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arxiv: 2606.25033 · v1 · pith:YXJDGSG5new · submitted 2026-06-23 · ✦ hep-ph · astro-ph.CO

Gravitational ultra-relativistic freeze-out during general reheating

Mathieu Gross , Stephen E. Henrich , Fotis Koutroulis This is my paper

Pith reviewed 2026-06-25 22:54 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords ultra-relativistic freeze-outgravitational particle productionreheating scenariosdark matter relic abundancetemperature scalingWIMP paradigmUV/IR regimes
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The pith

Gravitational particle production at reheating onset alters ultra-relativistic freeze-out dynamics and expands viable dark matter parameter space.

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

The paper generalizes ultrarelativistic freeze-out to arbitrary reheating temperature profiles of the form T ~ a^{-ξ}. It demonstrates that an early radiation bath sourced by gravitational particle production modifies the freeze-out process, creating an effect termed GUFO. For a thermally averaged cross section scaling as T^n / Λ^{n+2}, this changes whether the mechanism behaves as UV or IR dominated. Specializing to n=2 shows that matter-like reheating then permits dark matter masses up to 10^7 GeV for Λ ≲ 10^9 GeV, while radiation-like reheating requires the gravitational contribution to remain compatible across channels.

Core claim

By treating the reheating temperature evolution as T ~ a^{-ξ} with constant ξ and including a non-negligible initial radiation abundance from gravitational production, the UFO dynamics shift such that the relic abundance calculation incorporates both the initial hot bath and subsequent temperature scaling. This GUFO mechanism relaxes thermalization constraints and allows higher dark matter masses in matter-like reheating (V ~ ϕ²) compared to the standard φ → f f-bar channel.

What carries the argument

The power-law temperature profile T ~ a^{-ξ} acting on the cross section ⟨σv⟩ ~ T^n / Λ^{n+2}, with an added early radiation bath from gravitational particle production that seeds the initial conditions for freeze-out.

If this is right

  • Matter-like reheating accommodates dark matter masses up to 10^7 GeV for Λ ≲ 10^9 GeV because thermalization constraints weaken.
  • Radiation-like reheating remains compatible with GUFO across channels only when gravitational processes supply the initial bath.
  • Changes in the temperature scaling can flip the IR/UV character of the freeze-out and produce post-freeze-out freeze-in phases.
  • The exact temperature profile must be tracked to obtain the correct relic abundance, unlike in standard WIMP calculations.

Where Pith is reading between the lines

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

  • Similar gravitational seeding effects could modify freeze-out calculations in other non-standard cosmologies with power-law temperature evolution.
  • The mechanism suggests that early-universe gravitational production may be necessary to reconcile high-mass dark matter candidates with observed relic density in a wider range of inflationary models.
  • Extending the analysis to n ≠ 2 could identify additional regimes where the initial bath dominates the abundance calculation.

Load-bearing premise

The temperature evolution during reheating can be parameterized as a power-law T ~ a^{-ξ} with constant ξ, and gravitational particle production at the onset of reheating sources a non-negligible initial radiation bath that alters the UFO dynamics.

What would settle it

An observation of dark matter with mass above 10^7 GeV produced via thermal freeze-out in a matter-like reheating scenario where the initial radiation bath is shown to be negligible would contradict the GUFO prediction for n=2.

Figures

Figures reproduced from arXiv: 2606.25033 by Fotis Koutroulis, Mathieu Gross, Stephen E. Henrich.

Figure 1
Figure 1. Figure 1: Parameter space between UV and IR UFO in the wϕ, ξ plane for different temperature scaling of the thermally averaged cross section. For each n value the part above the crimson line correspond to UV UFO while the part below correspond to IR UFO. We show the various reheating channels with the colored full lines. The cases k = 2, 4 on which we will focus respectively correspond to wϕ = 0, 1 3 . the entropy i… view at source ↗
Figure 2
Figure 2. Figure 2: Temperature profile during reheating consid [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Parameter space for GUFO to be accessible for the 4 possibilities [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: mχ vs TRH plane for consistent relic abundance with Ωχh 2 for k = 2, n = 2 (left panel) and for k = 4, n = 2, ϕ → bb (right panel). In each case we display in solid line the standard UFO prediction while the GUFO prediction is showed in dotted lines. Additionally, we present relevant limits such as mχ = TRH, mχ = T× and the standard UFO limit for the left panel to facilitate comparison with Ref. [24]. The … view at source ↗
read the original abstract

We investigate ultrarelativistic freeze-out (UFO) in the context of generic reheating scenarios. While the standard WIMP dark matter paradigm has been extensively studied, UFO has so far only been analyzed within the specific reheating channel $\phi \rightarrow f\bar{f}$. Unlike in the standard WIMP mechanism, where dark matter can only be diluted after freeze-out at $T_\mathrm{FO} \sim m_\chi/\mathcal{O}(10)$, UFO dark matter can undergo freeze-in like phases following the initial freeze-out, driven by the non-trivial temperature evolution. The exact temperature evolution then needs to be accounted for, as a change in the temperature scaling can modify the IR/UV nature of UFO, impacting the relic abundance. We first generalize UFO to an arbitrary temperature profile $T \sim a^{-\xi}$, making explicit the UV and IR regimes for a thermally averaged cross section $\langle \sigma v \rangle \sim T^n / \Lambda^{n+2}$. Then, as a concrete example, we consider the minimal scenario in which gravitational particle production at the onset of reheating sources an initial radiation abundance, and show that this early hot bath changes the UFO parameter space. We refer to this effect as GUFO. Specializing to $n = 2$, we find that matter-like reheating ($V \sim \phi^2$) accommodates dark matter masses up to $10^7~\mathrm{GeV}$ for $\Lambda \lesssim 10^9~\mathrm{GeV}$ as thermalization becomes less stringent, while radiation-like reheating ($V \sim \phi^4$) is compatible with GUFO across all reheating channels only if gravitational processes are taken into account.

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 generalizes ultrarelativistic freeze-out (UFO) of dark matter to arbitrary reheating temperature profiles T ∼ a^{-ξ} and introduces GUFO by adding an initial radiation bath sourced by gravitational particle production at reheating onset. For a thermally averaged cross section ⟨σv⟩ ∼ T^n / Λ^{n+2}, it identifies UV and IR regimes, then specializes to n=2 to report that matter-like reheating (V ∼ ϕ²) accommodates DM masses up to 10^7 GeV for Λ ≲ 10^9 GeV while radiation-like reheating (V ∼ ϕ^4) is compatible with GUFO across channels only when gravitational processes are included.

Significance. If the central derivations hold, the work extends the UFO framework to generic reheating histories and relaxes thermalization constraints for heavier DM candidates. The explicit inclusion of gravitational production as a source of early radiation is a concrete modeling choice that yields falsifiable relic-abundance predictions; this is a strength worth crediting. The n=2 results could inform model-building in non-standard cosmologies provided the temperature-profile assumptions are verified.

major comments (2)
  1. [generalization section] § on generalization to T ∼ a^{-ξ} (preceding the n=2 specialization): the UV/IR regime classification for general n is load-bearing for the quoted mass bounds, yet the manuscript presents the relic-abundance expressions only after specializing to n=2 without showing the intermediate steps that connect the Boltzmann solution to the 10^7 GeV and 10^9 GeV thresholds.
  2. [GUFO section] GUFO section (following the initial-radiation discussion): the claim that radiation-like reheating is compatible with GUFO 'only if gravitational processes are taken into account' requires an explicit side-by-side comparison of the relic density with and without the gravitational-production term; without this, the 'only if' qualifier is not substantiated by the given temperature evolution.
minor comments (2)
  1. [Abstract] Abstract: the mapping V ∼ ϕ² → matter-like and V ∼ ϕ^4 → radiation-like reheating is stated without a brief reminder of the underlying equation-of-state relation, which would aid readers outside the immediate subfield.
  2. [Introduction or generalization paragraph] Notation: the constant ξ in T ∼ a^{-ξ} is introduced without an immediate statement of its range or its relation to the inflaton potential index, which could be clarified in the first paragraph of the generalization.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below and will revise the manuscript to incorporate the requested clarifications.

read point-by-point responses

  1. Referee: [generalization section] § on generalization to T ∼ a^{-ξ} (preceding the n=2 specialization): the UV/IR regime classification for general n is load-bearing for the quoted mass bounds, yet the manuscript presents the relic-abundance expressions only after specializing to n=2 without showing the intermediate steps that connect the Boltzmann solution to the 10^7 GeV and 10^9 GeV thresholds.

    Authors: We agree that the intermediate steps should be shown explicitly. In the revised manuscript we will insert the general-n relic-abundance expressions (UV and IR regimes) immediately after the Boltzmann-equation solution for arbitrary ξ, before the n=2 specialization, and will derive how these expressions yield the quoted 10^7 GeV (matter-like) and 10^9 GeV (Λ) thresholds. revision: yes

  2. Referee: [GUFO section] GUFO section (following the initial-radiation discussion): the claim that radiation-like reheating is compatible with GUFO 'only if gravitational processes are taken into account' requires an explicit side-by-side comparison of the relic density with and without the gravitational-production term; without this, the 'only if' qualifier is not substantiated by the given temperature evolution.

    Authors: We accept the request for an explicit comparison. The revised manuscript will include a direct side-by-side evaluation (text or additional figure panel) of the relic density for radiation-like reheating with and without the gravitational-production term, thereby substantiating the 'only if' statement. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The derivation begins with an explicit generalization of UFO to arbitrary T ~ a^{-ξ} (constant ξ) plus an initial radiation component sourced by gravitational production at reheating onset. The relic abundance and the quoted mass reach (10^7 GeV for n=2, matter-like reheating) are obtained by solving the Boltzmann equation under these stated assumptions; the results are not fitted to the target outcome, nor do any load-bearing steps reduce by definition or self-citation to the inputs. The modeling choices are declared up front and the calculation proceeds from them without circular reduction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions of thermal equilibrium, Boltzmann-equation validity in an expanding universe, and the existence of a reheating phase with power-law temperature evolution; no new particles or forces are postulated beyond gravitational production already considered in the literature.

free parameters (2)
  • n
    Exponent in <σv> ~ T^n / Λ^{n+2}; specialized to n=2 for the quoted results.
  • ξ
    Power-law index in T ~ a^{-ξ}; different values correspond to matter-like or radiation-like reheating.
axioms (2)
  • domain assumption Temperature during reheating follows T ~ a^{-ξ} for constant ξ
    Invoked to generalize UFO beyond the ϕ → f fbar channel.
  • domain assumption Gravitational particle production at reheating onset produces a non-negligible initial radiation abundance
    Required for the GUFO modification of the parameter space.

pith-pipeline@v0.9.1-grok · 5847 in / 1415 out tokens · 21179 ms · 2026-06-25T22:54:43.218045+00:00 · methodology

discussion (0)

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