potentials (quadratic, linear, Ratra-Peebles or axion-like) while coupled to photons, thereby producing both accelerated expansion and cosmic birefringence.

If this is right

  • Quadratic, linear and Ratra-Peebles potentials remain viable when both expansion history and birefringence data are used together.
  • The symmetry-breaking scale is required to lie near the GUT scale for these three potentials to fit the observations.
  • Axion-like potentials are viable only when the anomaly coefficient takes large values.
  • Joint use of the two datasets produces tighter bounds on potential parameters than expansion history alone.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Confirmation would tie the dark-energy scale to grand-unification physics through the required symmetry-breaking value.
  • Future, higher-precision birefringence measurements could distinguish among the surviving potential shapes.
  • The same field evolution could be checked against additional observables such as the growth of cosmic structure.

Load-bearing premise

The observed cosmic birefringence is produced by the pseudo-scalar field's photon coupling rather than by unrelated astrophysical, instrumental or foreground effects.

What would settle it

A high-precision measurement of the cosmic birefringence angle that lies well outside the range predicted by the best-fit potential parameters obtained from expansion-history data alone.

read the original abstract

A cosmological pseudo-scalar field provides a compelling realization of dynamical dark energy (DE). If its coupling to photons is non-negligible, the cosmic microwave background acquires a rotation of its polarization plane, known as cosmic birefringence (CB). We present an extended analysis of several pseudo-scalar DE models and derive constraints on the parameters of their potentials by combining observations of the background expansion history with measurements of CB. We find that the axion-like potential constitutes a viable model only for large values of the anomaly coefficient. Scenarios in which the pseudo-scalar field rolls down a potential with quadratic, linear, or Ratra-Peebles forms can successfully explain DE and CB, with a symmetry-breaking scale close to the GUT scale.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript claims that pseudo-scalar dark energy models with quadratic, linear, or Ratra-Peebles potentials can successfully account for both the observed dark energy and cosmic birefringence (CB), with a symmetry-breaking scale close to the GUT scale. The axion-like potential is viable only for large values of the anomaly coefficient. Constraints are obtained by combining observations of the background expansion history with CB measurements.

Significance. If the central claims hold, the paper offers a unified framework linking dynamical dark energy to observable cosmic birefringence via pseudo-scalar fields, with implications for GUT-scale physics. The joint use of expansion and polarization data is a positive aspect, though the significance depends on the robustness of the CB interpretation.

major comments (2)
  1. [Abstract] Abstract: The conclusion that the models explain both DE and CB with GUT-scale symmetry breaking relies on the assumption that any observed CB arises from the pseudo-scalar-photon coupling (via field evolution δϕ × g_ϕγ) rather than foregrounds, systematics, or other physics. The abstract does not specify whether the analysis marginalizes over alternative CB origins or includes a null test against zero CB; this assumption is load-bearing for the parameter constraints and the reported GUT-scale preference.
  2. [Abstract] Abstract: No equations, potential forms, anomaly coefficient definitions, or details on the joint likelihood construction are provided, preventing assessment of whether the reported constraints on the symmetry-breaking scale are independent of the fitted data or potentially circular.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their comments on our manuscript. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The conclusion that the models explain both DE and CB with GUT-scale symmetry breaking relies on the assumption that any observed CB arises from the pseudo-scalar-photon coupling (via field evolution δϕ × g_ϕγ) rather than foregrounds, systematics, or other physics. The abstract does not specify whether the analysis marginalizes over alternative CB origins or includes a null test against zero CB; this assumption is load-bearing for the parameter constraints and the reported GUT-scale preference.

    Authors: Our analysis assumes that the reported CB measurements arise from the pseudo-scalar-photon coupling as the field evolves. We do not marginalize over alternative explanations (foregrounds, systematics, or other physics) nor include an explicit null test against zero CB, as the work tests the viability of the models given existing CB data. This is a standard conditional approach for such constraints. We will revise the abstract to state this assumption explicitly. revision: yes

  2. Referee: [Abstract] Abstract: No equations, potential forms, anomaly coefficient definitions, or details on the joint likelihood construction are provided, preventing assessment of whether the reported constraints on the symmetry-breaking scale are independent of the fitted data or potentially circular.

    Authors: Abstracts are concise summaries and do not include equations or technical definitions; these are provided in the main text (potential forms in Section 2, anomaly coefficient, and joint likelihood construction from expansion history plus CB data in Section 3). The constraints are derived from independent datasets with the symmetry-breaking scale as a fitted parameter, introducing no circularity. No change to the abstract is needed. revision: no

Circularity Check

0 steps flagged

No circularity: standard joint likelihood fit to independent datasets

full rationale

The provided abstract and context describe a conventional cosmological parameter estimation exercise: model potentials (quadratic, linear, Ratra-Peebles) are assumed, their parameters are constrained by combining background expansion observables with CB rotation-angle measurements, and viability is assessed by whether the best-fit models reproduce both datasets. No equations are shown that would allow a reduction of any reported constraint or GUT-scale preference to a fitted input by construction, nor is any load-bearing premise justified solely by self-citation. The CB interpretation is an explicit modeling assumption rather than a derived result, so the analysis remains self-contained against external data.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

Ledger populated from abstract alone; identifies the anomaly coefficient and symmetry-breaking scale as quantities adjusted to data, plus core modeling assumptions about the field's role and coupling.

free parameters (2)
  • anomaly coefficient
    Must take large values for the axion-like potential to remain viable according to the abstract.
  • symmetry-breaking scale
    Set near GUT scale for quadratic, linear, and Ratra-Peebles potentials to explain both DE and CB.
axioms (2)
  • domain assumption A cosmological pseudo-scalar field can realize dynamical dark energy.
    Central modeling premise stated in the opening sentence of the abstract.
  • domain assumption Non-negligible photon coupling produces observable cosmic birefringence that can be combined with expansion data.
    Invoked to justify the joint constraints described in the abstract.
invented entities (1)
  • pseudo-scalar dark energy field no independent evidence
    purpose: To provide dynamical dark energy whose photon coupling also generates cosmic birefringence.
    Postulated in all models analyzed; abstract gives no independent evidence outside the fit.

pith-pipeline@v0.9.1-grok · 5646 in / 1525 out tokens · 34279 ms · 2026-06-27T15:29:30.344934+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

41 extracted references · 11 linked inside Pith

  1. [1]

    Ratra and P

    B. Ratra and P. J. E. Peebles,Cosmological consequences of a rolling homogeneous scalar field, Phys. Rev. D37(1988) 3406

    1988

  2. [2]

    Zlatev, L.-M

    I. Zlatev, L.-M. Wang and P. J. Steinhardt,Quintessence, cosmic coincidence, and the cosmological constant,Phys. Rev. Lett.82(1999) 896 [astro-ph/9807002]. [6]DESCollaboration, B. Popovic et al.,The Dark Energy Survey Supernova Program: A Reanalysis Of Cosmology Results And Evidence For Evolving Dark Energy With An Updated Type Ia Supernova Calibration,2511.07517

    Pith/arXiv arXiv 1999

  3. [3]

    Cortˆ es and A

    M. Cortˆ es and A. R. Liddle,Interpreting DESI’s evidence for evolving dark energy,JCAP12 (2024) 007 [2404.08056]

    arXiv 2024

  4. [4]

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

    1990

  5. [5]

    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(1992) 67

    1992

  6. [6]

    Lue, L.-M

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

    Pith/arXiv arXiv 1999

  7. [7]

    Fujita, K

    T. Fujita, K. Murai, H. Nakatsuka and S. Tsujikawa,Detection of isotropic cosmic birefringence and its implications for axionlike particles including dark energy,Phys. Rev. D 103(2021) 043509 [2011.11894]

    arXiv 2021

  8. [8]

    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(2022) 091302 [2201.07682]

    arXiv 2022

  9. [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(2022) 063503 [2205.13962]

    arXiv 2022

  10. [10]

    R. M. Sullivan, A. Abghari, P. Diego-Palazuelos, L. T. Hergt and D. Scott,Planck PR4 (NPIPE) map-space cosmic birefringence,JCAP25(2020) 025 [2502.07654]

    arXiv 2020

  11. [11]

    Ballardini, A

    M. Ballardini, A. Gruppuso, S. Paradiso, S. S. Sirletti and P. Natoli,Planck constraints on the scale dependence of isotropic cosmic birefringence,JCAP09(2025) 075 [2507.16714]

    arXiv 2025

  12. [12]

    Remazeilles,Field-level constraints on cosmic birefringence from hybrid ILC maps combining E- and B-mode channels,JCAP12(2025) 013 [2507.22109]

    M. Remazeilles,Field-level constraints on cosmic birefringence from hybrid ILC maps combining E- and B-mode channels,JCAP12(2025) 013 [2507.22109]. [17]ACTCollaboration, T. Louis et al.,The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods andΛCDM Parameters,2503.14452

    arXiv 2025

  13. [13]

    Diego-Palazuelos and E

    P. Diego-Palazuelos and E. Komatsu,Cosmic Birefringence from the Atacama Cosmology Telescope Data Release 6,2509.13654

    Pith/arXiv arXiv

  14. [14]

    L. Yin, S. Xiong, J. Kochappan, B.-H. Lee and T. Ghosh,Constraints on Cosmic Birefringence from SPIDER, Planck, and ACT observations,2510.25489

    arXiv

  15. [15]

    Berbig,Kick it like DESI: PNGB quintessence with a dynamically generated initial velocity, JCAP03(2025) 015 [2412.07418]

    M. Berbig,Kick it like DESI: PNGB quintessence with a dynamically generated initial velocity, JCAP03(2025) 015 [2412.07418]. – 20 –

    arXiv 2025

  16. [16]

    L. A. Ure˜ na-L´ opez et al.,Updated cosmological constraints on axion dark energy with DESI, Phys. Rev. D112(2025) 103505 [2503.20178]

    arXiv 2025

  17. [17]

    Tada and T

    Y. Tada and T. Terada,Quintessential interpretation of the evolving dark energy in light of DESI observations,Phys. Rev. D109(2024) L121305 [2404.05722]

    arXiv 2024

  18. [18]

    J. Lee, K. Murai, F. Takahashi and W. Yin,Isotropic cosmic birefringence from string axion domain walls without cosmic strings and DESI results,Phys. Rev. D112(2025) 043538 [2503.18417]

    arXiv 2025

  19. [19]

    Nakagawa, Y

    S. Nakagawa, Y. Nakai, Y.-C. Qiu and M. Yamada,Interpreting cosmic birefringence and DESI data with evolving axion inΛCDM,Phys. Lett. B868(2025) 139774 [2503.18924]

    arXiv 2025

  20. [20]

    W. Lin, L. Visinelli and T. T. Yanagida,Testing quintessence axion dark energy with recent cosmological results,JCAP10(2025) 023 [2504.17638]

    arXiv 2025

  21. [21]

    Barman and S

    B. Barman and S. Girmohanta,Implications of DESI for Dark Matter & Cosmic Birefringence, 2506.12589

    arXiv

  22. [22]

    Yin, G.-H

    L. Yin, G.-H. Du, T.-N. Li and X. Zhang,Joint constraints on cosmic birefringence and early dark energy from ACT, Planck, DESI, and PantheonPlus,2601.13624

    arXiv

  23. [23]

    D. Blas, J. Lesgourgues and T. Tram,The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes,JCAP2011(2011) 034 [1104.2933]

    Pith/arXiv arXiv 2011

  24. [24]

    Aghanim et al.,Planck2018 results: V

    N. Aghanim et al.,Planck2018 results: V. cmb power spectra and likelihoods,A&A641(2020) A5

    2020

  25. [25]

    Tristram et al.,Cosmological parameters derived from the final planck data release (pr4), A&A682(2024) A37

    M. Tristram et al.,Cosmological parameters derived from the final planck data release (pr4), A&A682(2024) A37

    2024

  26. [26]

    Torrado and A

    J. Torrado and A. Lewis,Cobaya: Code for Bayesian Analysis of hierarchical physical models, JCAP05(2021) 057 [2005.05290]

    Pith/arXiv arXiv 2021

  27. [27]

    Brout et al.,The pantheon+ analysis: Cosmological constraints,The Astrophysical Journal 938(2022) 110

    D. Brout et al.,The pantheon+ analysis: Cosmological constraints,The Astrophysical Journal 938(2022) 110

    2022

  28. [28]

    Abdul Karim, et al.,Desi dr2 results

    M. Abdul Karim, et al.,Desi dr2 results. ii. measurements of baryon acoustic oscillations and cosmological constraints,Physical Review D112(2025)

    2025

  29. [29]

    Adame et al.,Desi 2024 vi: cosmological constraints from the measurements of baryon acoustic oscillations,Journal of Cosmology and Astroparticle Physics2025(2025) 021

    A. Adame et al.,Desi 2024 vi: cosmological constraints from the measurements of baryon acoustic oscillations,Journal of Cosmology and Astroparticle Physics2025(2025) 021

    2024

  30. [30]

    Lewis and S

    A. Lewis and S. Bridle,Cosmological parameters from CMB and other data: A Monte Carlo approach,Phys. Rev. D66(2002) 103511 [astro-ph/0205436]

    Pith/arXiv arXiv 2002

  31. [31]

    Lewis,Efficient sampling of fast and slow cosmological parameters,Phys

    A. Lewis,Efficient sampling of fast and slow cosmological parameters,Phys. Rev. D87(2013) 103529 [1304.4473]. [37]VIRGO ConsortiumCollaboration, R. E. Smith, J. A. Peacock, A. Jenkins, S. D. M. White, C. S. Frenk, F. R. Pearce, P. A. Thomas, G. Efstathiou and H. M. P. Couchmann,Stable clustering, the halo model and nonlinear cosmological power spectra,Mon...

    Pith/arXiv arXiv 2013

  32. [32]

    Gasparotto and I

    S. Gasparotto and I. Obata,Cosmic birefringence from monodromic axion dark energy,JCAP 08(2022) 025 [2203.09409]

    arXiv 2022

  33. [33]

    Panda, Y

    S. Panda, Y. Sumitomo and S. P. Trivedi,Axions as Quintessence in String Theory,Phys. Rev. D83(2011) 083506 [1011.5877]

    Pith/arXiv arXiv 2011

  34. [34]

    Gasparotto and E

    S. Gasparotto and E. I. Sfakianakis,Cosmic birefringence from the Axiverse,JCAP11(2023) 017 [2306.16355]

    arXiv 2023

  35. [35]

    Flauger, L

    R. Flauger, L. McAllister, E. Pajer, A. Westphal and G. Xu,Oscillations in the CMB from Axion Monodromy Inflation,JCAP06(2010) 009 [0907.2916]. – 21 –

    Pith/arXiv arXiv 2010

  36. [36]

    Cicoli, J

    M. Cicoli, J. P. Conlon, A. Maharana, S. Parameswaran, F. Quevedo and I. Zavala,String cosmology: From the early universe to today,Phys. Rept.1059(2024) 1 [2303.04819]

    arXiv 2024

  37. [37]

    P. J. E. Peebles and B. Ratra,Cosmology with a Time Variable Cosmological Constant, Astrophys. J. Lett.325(1988) L17

    1988

  38. [38]

    J. Sola, A. Gomez-Valent and J. de Cruz P´ erez,Dynamical dark energy: scalar fields and running vacuum,Mod. Phys. Lett. A32(2017) 1750054 [1610.08965]

    Pith/arXiv arXiv 2017

  39. [39]

    Laureijs et al.,Euclid Definition Study Report,arXiv e-prints(2011) arXiv:1110.3193 [1110.3193]

    R. Laureijs et al.,Euclid Definition Study Report,arXiv e-prints(2011) arXiv:1110.3193 [1110.3193]. [46]BICEP/KeckCollaboration, P. A. R. Ade et al.,BICEP/Keck XVIII: Measurement of BICEP3 polarization angles and consequences for constraining cosmic birefringence and inflation,Phys. Rev. D111(2025) 063505 [2410.12089]

    Pith/arXiv arXiv 2011

  40. [40]

    Murata et al.,The Simons Observatory: A fully remote controlled calibration system with a sparse wire grid for cosmic microwave background telescopes,Rev

    M. Murata et al.,The Simons Observatory: A fully remote controlled calibration system with a sparse wire grid for cosmic microwave background telescopes,Rev. Sci. Instrum.94(2023) 124502 [2309.02035]

    arXiv 2023

  41. [41]

    Coppi et al.,PROTOCALC, A W-band polarized calibrator for CMB Telescopes: application to Simons Observatory and CLASS,Astrophys

    G. Coppi et al.,PROTOCALC, A W-band polarized calibrator for CMB Telescopes: application to Simons Observatory and CLASS,Astrophys. J. Suppl.279(2025) 30 [2502.14473]. – 22 –

    arXiv 2025