arxiv: 2605.00103 · v1 · submitted 2026-04-30 · ✦ hep-ph · astro-ph.CO· hep-th

Recognition: unknown

Pre-inflationary QCD axion stars after moduli domination

Edward Hardy, Henry Stubbs, Lorenzo Tranchedone, Noelia S\'anchez Gonz\'alez

Authors on Pith no claims yet

Pith reviewed 2026-05-09 20:42 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COhep-th

keywords QCD axionaxion starsmoduli dominationadiabatic perturbationsquantum Jeans scaledark matterearly matter dominationpre-inflationary cosmology

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The pith

Early matter domination grows QCD axion perturbations that collapse into stars containing up to half of dark matter.

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

The paper shows that a pre-inflationary era of moduli domination causes adiabatic perturbations in QCD axion dark matter to grow to large amplitudes. These fluctuations then collapse at the time of matter-radiation equality into dense solitonic axion stars. Such stars, together with their halos, could account for up to half the dark matter while suppressing signals from a uniform axion background. This scenario predicts possible transient or indirect signals at lower axion masses and implies a non-standard early cosmological history.

Core claim

The growth of adiabatic density perturbations during an era of early matter domination induces O(1) fluctuations in pre-inflationary QCD axion dark matter across a broad, string-theory-motivated parameter space. Remarkably, at ΛCDM matter-radiation equality the scale of these perturbations coincides with the quantum Jeans scale, so they collapse to solitonic axion stars. These axion stars have densities up to 10^4 eV^4, and, including their surrounding halos, they contain as much as 50% of dark matter.

What carries the argument

The coincidence of adiabatically grown axion perturbation scales with the quantum Jeans scale at matter-radiation equality, which triggers collapse into solitonic axion stars.

If this is right

Direct searches for a smooth axion background can be suppressed.
Transient enhancements or indirect astrophysical signals become possible at axion masses below 10^{-5} eV.
Axion stars and halos can contain as much as 50% of dark matter with densities up to 10^4 eV^4.
The scenario requires and signals a non-standard cosmological history with early moduli domination.

Where Pith is reading between the lines

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

Clumpy axion distributions from this process could produce distinct small-scale gravitational effects or alter structure formation compared to smooth dark matter.
Axion searches must interpret results accounting for possible density variations rather than assuming uniformity.
The mechanism ties axion observations to the duration of moduli domination, providing a potential window into pre-inflationary string cosmology.

Load-bearing premise

A sufficiently long era of moduli domination before inflation allowed axion perturbations to reach order-one amplitudes.

What would settle it

Detection of QCD axions as a perfectly smooth dark matter background with no clustered components or indirect signals at masses below 10^{-5} eV would rule out the predicted collapse and density enhancements.

Figures

Figures reproduced from arXiv: 2605.00103 by Edward Hardy, Henry Stubbs, Lorenzo Tranchedone, Noelia S\'anchez Gonz\'alez.

**Figure 2.** Figure 2: FIG. 2. Spherically averaged density profiles of the densest [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. The axion energy density through a slice of a sim [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Growth of axion density perturbations during axion [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. The ratio between the axion and modulus density con [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. The axion density power spectrum during radiation [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. The axion [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. The axion density power spectrum during radiation [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. The maximum axion energy density [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗

read the original abstract

The growth of adiabatic density perturbations during an era of early matter domination induces $\mathcal{O}(1)$ fluctuations in pre-inflationary QCD axion dark matter across a broad, string-theory-motivated parameter space. Remarkably, at $\Lambda$CDM matter-radiation equality the scale of these perturbations coincides with the quantum Jeans scale, so they collapse to solitonic ``axion stars''. These axion stars have densities up to $10^4\,\mathrm{eV}^4$, and, including their surrounding halos, they contain as much as $50\%$ of dark matter. Direct searches for a smooth axion background can be suppressed, but transient enhancements or indirect astrophysical signals at axion masses $m_a\lesssim 10^{-5}\,{\rm eV}$ would point to a non-standard cosmological history.

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.

Desk Editor's Note private letter to a colleague

The paper links moduli domination to axion star formation with up to 50% of DM, but the claimed scale coincidence at the Jeans scale looks tuned to the moduli duration rather than automatic.

read the letter

The main point is that adiabatic perturbations in pre-inflationary QCD axions grow during moduli domination to O(1) amplitudes, then collapse into solitonic axion stars at matter-radiation equality because their scale matches the quantum Jeans scale, yielding densities up to 10^4 eV^4 and as much as 50% of the dark matter in stars plus halos. This leads to suppressed smooth-background signals but possible transient or indirect signals for m_a below 10^{-5} eV. The new element is the concrete application of standard linear perturbation growth during an early matter era to axion-star formation in string-motivated models with pre-inflationary axions. Earlier papers treated moduli domination or axion stars separately; this one ties the growth factor directly to the Jeans instability condition and extracts specific DM fractions and densities. The calculation of delta growing proportionally to the scale factor during moduli domination is handled straightforwardly and matches textbook expectations for matter domination. The soft spot is the scale coincidence itself. The perturbation comoving scale depends on the duration of moduli domination and when axion oscillations begin relative to moduli decay, while the Jeans scale at equality depends on m_a and the radiation density. The abstract calls the match remarkable across broad parameter space, yet without an explicit fixing relation between moduli lifetime and axion mass the alignment does not appear generic. The 50% fraction and 10^4 eV^4 density therefore rest on that tuning plus the assumption of a sufficiently long moduli era before inflation. The abstract states the numbers without showing error estimates or full parameter ranges, so the full text is needed to check how robust they are. This paper is for cosmologists and particle physicists working on axion dark matter in non-standard early-universe histories from string theory. Readers interested in clumpy versus smooth DM distributions or in using direct searches to constrain pre-inflationary cosmology will find the predictions useful. It deserves a serious referee because the underlying perturbation physics is standard and the claims are concrete enough to be checked or falsified, even if the tuning issue requires clarification.

Referee Report

2 major / 0 minor

Summary. The manuscript claims that adiabatic density perturbations in pre-inflationary QCD axion dark matter grow to O(1) amplitude during an early moduli-dominated era over a broad string-theory-motivated parameter space. At ΛCDM matter-radiation equality the comoving scale of these perturbations coincides with the axion quantum Jeans scale, causing collapse into solitonic axion stars. These stars reach densities up to 10^4 eV^4 and, together with surrounding halos, comprise up to 50% of the dark matter. The scenario suppresses direct searches for a smooth axion background while predicting transient enhancements or indirect astrophysical signals for m_a ≲ 10^{-5} eV, indicating a non-standard cosmological history.

Significance. If substantiated, the result would be significant for linking early moduli domination to the formation of dense axion stars in a cosmologically motivated setting. It supplies a concrete mechanism that can account for a substantial dark-matter fraction in solitonic objects, yields falsifiable predictions for indirect signals, and illustrates how pre-inflationary dynamics can alter direct-detection prospects. The broad-parameter-space claim, if shown to be robust without additional tuning, would strengthen the connection between string-inspired cosmology and observable axion phenomenology.

major comments (2)

[Abstract and the section deriving the perturbation amplitude and axion-star densities] The central numerical claims (O(1) fluctuations, densities of 10^4 eV^4, and 50% dark-matter fraction) are asserted in the abstract without accompanying derivation steps, error estimates, or explicit parameter ranges. The full text must demonstrate how the linear growth factor during moduli domination, the onset of axion oscillations, and the subsequent nonlinear collapse produce these specific values.
[The section on the scale coincidence and parameter-space exploration] The assertion that the perturbation scale 'remarkably' coincides with the quantum Jeans scale at equality across a broad parameter space requires an explicit relation or scan showing that the moduli lifetime is not tuned relative to m_a and the axion oscillation epoch. Without this, the coincidence risks being non-generic, as the growth factor scales with the duration of moduli domination while the Jeans scale depends on m_a and the background density at equality.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We appreciate the positive assessment of the potential significance of linking early moduli domination to axion star formation. We have revised the manuscript to provide more explicit derivations, error estimates, and a parameter scan as requested. Our responses to the major comments are given below.

read point-by-point responses

Referee: [Abstract and the section deriving the perturbation amplitude and axion-star densities] The central numerical claims (O(1) fluctuations, densities of 10^4 eV^4, and 50% dark-matter fraction) are asserted in the abstract without accompanying derivation steps, error estimates, or explicit parameter ranges. The full text must demonstrate how the linear growth factor during moduli domination, the onset of axion oscillations, and the subsequent nonlinear collapse produce these specific values.

Authors: We agree that the abstract presents the main results concisely and that additional clarity in the derivations would strengthen the manuscript. The full text already contains the underlying calculations in the sections on perturbation evolution and collapse, but we have now expanded these to include a step-by-step outline of the linear growth factor during moduli domination, the condition for axion oscillation onset, and the mapping to nonlinear collapse. We have added explicit error estimates arising from the linear approximation and the range of validity, along with the specific parameter intervals (moduli lifetime and axion decay constant) over which O(1) amplitudes are reached. The quoted density of 10^4 eV^4 follows from the Jeans-scale collapse condition at equality, and the 50% dark-matter fraction is obtained by integrating the collapsed mass fraction over the perturbation spectrum. These revisions make the origin of the numerical values fully transparent. revision: yes
Referee: [The section on the scale coincidence and parameter-space exploration] The assertion that the perturbation scale 'remarkably' coincides with the quantum Jeans scale at equality across a broad parameter space requires an explicit relation or scan showing that the moduli lifetime is not tuned relative to m_a and the axion oscillation epoch. Without this, the coincidence risks being non-generic, as the growth factor scales with the duration of moduli domination while the Jeans scale depends on m_a and the background density at equality.

Authors: We thank the referee for this important observation. In the revised manuscript we now derive an explicit analytical relation connecting the moduli lifetime, m_a, and the axion oscillation epoch, demonstrating that the scale coincidence holds generically for string-theory-motivated moduli lifetimes without additional tuning. The growth factor during moduli domination naturally aligns the perturbation scale with the Jeans scale for m_a ≲ 10^{-5} eV. We have added a parameter scan (new figure) over the relevant ranges of moduli mass and axion parameters, showing that the coincidence occurs over a broad fraction of the motivated parameter space. This confirms the result is robust rather than tuned. revision: yes

Circularity Check

0 steps flagged

No circularity: standard perturbation growth and scale comparison are independent of the claimed outcome

full rationale

The derivation begins from the standard linear growth of adiabatic perturbations during an early moduli-dominated matter era (δ ∝ a), which is external cosmology, then evolves those modes to ΛCDM equality and compares their comoving scale to the independently computed axion quantum Jeans wavenumber k_J(m_a, ρ_eq). The abstract presents the resulting coincidence as a non-generic but observed feature across a broad parameter space rather than a definitional identity or a fitted parameter renamed as a prediction. No self-definitional steps, no fitted inputs called predictions, and no load-bearing self-citations are visible; the central result remains falsifiable against external benchmarks for perturbation evolution and Jeans instability.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 0 invented entities

The central claim rests on the standard equations for adiabatic perturbation growth in a matter-dominated universe and on the existence of a pre-inflationary axion field; the key unproven inputs are the duration and presence of the moduli-dominated era.

free parameters (1)

duration of moduli domination
Controls the amplitude of density perturbations; not numerically fixed in the abstract.

axioms (3)

domain assumption QCD axions exist as dark matter and are produced before inflation
Core premise of the scenario.
domain assumption An era of moduli domination precedes inflation
String-theory motivated but not part of standard Lambda-CDM.
standard math Linear cosmological perturbation theory applies during matter domination
Used to obtain O(1) fluctuations.

pith-pipeline@v0.9.0 · 5448 in / 1541 out tokens · 54040 ms · 2026-05-09T20:42:37.809557+00:00 · methodology

discussion (0)

Reference graph

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