Do primordial quark pellets solve the dark matter puzzle?

Domenec Espriu

Primordial quark pellets formed at ~1 GeV can make up the dark matter with only rare baryon overdensities and no entropy dilution.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-14 10:03 UTC pith:C7AXKBUB

load-bearing objection Clean TOV mass-radius window for hot quark pellets at T=1 GeV, but the all-DM claim rests on an unquantified domain-wall sweep and an uncontrolled free-quark EOS in the deep interior. the 3 major comments →

arxiv 2607.10672 v2 pith:C7AXKBUB submitted 2026-07-12 hep-ph astro-ph.COgr-qc

Do primordial quark pellets solve the dark matter puzzle?

Domenec Espriu This is my paper

classification hep-ph astro-ph.COgr-qc

keywords primordial quark pelletsdark matterTolman-Oppenheimer-Volkoffquark equation of statePeccei-Quinn domain wallsmicrolensingBig Bang Nucleosynthesisstrange matter

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that ultra-dense mini-stars of hot quark matter, formed around 1 GeV in a radiation-dominated early universe, are a viable cold dark matter candidate. Rare baryon overdensities, seeded by collapsing Peccei–Quinn domain walls or similar super-horizon structures, allow these objects to form without the universe being baryon-dominated and without spoiling Big Bang Nucleosynthesis. Solving the Tolman–Oppenheimer–Volkoff equation with a hot quark equation of state yields stable configurations whose maximum mass is about 0.01 solar masses and whose radii are tens of meters; the same formation physics naturally produces far lighter objects. Once they cool they become either mini neutron stars or stable strange-matter nuggets. Only one such object per 10^9 horizon volumes (or a larger number of lighter ones) is enough to match today’s dark-matter density, and objects below 10^{-7} solar masses automatically evade existing microlensing bounds.

Core claim

Stable solutions of the Tolman–Oppenheimer–Volkoff equation with a hot quark equation of state at T = 1 GeV exist with maximum mass ~0.013 M_⊙ and radii ~80–100 m. Formation probabilities of only 10^{-9}–10^{-4} per horizon volume then suffice to reproduce the present dark-matter density without altering BBN or requiring entropy dilution.

What carries the argument

The Tolman–Oppenheimer–Volkoff equation integrated with a hot, degenerate quark equation of state whose surface pressure matches the ambient radiation pressure at T = 1 GeV; this fixes a unique boundary density and yields a family of stable mini-star solutions.

Load-bearing premise

Collapsing Peccei–Quinn domain walls or similar super-horizon structures can sweep ambient baryons into rare overdensities large enough to form the pellets while leaving the average horizon baryon content compatible with standard cosmology.

What would settle it

A quantitative calculation of domain-wall sweep efficiency and resulting mass function that fails to produce enough objects below 10^{-7} M_⊙, or a microlensing or gravitational-wave observation that rules out the predicted low-mass tail.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

PQPs below ~10^{-7} M_⊙ can constitute 100 % of dark matter while remaining invisible to current optical microlensing surveys.
The same objects cool into either mini neutron stars or stable strange-matter nuggets, both of which are free-streaming and interact only gravitationally.
A first-order phase transition near 1 TeV that produces the required domain walls would generate a stochastic gravitational-wave background peaking in the LISA band.
No entropy-injection mechanism is required prior to BBN; the excess baryons are simply sequestered inside the pellets.

Where Pith is reading between the lines

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

Because the predicted mass function is steeply falling, most of the dark-matter density would reside in Earth-mass or lighter objects, making finite-source-size effects and future sub-Earth microlensing surveys the decisive tests.
If the QCD ground state is strange matter, the pellets become absolute ground-state nuggets whose surface tension and possible evaporation rates could leave additional astrophysical signatures not yet constrained.
The same sweep-and-collapse mechanism could also seed a small population of near-horizon-mass objects that later collapse into primordial black holes, linking the dark-matter and PBH problems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

Clean TOV mass-radius window for hot quark pellets at T=1 GeV, but the all-DM claim rests on an unquantified domain-wall sweep and an uncontrolled free-quark EOS in the deep interior.

read the letter

The new piece here is a concrete TOV integration for hot u/d/s quark matter at fixed ambient T=1 GeV (and a check at 400 MeV) with radiation-pressure matching at the surface. That gives a stable branch with max mass ~0.013 M⊙ and radii ~80–100 m, comfortably inside the horizon at that epoch. The bookkeeping that follows is standard: once you have those masses, formation probabilities of order 10^{-9}–10^{-4} per horizon would match today’s DM density without entropy dilution or spoiling BBN. That is a clear, quantitative improvement on the Krnjaic et al. primordial-neutron-star idea, which needed a huge global baryon asymmetry and later dilution.

What the paper does well is keep the microphysics simple and the GR part transparent. The surface density is fixed by pressure matching, the free-quark EOS is written down, the TOV is integrated, and the horizon-mass comparison is done carefully. The late-time cooling argument (thermal support disappears, objects become either mini-NS or strangelets) is also clean. Microlensing evasion below ~10^{-7} M⊙ is correctly noted, and the LISA GW remark for a TeV-scale first-order transition is a useful observational hook.

The soft spots are real but of different sizes. The formation mechanism (PQ domain-wall sweep-and-collapse) is only sketched; the author explicitly defers bubble statistics, sweep efficiency and diffusion to a companion paper. Without that, the abundance is a free parameter. More importantly for the mass window itself, the free-quark EOS is only marginally controlled at the surface (μ~1.2 GeV, α_s~0.3) and is uncontrolled at the center (x_c up to ~7, μ~few GeV). No bag-model, NJL or lattice-informed sequence is shown, so the quoted 0.013 M⊙ could easily move by tens of percent. There is also a minor abstract/body temperature slip (1 TeV vs 1 GeV). None of these kill the idea, but they keep the DM claim conditional.

This is for people who work on compact-object DM, axion cosmology or early-universe phase transitions. The TOV calculation is solid enough to deserve a referee; the formation and EOS caveats will force a revision, but that is normal. I would send it out.

Referee Report

3 major / 4 minor

Summary. The paper proposes that primordial quark pellets (PQPs)—ultra-dense, hot quark-matter mini-stars—form at T ≈ 1 GeV in a radiation-dominated universe from rare baryon overdensities seeded by collapsing Peccei–Quinn domain walls (or analogous super-horizon structures). Solving the TOV equation with a free-quark EOS that includes thermal corrections yields stable configurations with maximum mass ≈ 0.013 M_⊙ and radii ≈ 80–100 m (lighter objects preferred by the formation mechanism). After cooling they become either mini neutron stars or stable strange-matter nuggets. Formation probabilities of only 10^{-9}–10^{-4} per horizon volume are argued to reproduce the observed dark-matter density without entropy dilution or disruption of BBN; objects below 10^{-7} M_⊙ automatically evade existing microlensing bounds. The scenario is presented as a conservative, essentially Standard-Model-based DM candidate.

Significance. If the formation mechanism can be shown to operate at the required efficiency, the work would supply a falsifiable, particle-physics-minimal cold-DM candidate whose mass–radius window is fixed by general relativity and a QCD EOS rather than by free parameters. The clean TOV integration, the explicit horizon-mass bookkeeping, the comparison with the earlier primordial-neutron-star proposal of Krnjaic et al., and the concrete microlensing and LISA targets are genuine strengths. The result would therefore be of clear interest to both the particle-astrophysics and compact-object communities, provided the two load-bearing assumptions (EOS reliability at high central density and the viability of the sweep-and-collapse seeding) are placed on firmer ground.

major comments (3)

[Section II, Eqs. (1)–(2), (6)–(7), Fig. 1] Section II, Eqs. (1)–(2) and (6)–(7), Fig. 1: The free-quark EOS is controlled only near the surface (n_R ≈ 1.8 GeV^{3}, μ ≈ 1.1–1.3 GeV, α_s ≈ 0.25–0.35). The stable branch, however, extends to central densities x_c ≲ 7 (n_c ≈ 12.5 GeV^{3}, μ_c ∼ 2–3 GeV). At these densities non-perturbative QCD, possible color-superconducting gaps and higher-order thermal corrections become O(1). Because the TOV mass is an integral over the entire density profile, an uncontrolled interior EOS can shift the maximum mass by tens of percent or remove the stable branch. The paper never recomputes the sequence with any alternative EOS (MIT bag, NJL, or lattice-informed) that remains valid at few-GeV chemical potentials. The quoted mass–radius window that underpins the entire DM-abundance argument is therefore only as reliable as this uncontrolled extrapolation.
[Section III.D] Section III.D: Cosmological viability rests entirely on the existence of a sweep-and-collapse mechanism capable of generating baryon overdensities of order 10^4–10^9 relative to the average horizon content while leaving the homogeneous background compatible with the observed η and with BBN. The discussion is purely qualitative; bubble statistics, sweep efficiency, diffusion timescales and the resulting mass-function normalization are all deferred to a companion study. Without even an order-of-magnitude estimate of these quantities, the statement that formation probabilities of 10^{-9}–10^{-4} “could suffice” remains an assumption rather than a demonstrated possibility. This is load-bearing for the central claim that PQPs can solve the dark-matter puzzle.
[Abstract and Sections II–III] Abstract versus body: The abstract states that PQPs form “at around 1 TeV,” while Sections II–III fix the formation temperature at T = 1 GeV (with a brief excursion to 400 MeV) and the gravitational-wave discussion later invokes a 1 TeV phase transition only for the seeding of overdensities. This inconsistency must be resolved; if the overdensities are generated at the TeV scale and the pellets themselves form at the GeV scale, the abstract and the subsequent abundance and horizon calculations should reflect that chronology unambiguously.

minor comments (4)

[Throughout] Numerous typographical and formatting defects appear throughout (e.g., “evolve intro mini,” “Theministarssocreated,” “Sincenofullysatisfying,” missing spaces after periods, run-together words). A careful copy-edit is required.
[Figure 1] Figure 1 captions and axis labels use mixed units (GeV and solar masses) without conversion factors stated in the caption; a single consistent set of units (or explicit conversion) would improve readability.
[Abstract and Section V] The phrase “Standard-Model based” in the abstract and conclusions is slightly overstated: the seeding mechanism relies on Peccei–Quinn domain walls, which lie beyond the minimal SM. A more precise wording would be “essentially Standard-Model degrees of freedom plus a PQ sector.”
[References] Reference [1] is cited as arXiv:2604.08651; the year 2604 is presumably a typographical error and should be corrected once the correct identifier is known.

Circularity Check

0 steps flagged

No circularity: TOV masses/radii follow from an independent EOS and boundary conditions; DM abundance is ordinary bookkeeping that matches observed density to those masses, not a re-labeling of a fit.

full rationale

The paper’s central quantitative claim is the existence of stable hot-quark TOV solutions (max M ≈ 0.013 M⊙, R ≈ 80–100 m) obtained by integrating Eqs. (9)–(10) with the free-quark EOS (1)–(2)/(6)–(7) and the surface matching condition (3)–(4) fixed by the ambient radiation pressure at T = 1 GeV. Those inputs are standard relativistic hydrodynamics and a first-principles (if approximate) EOS; they do not encode the final mass or the dark-matter fraction. The subsequent abundance estimate (MDM,hor / MPQP ≈ 10^{-9} per horizon) simply divides the observed DM density, redshifted to T = 1 GeV, by the TOV mass; this is ordinary candidate bookkeeping, not a fitted parameter re-presented as a prediction. The domain-wall sweep-and-collapse mechanism is offered only qualitatively and is deferred to a companion study; it is not used to derive the mass–radius window. No self-citation is load-bearing for the TOV results, no uniqueness theorem is imported, and no ansatz is smuggled in via prior work by the same author. The derivation is therefore self-contained against its stated assumptions; any remaining concerns (validity of the free-quark EOS at high central density, realism of the seeding mechanism) are correctness/physics issues, not circularity.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 1 invented entities

The TOV part rests on standard GR and a simplified quark EOS. The dark-matter claim additionally requires an unquantified baryon-concentration mechanism and a free formation probability chosen to match Ω_DM. No new fundamental particles are introduced beyond the already-postulated axion/PQ sector.

free parameters (3)

formation probability per horizon = 10^{-9} to 10^{-4}
Chosen in the range 10^{-9}–10^{-4} so that the integrated PQP mass density equals the observed dark-matter density; not derived from microphysics.
formation temperature = 1 GeV (primary)
Fixed by hand at T=1 GeV (also explored at 400 MeV) to lie between the charm threshold and the QCD transition; controls horizon mass and boundary density.
minimum PQP mass / mass-function cutoff
Needed to normalize the dN/dM ∝ M^{-2} spectrum once a maximum mass is set; left free pending a quantitative domain-wall calculation.

axioms (4)

domain assumption Hot three-flavor quark matter is described by the free Fermi-gas EOS with thermal corrections given in Eqs. (1)–(2), and α_s corrections may be neglected.
Invoked throughout Sec. II to close the TOV system; justified only by order-of-magnitude estimates of α_s.
domain assumption The early universe remains radiation-dominated at T~1 GeV with the standard g_*=61.75 and the observed average baryon-to-photon ratio outside the rare overdense patches.
Used for horizon mass, DM fraction and BBN safety arguments in Sec. III.
ad hoc to paper Collapsing Peccei–Quinn domain walls (or analogous super-horizon structures) can concentrate ambient baryons into rare overdensities sufficient to form stable PQPs.
Stated in Sec. III.D as the seeding mechanism; no calculation of sweep efficiency or diffusion is supplied.
domain assumption Once formed, PQPs cool and either hadronize into mini neutron stars or freeze as stable strange-matter nuggets, remaining free-streaming and non-interacting thereafter.
Sec. III.B; depends on the still-open question of the QCD ground state at zero temperature.

invented entities (1)

primordial quark pellet (PQP) no independent evidence
purpose: The compact object that stores the sequestered baryons and constitutes the dark-matter candidate.
Defined as the stable TOV solution of hot quark matter at the radiation-pressure boundary; no independent laboratory or astrophysical detection is claimed.

pith-pipeline@v1.1.0-grok45 · 14037 in / 3194 out tokens · 40866 ms · 2026-07-14T10:03:59.073340+00:00 · methodology

0 comments

read the original abstract

We show that primordial quark pellets (PQP), ultra dense quark matter mini-stars formed at around 1 TeV, naturally arise in a radiation dominated universe if rare baryon overdensities are produced by collapsing Peccei-Quinn domain walls or similar superhorizon structures. Solving the Tolman-Oppenheimer-Volkoff equation with a hot quark equation of state, we find stable solutions with a maximum mass of $10^{-2}$ solar masses and radii of approximately 100 meters, although the formation mechanism favours much smaller objects. Once formed, PQPs cool and evolve intro mini neutron stars or stable strange matter nuggets, depending on the QCD ground state. Formation probabilities of $10^{-9}$ to $10^{-4}$ per horizon volume could suffice to reproduce the present dark matter density without altering Big Bang Nucleosynthesis or requiring entropy dilution. PQPs completely evade microlensing constraints if their mass is below $10^{-7}$ solar masses, a range that could easily accommodate most of the dark matter. PQPs thus potentially constitute a conservative, Standard-Model based, and observationally testable solution to the dark matter puzzle.

Figures

Figures reproduced from arXiv: 2607.10672 by Domenec Espriu.

Do primordial quark pellets solve the dark matter puzzle?

Core claim

What carries the argument

Load-bearing premise

What would settle it

If this is right

Where Pith is reading between the lines

discussion (0)