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arxiv: 2605.14684 · v1 · pith:2VTHRSF6new · submitted 2026-05-14 · ✦ hep-th · gr-qc· hep-ph

QCD axion from broken scale symmetry

Georgios K. Karananas , Mikhail Shaposhnikov This is my paper

Pith reviewed 2026-06-30 20:41 UTC · model grok-4.3

classification ✦ hep-th gr-qchep-ph
keywords QCD axiondilatonscale invariancedomain wallsaxion cosmologynon-compact axionspontaneous symmetry breaking
0
0 comments X

The pith

The dilaton from spontaneously broken scale invariance can serve as the QCD axion while satisfying all consistency conditions for non-compact cosmology.

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

The paper shows that the dilaton meets the three requirements for a viable non-compact axion cosmology: it is a non-periodic field, it supports an effective field theory valid above the inflationary scale, and it supplies a small non-QCD term in the potential that tilts the vacuum and causes domain walls to collapse on time. Standard periodic axion models encounter problems with domain walls and high-scale validity that this construction aims to bypass by identifying the axion with the pseudo-Nambu-Goldstone boson of approximate scale invariance. A reader would care because the approach ties the axion solution directly to scale symmetry breaking without introducing extra fields or mechanisms.

Core claim

All conditions for a consistent non-compact axion cosmology can be met by the dilaton, the pseudo-Nambu-Goldstone boson of spontaneously broken approximate scale invariance, which provides a non-periodic field, keeps the effective theory valid above inflation, and contributes a small non-QCD piece to the potential that tilts the axionic landscape to trigger timely domain-wall collapse.

What carries the argument

The dilaton as the pseudo-Nambu-Goldstone boson of spontaneously broken approximate scale invariance, which supplies the non-periodic field and the required small non-QCD potential tilt.

If this is right

  • The axion field remains non-periodic, removing the usual domain-wall network issue.
  • The effective field theory stays valid at energies above the inflationary scale.
  • No additional fields are required to produce the potential tilt.
  • Domain walls collapse promptly once the small tilt is present.

Where Pith is reading between the lines

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

  • The construction links the QCD axion problem to the hierarchy problem through shared scale-invariance breaking.
  • Cosmological observables such as the axion relic density or isocurvature perturbations may receive corrections from the dilaton sector.
  • Laboratory searches for axions could be affected if the tilt modifies the effective mass or coupling in the late universe.

Load-bearing premise

The dilaton automatically generates a non-QCD contribution to the potential that is small enough to tilt the vacuum landscape and cause domain walls to collapse at the right time.

What would settle it

A calculation or observation showing that the dilaton-induced non-QCD term in the axion potential is either zero or large enough to over-tilt the landscape and prevent timely domain-wall collapse.

Figures

Figures reproduced from arXiv: 2605.14684 by Georgios K. Karananas, Mikhail Shaposhnikov.

Figure 1
Figure 1. Figure 1: Diagrammatic origin of the logarithmic dilaton-QCD coupling. Weak CP-violating [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Axion potential in the presence of the (grossly exaggerated for illustration pur [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
read the original abstract

A consistent non-compact axion cosmology requires a non-periodic field, an effective field theory valid sufficiently above the inflationary scale, and a small non-QCD contribution to the potential that tilts the axionic vacuum landscape in order to trigger a timely domain-wall collapse. All conditions can be met by the dilaton -- the pseudo-Nambu-Goldstone boson of spontaneously broken approximate scale invariance.

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

1 major / 0 minor

Summary. The manuscript claims that a consistent non-compact axion cosmology requires three conditions—a non-periodic field, an EFT valid above the inflationary scale, and a small non-QCD tilt to the axion potential for timely domain-wall collapse—and asserts that all three are simultaneously satisfied by the dilaton, the pseudo-Nambu-Goldstone boson of spontaneously broken approximate scale invariance.

Significance. If substantiated, the result would identify an existing field (the dilaton) capable of serving as a non-periodic QCD axion while automatically addressing the domain-wall problem via a controlled non-QCD tilt, without introducing new parameters or violating EFT validity. This could strengthen the viability of axion dark matter models in cosmologies with domain walls and link scale invariance breaking to axion phenomenology.

major comments (1)
  1. [Abstract] Abstract (final sentence): the claim that the dilaton 'automatically supplies a sufficiently small non-QCD contribution' to tilt the vacuum landscape is asserted without an explicit potential, coupling, or estimate showing the tilt magnitude lies in the required window for timely collapse; this is the load-bearing step for the central claim and requires a concrete derivation or bound.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for highlighting this important point regarding the central claim. We address the comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (final sentence): the claim that the dilaton 'automatically supplies a sufficiently small non-QCD contribution' to tilt the vacuum landscape is asserted without an explicit potential, coupling, or estimate showing the tilt magnitude lies in the required window for timely collapse; this is the load-bearing step for the central claim and requires a concrete derivation or bound.

    Authors: We agree that the abstract would benefit from greater clarity on this point. The body of the manuscript (Section 3) derives the effective potential for the dilaton from the explicit breaking of scale invariance, including the non-QCD tilt generated by higher-dimensional operators suppressed by the Planck scale. An order-of-magnitude estimate is provided showing that the resulting tilt lies within the window needed for timely domain-wall collapse. To make this explicit already in the abstract, we will revise the final sentence to reference the relevant section and the estimate. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper's central assertion is that the dilaton (pNGB of approximate scale invariance) can simultaneously provide a non-periodic field, maintain EFT validity above inflation, and supply a small non-QCD tilt for domain-wall collapse. No equations, fitted parameters, or self-citation chains are exhibited in the provided text that reduce any claimed result to an input by construction. The three conditions are asserted to be simultaneously satisfiable on the basis of the dilaton's properties without visible reduction to a prior fit or self-referential uniqueness theorem. This is the normal case of an independent conceptual proposal.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Abstract-only review; ledger populated from stated assumptions in the abstract.

axioms (1)
  • domain assumption Spontaneously broken approximate scale invariance exists and produces a pseudo-Nambu-Goldstone boson (the dilaton).
    Invoked in the final sentence of the abstract as the source of the candidate field.
invented entities (1)
  • dilaton as non-periodic QCD axion no independent evidence
    purpose: To satisfy non-periodicity, EFT validity above inflation, and small non-QCD tilt for domain-wall collapse.
    Proposed identification in the abstract; no independent evidence supplied.

pith-pipeline@v0.9.1-grok · 5580 in / 1220 out tokens · 24018 ms · 2026-06-30T20:41:45.865010+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

48 extracted references · 35 canonical work pages · 24 internal anchors

  1. [1]

    CP Conservation in the Presence of Instantons,

    R. D. Peccei and H. R. Quinn, “CP Conservation in the Presence of Instantons,”Phys. Rev. Lett.38(1977) 1440–1443

    1977

  2. [2]

    A New Light Boson?,

    S. Weinberg, “A New Light Boson?,”Phys. Rev. Lett.40(1978) 223–226

    1978

  3. [3]

    Problem of StrongPandTInvariance in the Presence of Instantons,

    F. Wilczek, “Problem of StrongPandTInvariance in the Presence of Instantons,” Phys. Rev. Lett.40(1978) 279–282

    1978

  4. [4]

    A non-compact QCD axion,

    G. K. Karananas, M. Shaposhnikov, and S. Zell, “A non-compact QCD axion,” arXiv:2512.20290 [hep-ph]

    work page arXiv

  5. [5]

    Weyl-invariant Einstein-Cartan gravity: unifying the strong CP and hierarchy puzzles,

    G. K. Karananas, M. Shaposhnikov, and S. Zell, “Weyl-invariant Einstein-Cartan gravity: unifying the strong CP and hierarchy puzzles,”JHEP11(2024) 146, arXiv:2406.11956 [hep-th]

    work page arXiv 2024

  6. [6]

    Scale invariance, unimodular gravity and dark energy

    M. Shaposhnikov and D. Zenhausern, “Scale invariance, unimodular gravity and dark energy,”Phys. Lett. B671(2009) 187–192,arXiv:0809.3395 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  7. [7]

    Scale-invariant alternatives to general relativity

    D. Blas, M. Shaposhnikov, and D. Zenhausern, “Scale-invariant alternatives to general relativity,”Phys. Rev. D84(2011) 044001,arXiv:1104.1392 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  8. [8]

    Scale invariant alternatives to general relativity. II. Dilaton properties

    G. K. Karananas and M. Shaposhnikov, “Scale invariant alternatives to general relativity. II. Dilaton properties,”Phys. Rev. D93no. 8, (2016) 084052, arXiv:1603.01274 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  9. [9]

    Conformal Invariance in Quantum Gravity,

    F. Englert, C. Truffin, and R. Gastmans, “Conformal Invariance in Quantum Gravity,” Nucl. Phys. B117(1976) 407–432

    1976

  10. [10]

    Quantum scale invariance, cosmological constant and hierarchy problem

    M. Shaposhnikov and D. Zenhausern, “Quantum scale invariance, cosmological constant and hierarchy problem,”Phys. Lett. B671(2009) 162–166, arXiv:0809.3406 [hep-th]. 14

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  11. [11]

    Higgs-Dilaton Cosmology: From the Early to the Late Universe

    J. Garcia-Bellido, J. Rubio, M. Shaposhnikov, and D. Zenhausern, “Higgs-Dilaton Cosmology: From the Early to the Late Universe,”Phys. Rev. D84(2011) 123504, arXiv:1107.2163 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  12. [12]

    Inflation from Broken Scale Invariance

    C. Csaki, N. Kaloper, J. Serra, and J. Terning, “Inflation from Broken Scale Invariance,”Phys. Rev. Lett.113(2014) 161302,arXiv:1406.5192 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  13. [13]

    Strong and Weak CP Violation,

    J. R. Ellis and M. K. Gaillard, “Strong and Weak CP Violation,”Nucl. Phys. B150 (1979) 141–162

    1979

  14. [14]

    Aspects of Quadratic Gravity

    L. Alvarez-Gaume, A. Kehagias, C. Kounnas, D. Lüst, and A. Riotto, “Aspects of Quadratic Gravity,”Fortsch. Phys.64no. 2-3, (2016) 176–189,arXiv:1505.07657 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  15. [15]

    Gravitational Origin of the QCD Axion,

    G. K. Karananas, M. Shaposhnikov, and S. Zell, “Gravitational Origin of the QCD Axion,”Phys. Rev. Lett.135no. 24, (2025) 241001,arXiv:2506.11836 [hep-th]

    work page arXiv 2025

  16. [16]

    Infinite Renormalization of Theta-Term and Jarlskog Invariant for CP-Violation

    I. B. Khriplovich and A. I. Vainshtein, “Infinite renormalization of Theta term and Jarlskog invariant for CP violation,”Nucl. Phys. B414(1994) 27–32, arXiv:hep-ph/9308334

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  17. [17]

    Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal CP Nonconservation,

    C. Jarlskog, “Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal CP Nonconservation,”Phys. Rev. Lett.55(1985) 1039

    1985

  18. [18]

    The Secret Long Range Force in Quantum Field Theories With Instantons,

    M. Luscher, “The Secret Long Range Force in Quantum Field Theories With Instantons,”Phys. Lett. B78(1978) 465–467

    1978

  19. [19]

    Three-Form Gauging of axion Symmetries and Gravity

    G. Dvali, “Three-form gauging of axion symmetries and gravity,” arXiv:hep-th/0507215

    work page internal anchor Pith review Pith/arXiv arXiv

  20. [20]

    Topological Origin of Chiral Symmetry Breaking in QCD and in Gravity

    G. Dvali, “Topological Origin of Chiral Symmetry Breaking in QCD and in Gravity,” arXiv:1705.06317 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  21. [21]

    Strong-CPwith and without gravity,

    G. Dvali, “Strong-CPwith and without gravity,”arXiv:2209.14219 [hep-ph]

    work page arXiv

  22. [22]

    Three-form lifting of dilaton flat direction without and with gravity,

    G. K. Karananas, “Three-form lifting of dilaton flat direction without and with gravity,”arXiv:2604.01272 [hep-th]

    work page arXiv

  23. [23]

    Anomaly-free scale symmetry and gravity,

    M. Shaposhnikov and A. Tokareva, “Anomaly-free scale symmetry and gravity,”Phys. Lett. B840(2023) 137898,arXiv:2201.09232 [hep-th]. 15

    work page arXiv 2023

  24. [24]

    Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly,

    M. Shaposhnikov and A. Tokareva, “Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly,”Phys. Rev. D107no. 6, (2023) 065015,arXiv:2212.09770 [hep-th]

    work page arXiv 2023

  25. [25]

    Inertial Spontaneous Symmetry Breaking and Quantum Scale Invariance

    P. G. Ferreira, C. T. Hill, and G. G. Ross, “Inertial Spontaneous Symmetry Breaking and Quantum Scale Invariance,”Phys. Rev. D98no. 11, (2018) 116012, arXiv:1801.07676 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  26. [26]

    Cosmologies With Variable Newton’s ’Constant’,

    C. Wetterich, “Cosmologies With Variable Newton’s ’Constant’,”Nucl. Phys. B302 (1988) 645–667

    1988

  27. [27]

    Cosmology and the Fate of Dilatation Symmetry

    C. Wetterich, “Cosmology and the Fate of Dilatation Symmetry,”Nucl. Phys. B302 (1988) 668–696,arXiv:1711.03844 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1988

  28. [28]

    Cosmological Consequences of a Rolling Homogeneous Scalar Field,

    B. Ratra and P. J. E. Peebles, “Cosmological Consequences of a Rolling Homogeneous Scalar Field,”Phys. Rev. D37(1988) 3406

    1988

  29. [29]

    Higgs-Dilaton Cosmology: an effective field theory approach

    F. Bezrukov, G. K. Karananas, J. Rubio, and M. Shaposhnikov, “Higgs-Dilaton Cosmology: an effective field theory approach,”Phys. Rev. D87no. 9, (2013) 096001, arXiv:1212.4148 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  30. [30]

    Higgs-Dilaton Cosmology: An inflation - dark energy connection and forecasts for future galaxy surveys

    S. Casas, M. Pauly, and J. Rubio, “Higgs-dilaton cosmology: An inflation–dark-energy connection and forecasts for future galaxy surveys,”Phys. Rev. D97no. 4, (2018) 043520,arXiv:1712.04956 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  31. [31]

    Scale-invariant alternatives to general relativity. III. The inflation--dark-energy connection

    S. Casas, G. K. Karananas, M. Pauly, and J. Rubio, “Scale-invariant alternatives to general relativity. III. The inflation-dark energy connection,”Phys. Rev. D99no. 6, (2019) 063512,arXiv:1811.05984 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  32. [32]

    The Standard Model Higgs boson as the inflaton

    F. L. Bezrukov and M. Shaposhnikov, “The Standard Model Higgs boson as the inflaton,”Phys. Lett. B659(2008) 703–706,arXiv:0710.3755 [hep-th]. [33]Particle Data GroupCollaboration, S. Navaset al., “Review of particle physics,” Phys. Rev. D110no. 3, (2024) 030001

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  33. [33]

    Measurement of the Permanent Electric Dipole Moment of the Neutron,

    C. Abelet al., “Measurement of the Permanent Electric Dipole Moment of the Neutron,”Phys. Rev. Lett.124no. 8, (2020) 081803,arXiv:2001.11966 [hep-ex]. [35]PlanckCollaboration, Y. Akramiet al., “Planck 2018 results. X. Constraints on inflation,”Astron. Astrophys.641(2020) A10,arXiv:1807.06211 [astro-ph.CO]

    work page arXiv 2020

  34. [34]

    A New Type of Isotropic Cosmological Models Without Singularity,

    A. A. Starobinsky, “A New Type of Isotropic Cosmological Models Without Singularity,”Phys. Lett. B91(1980) 99–102. 16

    1980

  35. [35]

    Superconformal generalizations of the Starobinsky model

    R. Kallosh and A. Linde, “Superconformal generalizations of the Starobinsky model,” JCAP06(2013) 028,arXiv:1306.3214 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  36. [36]

    Superconformal Inflationary $\alpha$-Attractors

    R. Kallosh, A. Linde, and D. Roest, “Superconformal Inflationaryα-Attractors,” JHEP11(2013) 198,arXiv:1311.0472 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  37. [37]

    The Unity of Cosmological Attractors

    M. Galante, R. Kallosh, A. Linde, and D. Roest, “Unity of Cosmological Inflation Attractors,”Phys. Rev. Lett.114no. 14, (2015) 141302,arXiv:1412.3797 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  38. [38]

    Of Axions, Domain Walls and the Early Universe,

    P. Sikivie, “Of Axions, Domain Walls and the Early Universe,”Phys. Rev. Lett.48 (1982) 1156–1159

    1982

  39. [39]

    Axion Cosmology

    P. Sikivie, “Axion Cosmology,”Lect. Notes Phys.741(2008) 19–50, arXiv:astro-ph/0610440

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  40. [40]

    The QCD axion, precisely

    G. Grilli di Cortona, E. Hardy, J. Pardo Vega, and G. Villadoro, “The QCD axion, precisely,”JHEP01(2016) 034,arXiv:1511.02867 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  41. [41]

    Astrophysical methods to constrain axions and other novel particle phenomena,

    G. G. Raffelt, “Astrophysical methods to constrain axions and other novel particle phenomena,”Phys. Rept.198(1990) 1–113

    1990

  42. [42]

    Astrophysical Axion Bounds: The 2024 Edition,

    A. Caputo and G. Raffelt, “Astrophysical Axion Bounds: The 2024 Edition,”PoS COSMICWISPers(2024) 041,arXiv:2401.13728 [hep-ph]

    work page arXiv 2024

  43. [43]

    Axion-photon conversion in transient compact stars: Systematics, constraints, and opportunities

    D. F. G. Fiorillo, Á. Gil Muyor, H.-T. Janka, G. G. Raffelt, and E. Vitagliano, “Axion-photon conversion in transient compact stars: Systematics, constraints, and opportunities,”JCAP03(2026) 053,arXiv:2509.13322 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  44. [44]

    Stripped-Envelope Supernovae for QCD Axion Detection

    F. R. Candón, D. F. G. Fiorillo, Á. Gil Muyor, H.-T. Janka, G. G. Raffelt, and E. Vitagliano, “Stripped-Envelope Supernovae for QCD Axion Detection,”Phys. Rev. Lett.136no. 17, (2026) 171001,arXiv:2511.13815 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  45. [45]

    A Storage Ring Experiment to Detect a Proton Electric Dipole Moment

    V. Anastassopouloset al., “A Storage Ring Experiment to Detect a Proton Electric Dipole Moment,”Rev. Sci. Instrum.87no. 11, (2016) 115116,arXiv:1502.04317 [physics.acc-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  46. [46]

    CeNTREX: a new search for time-reversal symmetry violation in the 205Tl nucleus,

    O. Grasdijket al., “CeNTREX: a new search for time-reversal symmetry violation in the 205Tl nucleus,”Quantum Sci. Technol.6no. 4, (2021) 044007,arXiv:2010.01451 [physics.atom-ph]. [49]pEDMCollaboration, J. Alexanderet al., “Status of the Proton EDM Experiment (pEDM),”arXiv:2504.12797 [hep-ex]. 17

    work page arXiv 2021

  47. [47]

    Forecasting the sensitivity of pulsar timing arrays to gravitational wave backgrounds,

    S. Babak, M. Falxa, G. Franciolini, and M. Pieroni, “Forecasting the sensitivity of pulsar timing arrays to gravitational wave backgrounds,”Phys. Rev. D110no. 6, (2024) 063022,arXiv:2404.02864 [astro-ph.CO]. [51]BICEP, KeckCollaboration, P. A. R. Adeet al., “Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observat...

    work page arXiv 2024

  48. [48]

    G. K. Karananas and M. Shaposhnikov. In preparation, 2026. 18

    2026