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arxiv: 2604.14688 · v1 · submitted 2026-04-16 · ✦ hep-ph · astro-ph.CO

Recognition: unknown

Exploring non-equilibrium effects in sequential freeze-in

Shiuli Chatterjee , Andrzej Hryczuk
Authors on Pith no claims yet

Pith reviewed 2026-05-10 11:18 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords dark matterfreeze-innon-equilibriumphase-spacerelic abundancemulti-component dark sectortwo-scalar modelnon-thermal evolution
0
0 comments X

The pith

In a two-scalar dark sector, non-equilibrium evolution shifts the dark matter relic abundance by up to an order of magnitude from standard calculations.

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

The paper examines freeze-in production in multi-component dark sectors where the dark sector itself may not reach local thermal equilibrium. In a minimal two-scalar model chosen for its potential observable signatures, the authors solve the full phase-space evolution instead of the usual number-density equations. They report that the resulting dark matter abundance can differ by as much as a factor of ten from the traditional approach in regions consistent with current constraints. This matters because relic density predictions directly affect expected rates in indirect detection and long-lived particle searches.

Core claim

Focusing on the phenomenologically viable regions, we analyse the impact of non-thermal evolution on the dark matter abundance, finding deviations of up to an order of magnitude between the full phase-space treatment and the traditional number-density approach.

What carries the argument

Numerical solution of the phase-space Boltzmann equations for the two-scalar model, tracking non-thermal momentum distributions during sequential freeze-in.

If this is right

  • Relic density calculations for multi-particle dark sectors must move beyond integrated number densities to full momentum distributions.
  • Parameter spaces derived from number-density freeze-in can mis-predict indirect detection fluxes by up to an order of magnitude.
  • Forward physics searches for long-lived particles will require adjusted production rates once non-equilibrium effects are included.
  • Dedicated phase-space codes become necessary for any dark sector with sequential production channels.

Where Pith is reading between the lines

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

  • Similar order-of-magnitude shifts may appear in other freeze-in scenarios involving multiple dark states, even if the paper only studies one model.
  • Existing cosmological bounds on dark matter from structure formation could tighten or loosen once non-thermal momentum distributions are properly accounted for.
  • The result motivates building general-purpose phase-space solvers that can handle arbitrary dark sector interactions beyond the two-scalar case.

Load-bearing premise

The chosen minimal two-scalar model and its numerical phase-space implementation faithfully capture the non-equilibrium dynamics without hidden fitting or uncontrolled approximations.

What would settle it

Re-running the phase-space solver for the same benchmark points and finding that the dark matter yield differs from the number-density result by less than a factor of a few.

read the original abstract

Freeze-in of multi-component dark sectors is governed not only by the interaction with the thermal plasma, but also by their internal dynamics. Full thermalisation within the dark sector is not guaranteed, raising the question of impact of departures from local thermal equilibrium onto the evolution and ultimately relic abundance and momentum distribution of dark matter. In this work we explore this question in a minimal two-scalar model, which can give rise to observable signatures in indirect detection and long-lived particle searches at forward physics experiments. Focusing on the phenomenologically viable regions, we analyse the impact of non-thermal evolution on the dark matter abundance, finding deviations of up to an order of magnitude between the full phase-space treatment and the traditional number-density approach. Our results highlight the importance of phase-space level computation for accurate freeze-in predictions and further motivate dedicated numerical tools for studying the evolution of multi-component dark sectors at the phase space level.

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 paper studies non-equilibrium dynamics in sequential freeze-in of a multi-component dark sector using a minimal two-scalar model. It solves the full momentum-dependent Boltzmann equations for the phase-space distributions and compares the resulting dark matter relic abundance to the standard integrated number-density approach, reporting deviations of up to an order of magnitude in phenomenologically viable regions. The work argues that these differences arise from non-thermal evolution within the dark sector and calls for dedicated phase-space numerical tools.

Significance. If the reported deviations are confirmed to be physical rather than numerical artifacts, the result would demonstrate that the number-density approximation can fail at the order-of-magnitude level for sequential freeze-in scenarios, with direct consequences for indirect detection signals and long-lived particle searches. The choice of a concrete, minimal model and the quantitative comparison provide a useful benchmark for future phase-space studies in dark matter cosmology.

major comments (2)
  1. [§3.2] §3.2 (Numerical Implementation): No convergence tests are presented for the momentum-grid resolution, time-stepping accuracy, or collision-integral discretization in the phenomenologically viable parameter regions. The central claim of order-of-magnitude deviations between the full phase-space treatment and the number-density approach is therefore not yet shown to be robust against the numerical method, as the difference can be sensitive to these choices.
  2. [§4] §4 (Results): The comparison plots and tables do not include error estimates, sensitivity scans over numerical parameters, or explicit checks against known thermal limits. Without these, it remains unclear whether the reported deviations are driven by genuine non-equilibrium phase-space effects or by uncontrolled approximations in the solver.
minor comments (2)
  1. [§2] The notation for the interaction rates and distribution functions in §2 could be made more explicit to facilitate reproduction of the Boltzmann equations.
  2. A brief statement on the computational cost and typical runtime of the phase-space solver would help readers assess the practicality of the method.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive feedback on numerical robustness. We address the major comments point by point below. We agree that additional validation is needed and will revise the manuscript to incorporate the requested tests and checks.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (Numerical Implementation): No convergence tests are presented for the momentum-grid resolution, time-stepping accuracy, or collision-integral discretization in the phenomenologically viable parameter regions. The central claim of order-of-magnitude deviations between the full phase-space treatment and the number-density approach is therefore not yet shown to be robust against the numerical method, as the difference can be sensitive to these choices.

    Authors: We agree that explicit convergence tests were not included in the original submission and that they are necessary to substantiate the robustness of the results. In the revised manuscript we will add a new subsection (or appendix) that presents convergence studies with respect to momentum-grid resolution, time-stepping accuracy, and collision-integral discretization, performed specifically in the phenomenologically viable parameter regions. These tests will demonstrate that the reported order-of-magnitude deviations remain stable under refinement of the numerical parameters. revision: yes

  2. Referee: [§4] §4 (Results): The comparison plots and tables do not include error estimates, sensitivity scans over numerical parameters, or explicit checks against known thermal limits. Without these, it remains unclear whether the reported deviations are driven by genuine non-equilibrium phase-space effects or by uncontrolled approximations in the solver.

    Authors: We acknowledge that the original Section 4 lacks error estimates, sensitivity scans, and explicit thermal-limit checks. We will revise the results section to include (i) error estimates on the computed relic abundances, (ii) sensitivity scans over the principal numerical parameters, and (iii) direct comparisons to the expected thermal-equilibrium limits in appropriate regimes. These additions will confirm that the observed deviations originate from non-equilibrium phase-space evolution rather than numerical artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity: numerical comparison of Boltzmann solvers in a minimal model

full rationale

The paper performs a numerical exploration of non-equilibrium dynamics in a two-scalar sequential freeze-in scenario by solving the full phase-space Boltzmann equations and comparing the resulting dark-matter abundance to the integrated number-density approximation. No equations, parameters, or results are shown to be defined in terms of themselves; the claimed order-of-magnitude deviations are outputs of the solver rather than inputs, and no self-citation chain or ansatz smuggling is present in the abstract or description. The derivation chain is therefore self-contained and independent of the target observable.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review prevents identification of specific free parameters, axioms, or invented entities; the central claim rests on an unstated numerical implementation of phase-space evolution whose assumptions are not visible.

pith-pipeline@v0.9.0 · 5445 in / 1137 out tokens · 21686 ms · 2026-05-10T11:18:28.286593+00:00 · methodology

discussion (0)

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