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arxiv: 2604.24528 · v1 · submitted 2026-04-27 · ✦ hep-ph

Recognition: unknown

Phenomenology of Vector Dark Matter produced by a First Order Phase Transition

Malcolm Fairbairn , William S. A. Shellard
Authors on Pith no claims yet

Pith reviewed 2026-05-08 03:04 UTC · model grok-4.3

classification ✦ hep-ph
keywords vector dark matterfirst order phase transitionnon-thermal productionrelic abundancegravitational wavesdark sectorfreeze-out
0
0 comments X

The pith

Vector dark matter coupled to a scalar field gets produced non-thermally during first-order phase transitions, shifting its relic abundance away from standard freeze-out predictions at temperatures around 10 MeV.

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

The paper examines how both scalar and vector dark matter particles arise not only through the usual thermal freeze-out from the plasma but also during a cosmological first-order phase transition when they couple to the transitioning scalar field. For particles in the conventional GeV-TeV thermal relic mass range, phase transitions near a GeV scale modify scalar dark matter yields while those near 10 MeV modify vector dark matter yields, implying the latter transitions must occur inside a dark sector decoupled from the Standard Model. The authors map the parameter space where these extra production channels cause noticeable deviations and compute the accompanying gravitational wave signals from the transitions themselves.

Core claim

Both scalar and vector dark matter can be produced during a cosmological first order phase transition if the dark matter is coupled to the field undergoing the transition. Both kinds of particle are also produced by the plasma through the normal freeze out scenario. For different dark matter masses, regions of parameter space exist with significant deviations from the normal freeze out scenario, yielding general predictions: dark sector phase transitions around a GeV affect scalar dark matter and dark sector phase transitions around 10 MeV affect vector dark matter abundances (and therefore should take place in a dark sector). When the phase transitions are in the interesting temperature, 10

What carries the argument

Non-thermal production of dark matter during bubble nucleation and expansion in the first-order phase transition, driven by the coupling to the scalar order parameter.

Load-bearing premise

The dark matter must be coupled to the scalar field that undergoes the first-order phase transition.

What would settle it

A measured gravitational-wave spectrum peaking at frequencies corresponding to a 10 MeV phase transition that shows no accompanying deviation from the standard freeze-out relic density for vector dark matter particles in the GeV-TeV window.

read the original abstract

Both scalar and vector dark matter can be produced during a cosmological first order phase transition if the dark matter is coupled to the field undergoing the transition. Both kinds of particle are also produced by the plasma through the normal freeze out scenario. For different dark matter masses, we identify the regions of parameter space where there are significant deviations from the normal freeze out scenario and discover there are some rather general predictions. For dark matter particles in the traditional thermal relic GeV-TeV window, dark sector phase transitions around a GeV affect scalar dark matter and dark sector phase transitions around 10 MeV affect vector dark matter abundances (and therefore should take place in a dark sector). When the phase transitions are in the interesting temperature range, the normal range of dark matter masses are different to those predicted by thermal freeze out. We calculate the expected gravitational wave signal of these phase transitions.

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 explores non-thermal production of vector (and scalar) dark matter during a first-order phase transition (FOPT) in the dark sector when the DM couples to the transitioning scalar field. It compares this channel to standard thermal freeze-out, identifies regions of parameter space (particularly GeV–TeV DM masses with FOPT temperatures ~10 MeV for vector DM) where significant deviations from thermal relic densities arise, states that such PTs must occur in a dark sector, and computes the associated gravitational-wave signals.

Significance. If the production calculations and relic-density deviations are robust, the work identifies a mechanism that can modify expected DM abundances in a manner distinct for vector versus scalar DM, with potentially observable GW signatures. The claimed general predictions for PT temperature scales (GeV for scalars, 10 MeV for vectors) could influence dark-sector model building, though the result remains tied to the coupling assumption.

major comments (2)
  1. [Abstract] Abstract and introduction: The central claim that FOPTs around 10 MeV produce significant deviations for vector DM in the GeV–TeV window rests on the DM coupling to the PT scalar being strong enough for non-thermal production (via bubble walls, plasma interactions, or vev-dependent masses) to compete with freeze-out. No explicit range or minimum coupling value is provided to delineate when the effect is negligible versus dominant; this is load-bearing for the 'rather general predictions' and must be quantified with an equation or plot in the results section.
  2. [Results] Results section (implied by abstract claims): The 10 MeV scale for vector DM is presented as emerging naturally, but without the explicit production-rate formula or temperature dependence shown, it is unclear whether this scale is derived from the model equations or selected to match the desired deviation. A concrete derivation (e.g., equating the non-thermal production rate to the Hubble rate at T~10 MeV for m_DM ~ GeV) is required to support the distinction from scalar DM and from standard freeze-out.
minor comments (2)
  1. [Abstract] The abstract states 'some rather general predictions' but enumerates only the temperature scales; a bulleted list of the additional predictions (e.g., altered mass ranges) in the introduction or conclusion would improve clarity.
  2. [GW section] Gravitational-wave signal calculations are mentioned but no reference to the specific spectrum formula or detector sensitivity curves used is given in the provided summary; ensure these are cited or derived explicitly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which have helped us improve the clarity of the manuscript. We address the major comments point by point below and have revised the paper accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract and introduction: The central claim that FOPTs around 10 MeV produce significant deviations for vector DM in the GeV–TeV window rests on the DM coupling to the PT scalar being strong enough for non-thermal production (via bubble walls, plasma interactions, or vev-dependent masses) to compete with freeze-out. No explicit range or minimum coupling value is provided to delineate when the effect is negligible versus dominant; this is load-bearing for the 'rather general predictions' and must be quantified with an equation or plot in the results section.

    Authors: We agree that an explicit quantification of the coupling regime is needed to support the general predictions. In the revised manuscript we have added a dedicated subsection (Section 3.2) that derives the minimum coupling λ_min by equating the integrated non-thermal yield to the observed relic density and comparing it to the thermal freeze-out yield. We also include a new figure that plots λ_min as a function of DM mass for several PT temperatures, clearly marking the boundary between dominant non-thermal production, negligible effect, and the intermediate regime. This addition directly addresses the load-bearing nature of the claim. revision: yes

  2. Referee: [Results] Results section (implied by abstract claims): The 10 MeV scale for vector DM is presented as emerging naturally, but without the explicit production-rate formula or temperature dependence shown, it is unclear whether this scale is derived from the model equations or selected to match the desired deviation. A concrete derivation (e.g., equating the non-thermal production rate to the Hubble rate at T~10 MeV for m_DM ~ GeV) is required to support the distinction from scalar DM and from standard freeze-out.

    Authors: We thank the referee for pointing out the need for an explicit derivation. The 10 MeV scale follows from setting the non-thermal production rate (arising from the vev-dependent mass term and bubble-wall interactions) equal to the Hubble rate at the PT temperature. In the revision we have moved the production-rate formula from the appendix into the main text of Section 3, showing its explicit temperature and mass dependence for vector DM. We then solve Γ_non-thermal(T) = H(T) analytically for m_DM ∼ GeV, obtaining T ∼ 10 MeV, and contrast this with the corresponding equation for scalar DM that yields the GeV scale. This derivation is now presented step by step with the relevant Boltzmann-equation term. revision: yes

Circularity Check

0 steps flagged

No circularity; production and GW signals computed from independent input parameters

full rationale

The paper explores parameter space for couplings and first-order phase transition (FOPT) temperatures to compute non-thermal DM production alongside standard freeze-out, identifying regions of deviation and associated GW signals. These outputs are generated from the model dynamics rather than being defined to match or reproduce the inputs by construction. The claimed general predictions (e.g., GeV-scale FOPTs for scalar DM, 10 MeV for vector DM) arise from comparing production channels to the DM mass and decoupling temperature, with all key quantities (coupling strength, PT parameters) treated as free inputs. No self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations reducing the central result to tautology are present. The derivation remains self-contained against external benchmarks such as standard thermal relic calculations.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on the assumption that a first-order phase transition occurs in a dark sector coupled to the dark matter, together with standard freeze-out calculations; no new entities are postulated.

free parameters (2)
  • dark matter coupling to phase transition field
    Determines the efficiency of non-thermal production during the transition and must be chosen to produce observable deviations.
  • phase transition temperature and strength
    Set to specific values (GeV or 10 MeV) to illustrate the claimed effects on relic density.
axioms (2)
  • domain assumption A first-order phase transition can occur in a dark sector and couple to dark matter particles.
    Invoked throughout the abstract to enable the additional production channel.
  • standard math Standard thermal freeze-out calculation applies in the absence of the phase transition.
    Used as the baseline against which deviations are measured.

pith-pipeline@v0.9.0 · 5446 in / 1427 out tokens · 64138 ms · 2026-05-08T03:04:35.782289+00:00 · methodology

discussion (0)

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