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arxiv: 2606.17155 · v1 · pith:TAQBXLKJnew · submitted 2026-06-15 · ✦ hep-ph · astro-ph.CO

Freeze-in and ultra-relativistic freeze-out during general reheating scenarios

Kuldeep Deka This is my paper

Pith reviewed 2026-06-27 02:57 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords dark matterreheatingfreeze-infreeze-outrelic abundanceBoltzmann equationearly universe
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The pith

A general analytic framework shows dark matter production during reheating is controlled by two temperature exponents.

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

The paper derives an analytic framework for how dark matter is produced from the Standard Model particles while the universe is reheating after inflation. It parametrizes the reheating phase with an equation-of-state parameter and a cooling index, and the dark matter interaction with a scale and temperature power. This unifies different production mechanisms like freeze-in and ultra-relativistic freeze-out. A sympathetic reader would care because the relic density depends on the early thermal history, and this provides closed-form expressions instead of numerical solutions for many cases. The results explain how the same interaction can lead to different regimes depending on reheating details.

Core claim

The production history is organised by two critical temperature exponents: one controls whether a thermalised relativistic species decouples during reheating or after radiation domination begins, and the other controls whether post-decoupling production is infrared dominated, ultraviolet dominated or logarithmic. We derive analytic relic yields in the main regimes, including both the entropy-diluted freeze-out contribution and the post-freeze-out production term. These results explain the scaling of relic-density contours and are checked against numerical Boltzmann solutions. For matter-like reheating our framework reproduces the known IR/UV ultra-relativistic freeze-out structure, while mor

What carries the argument

The effective equation-of-state parameter ω and cooling index α describing the reheating background, together with the dark-matter interaction scale Λ and temperature power n, which determine the critical temperature exponents organizing the production history.

If this is right

  • The relic density contours scale according to the derived exponents for different reheating histories.
  • Post-decoupling production can be infrared, ultraviolet or logarithmic dominated depending on the second exponent.
  • Entropy dilution affects the freeze-out contribution during reheating.
  • General reheating can move a given interaction between freeze-in, ultra-relativistic freeze-out and ordinary freeze-out.

Where Pith is reading between the lines

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

  • Testing these analytic yields against more detailed numerical simulations with specific particle physics models could reveal when approximations break.
  • Extending the framework to include multiple interactions or non-power-law rates might connect to broader early-universe scenarios.
  • Observational constraints on dark matter could be reinterpreted in light of possible non-standard reheating to adjust the required interaction strengths.

Load-bearing premise

The reheating background follows an effective constant equation-of-state parameter and cooling index, and the dark matter interaction rate is a simple power of temperature times a scale.

What would settle it

A numerical integration of the Boltzmann equation for a specific choice of ω, α, Λ, n that yields a relic abundance differing from the analytic formula in one of the regimes.

read the original abstract

The dark-matter relic abundance can depend sensitively on the thermal history before radiation domination. We derive a general analytic framework for dark-matter production from the Standard Model bath during a non-instantaneous reheating era, unifying freeze-in, ultra-relativistic freeze-out and the approach to ordinary non-relativistic freeze-out. The reheating background is described by an effective equation-of-state parameter $\omega$ and a cooling index $\alpha$, while the dark-matter interaction rate is parametrised by an effective scale $\Lambda$ and a leading temperature power $n$. We show that the production history is organised by two critical temperature exponents: one controls whether a thermalised relativistic species decouples during reheating or after radiation domination begins, and the other controls whether post-decoupling production is infrared dominated, ultraviolet dominated or logarithmic. We derive analytic relic yields in the main regimes, including both the entropy-diluted freeze-out contribution and the post-freeze-out production term. These results explain the scaling of relic-density contours and are checked against numerical Boltzmann solutions. For matter-like reheating our framework reproduces the known IR/UV ultra-relativistic freeze-out structure, while more general reheating histories can shift the same microscopic interaction between freeze-in, ultra-relativistic freeze-out and ordinary freeze-out regimes.

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

0 major / 2 minor

Summary. The manuscript derives a general analytic framework for dark-matter production from the Standard Model bath during a non-instantaneous reheating era, unifying freeze-in, ultra-relativistic freeze-out and the approach to ordinary non-relativistic freeze-out. The reheating background is described by an effective equation-of-state parameter ω and a cooling index α, while the dark-matter interaction rate is parametrised by an effective scale Λ and a leading temperature power n. The production history is organised by two critical temperature exponents that control decoupling and the infrared/ultraviolet/logarithmic character of post-decoupling production; analytic relic yields are derived in the main regimes (including entropy-diluted freeze-out and post-freeze-out terms) and checked against numerical Boltzmann solutions. The framework reproduces known IR/UV structure for matter-like reheating and shows how general histories can shift a given microscopic interaction between regimes.

Significance. If the derivations hold, the work supplies a compact analytic tool for relic-density calculations across a broad class of reheating histories. The organisation by two critical temperature exponents, the explicit matching to known limits, and the stated numerical validation constitute clear strengths that can reduce reliance on case-by-case numerics and clarify the scaling of relic-density contours in non-standard cosmologies.

minor comments (2)
  1. [Abstract] Abstract: the two critical temperature exponents are central to the organisation of regimes; stating their explicit forms would make the abstract self-contained.
  2. The effective parameters ω, α, Λ, n are introduced without a compact summary table of their physical ranges and limiting cases; adding one would improve readability for readers scanning the framework.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive review and recommendation to accept the manuscript. The provided summary accurately captures the scope and contributions of our analytic framework for dark-matter production during general reheating.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained from Boltzmann equation with external effective parameters

full rationale

The paper presents an analytic derivation of relic yields for dark-matter production during reheating, organized by effective parameters (ω, α for background; Λ, n for interaction rate) and two critical temperature exponents. These are introduced as parametrizations of the reheating history and DM rate, with explicit matching to numerical Boltzmann solutions stated. No load-bearing step reduces by construction to a fit, self-citation chain, or renamed input; the central unification follows from solving the Boltzmann equation under the stated effective description. The framework reproduces known limits (e.g., matter-like reheating) as consistency checks rather than as the source of the result. This is the normal case of an independent derivation.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

Framework rests on effective parametrization of reheating (ω, α) and interactions (Λ, n) plus the standard Boltzmann equation; these are introduced as descriptive tools rather than derived from microphysics.

free parameters (4)
  • ω
    Effective equation-of-state parameter describing reheating background evolution
  • α
    Cooling index for the reheating phase
  • Λ
    Effective interaction scale for dark matter
  • n
    Leading temperature power in the interaction rate
axioms (2)
  • standard math Boltzmann equation governs the number density evolution of dark matter
    Standard tool for relic abundance calculations in cosmology
  • domain assumption Reheating phase can be captured by constant effective ω and α
    Core modeling choice enabling the analytic framework

pith-pipeline@v0.9.1-grok · 5750 in / 1432 out tokens · 48756 ms · 2026-06-27T02:57:15.768047+00:00 · methodology

discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Gravitational ultra-relativistic freeze-out during general reheating

    hep-ph 2026-06 unverdicted novelty 5.0

    Generalizes UFO to T ~ a^{-ξ} and introduces GUFO from gravitational production, extending DM mass reach to 10^7 GeV for n=2 in matter-like reheating.

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