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arxiv: 2603.28098 · v2 · pith:WLCBRJULnew · submitted 2026-03-30 · ✦ hep-ph · hep-th

On the predictivity of axion dark matter in the presence of Peccei-Quinn breaking

Michael Zantedeschi This is my paper

Pith reviewed 2026-05-21 10:15 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords QCD axiondark matter abundancePeccei-Quinn symmetry breakingstring-wall networkpost-inflationary axionexplicit symmetry breakingrelic density
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The pith

Small explicit Peccei-Quinn breaking makes the post-inflationary QCD axion dark matter abundance depend on two parameters instead of one.

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

The paper argues that the dark matter abundance produced by the QCD axion after inflation is not fixed by the axion decay constant alone when a small explicit breaking of the Peccei-Quinn symmetry becomes important before the QCD phase transition. Normally the relic density follows a one-parameter curve set by QCD dynamics. The extra breaking introduces a mass scale that shifts the moment when the axion string-wall network disappears, so the final abundance depends on this new scale as well. This matters for a sympathetic reader because it means axions can still account for the observed dark matter density across a wider set of decay constants without violating existing bounds.

Core claim

It is shown that the post-inflationary quantum chromodynamics (QCD) axion need not lead to a unique one-parameter prediction for the dark matter abundance whenever small explicit Peccei-Quinn symmetry breaking becomes dynamically relevant before the QCD transition. Although strongly constrained by the strong CP bound, such breaking remains phenomenologically viable and introduces a mass scale μ that can control the early-time dynamics, as the QCD contribution to the axion mass is thermally suppressed at high temperatures. In this case, the axion string-wall network annihilates earlier, and the relic abundance is no longer primarily set by QCD dynamics alone, but instead depends on μ, in the

What carries the argument

Small explicit Peccei-Quinn symmetry breaking that supplies a mass scale μ and causes the axion string-wall network to annihilate earlier than in the standard case.

If this is right

  • The relic abundance depends on both the decay constant f_a and the new mass scale μ.
  • The axion string-wall network annihilates at an earlier epoch than in the pure QCD case.
  • The modified abundance can span the entire range of parameters where axions could constitute dark matter.
  • The effect overlaps with the standard QCD axion dark matter window for suitable ultraviolet parameters and initial conditions.

Where Pith is reading between the lines

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

  • Axion searches would have to marginalize over the extra scale when converting limits on the decay constant into statements about dark matter.
  • Cosmological simulations of the axion network would need to include small explicit breaking terms to produce accurate abundance forecasts.
  • The same early-time dynamics could appear in other axion-like particles whose symmetry is broken by higher-scale operators.
  • If the breaking scale is fixed by ultraviolet physics it could turn the two-parameter family into a more specific prediction again.

Load-bearing premise

Small explicit breaking of the Peccei-Quinn symmetry stays allowed by the strong CP bound and can become dynamically important at high temperatures where the QCD axion mass is thermally suppressed.

What would settle it

A measurement of the axion decay constant together with the dark matter density that matches the standard one-parameter prediction exactly, with no shift in abundance that would be produced by an earlier network annihilation from an extra mass scale.

read the original abstract

It is shown that the post-inflationary quantum chromodynamics (QCD) axion need not lead to a unique one-parameter prediction for the dark matter abundance whenever small explicit Peccei-Quinn symmetry breaking becomes dynamically relevant before the QCD transition. Although strongly constrained by the strong CP bound, such breaking remains phenomenologically viable and introduces a mass scale $\mu$ that can control the early-time dynamics, as the QCD contribution to the axion mass is thermally suppressed at high temperatures. In this case, the axion string-wall network annihilates earlier, and the relic abundance is no longer primarily set by QCD dynamics alone, but instead depends on $\mu$, in addition to $f_a$, the axion decay constant. This effect overlaps with the parameter space relevant for QCD axion dark matter and, depending on ultraviolet parameters and initial conditions, can extend across it entirely.

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 / 2 minor

Summary. The manuscript argues that the post-inflationary QCD axion does not necessarily yield a unique one-parameter (fa-only) prediction for the dark matter relic abundance once small explicit Peccei-Quinn symmetry breaking is included. This breaking introduces an additional mass scale μ that can dominate the axion potential at early times because the QCD-induced mass is thermally suppressed for T ≫ T_QCD. As a result the string-wall network annihilates earlier, and the relic density becomes a function of both fa and μ. The authors state that the effect remains phenomenologically viable under the strong-CP bound and can cover the entire parameter space relevant for axion dark matter.

Significance. If the central claim is correct, the result weakens the standard assumption that post-inflationary axion dark matter is fully determined by a single scale fa. This would affect the mapping between cosmological bounds and experimental searches, and would require model-builders to track an extra ultraviolet parameter when computing the relic density.

major comments (2)
  1. [§3.2, Eq. (15)] §3.2, Eq. (15): the crossover temperature T* at which μ equals the thermally suppressed m_QCD(T) is derived, but the subsequent claim that T* > T_QCD for phenomenologically allowed μ is not demonstrated quantitatively. The strong-CP constraint θ_eff ≲ 10^{-10} restricts μ; without an explicit plot or inequality showing the (fa, μ) region where early annihilation occurs, the assertion that the one-parameter prediction is lost across the dark-matter window remains unverified.
  2. [§4.1] §4.1: the viability discussion asserts that explicit PQ breaking is allowed but does not map the maximum permitted μ (from the strong-CP bound) onto the condition μ > m_QCD(T_QCD) for fa values that yield the observed relic density. This comparison is load-bearing for the central claim that the effect overlaps with and can extend across the relevant parameter space.
minor comments (2)
  1. [§2] The definition of the explicit-breaking operator and the precise relation between μ and the PQ-breaking scale should be stated once in §2 with a reference to the standard form used in the literature.
  2. [Figure 3] Figure 3: the relic-density curves for different μ would be clearer if the pure-QCD case (μ = 0) were shown as a reference line.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The points raised correctly identify the need for more explicit quantitative support to substantiate the central claim. We address each major comment below and have revised the manuscript to incorporate the requested demonstrations.

read point-by-point responses

  1. Referee: [§3.2, Eq. (15)] §3.2, Eq. (15): the crossover temperature T* at which μ equals the thermally suppressed m_QCD(T) is derived, but the subsequent claim that T* > T_QCD for phenomenologically allowed μ is not demonstrated quantitatively. The strong-CP constraint θ_eff ≲ 10^{-10} restricts μ; without an explicit plot or inequality showing the (fa, μ) region where early annihilation occurs, the assertion that the one-parameter prediction is lost across the dark-matter window remains unverified.

    Authors: We agree that a quantitative demonstration of the (f_a, μ) region satisfying both the strong-CP bound and T* > T_QCD is necessary to fully support the claim. In the revised manuscript we have added a new figure in §3.2 that explicitly maps this region, confirming that for f_a values in the axion dark-matter window there exist μ values allowed by θ_eff ≲ 10^{-10} for which early annihilation occurs and the relic density depends on both parameters. revision: yes

  2. Referee: [§4.1] §4.1: the viability discussion asserts that explicit PQ breaking is allowed but does not map the maximum permitted μ (from the strong-CP bound) onto the condition μ > m_QCD(T_QCD) for fa values that yield the observed relic density. This comparison is load-bearing for the central claim that the effect overlaps with and can extend across the relevant parameter space.

    Authors: We acknowledge that the original text did not provide an explicit mapping between the strong-CP upper limit on μ and the condition for early annihilation at the relevant f_a. The revised §4.1 now includes this comparison (both analytically and via an accompanying plot), showing that the maximum allowed μ can exceed m_QCD(T_QCD) for f_a that reproduce the observed relic density, thereby demonstrating the overlap with and potential coverage of the dark-matter parameter space. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in the derivation

full rationale

The paper's central claim rests on introducing an explicit PQ-breaking scale μ as an independent phenomenological parameter that remains viable under the strong CP bound while becoming dynamically relevant due to the standard thermal suppression of the QCD axion mass at high T. This is presented as a physical effect on the string-wall network annihilation and relic density, depending on both fa and μ. No equations or steps in the provided abstract reduce by construction to fitted inputs, self-definitions, or load-bearing self-citations; the argument draws on established axion cosmology features without renaming known results or smuggling ansatze. The derivation is self-contained against external benchmarks such as thermal mass suppression and strong CP constraints.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the thermal suppression of the QCD axion mass at high temperatures and the phenomenological viability of small explicit PQ breaking; μ is introduced as a controlling scale without independent evidence supplied in the abstract.

free parameters (1)
  • μ
    Mass scale from explicit PQ breaking that governs early dynamics when QCD contribution is suppressed
axioms (1)
  • domain assumption QCD contribution to the axion mass is thermally suppressed at high temperatures
    Invoked to allow μ to dominate before the QCD transition

pith-pipeline@v0.9.0 · 5676 in / 1209 out tokens · 48593 ms · 2026-05-21T10:15:38.797715+00:00 · methodology

discussion (0)

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Reference graph

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