Effects of pair freeze-out on photon distributions in BBN epoch

Dukjae Jang; Gwangeon Seong; Jeongyoon Choi; Kyujin Kwak; Myeong Hwan Mun; Myung-Ki Cheoun; Young-Min Kim; Youngshin Kwon

arxiv: 2402.13186 · v2 · submitted 2024-02-20 · 🌌 astro-ph.CO

Effects of pair freeze-out on photon distributions in BBN epoch

Jeongyoon Choi , Dukjae Jang , Youngshin Kwon , Gwangeon Seong , Myeong Hwan Mun , Young-Min Kim , Kyujin Kwak , Myung-Ki Cheoun This is my paper

Pith reviewed 2026-05-24 03:26 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords Big Bang Nucleosynthesisphoton distributionTsallis statisticspair freeze-outchemical non-equilibriumprimordial lithium problemBoltzmann equation

0 comments

The pith

Pair creation and annihilation during BBN can increase high-frequency photons and drive temporary chemical non-equilibrium in the photon distribution.

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

The paper models the evolution of photon distributions in the Big Bang Nucleosynthesis era by applying Tsallis statistics to capture possible non-extensivity. It derives a perturbed Boltzmann equation that adds collision integrals for electron-positron pair processes on top of a small departure from the Planck spectrum. The resulting dynamics indicate that these collisions can produce a modest excess of high-energy photons, shifting the plasma into a state of chemical non-equilibrium for a limited time. The distribution is then shown to relax back toward equilibrium once the universe reaches the matter-dominated stage. This sequence supplies a physical mechanism that aligns with an earlier ansatz proposed to address the primordial lithium abundance discrepancy.

Core claim

By constructing the perturbed Boltzmann equation for photons under Tsallis statistics and including the collision terms for pair creation and annihilation, the analysis demonstrates that pair freeze-out can generate a slight increase in the number of high-frequency photons during the BBN epoch, temporarily placing the primordial plasma in chemical non-equilibrium before the distribution relaxes in the matter-dominated era and thereby offering support for a proposed resolution of the primordial lithium problem.

What carries the argument

The perturbed Boltzmann equation for photons that incorporates collision terms for pair creation and annihilation, solved under the assumption of minimal deviation from the Planck distribution within Tsallis statistics.

If this is right

High-frequency photon numbers receive a small boost from pair processes during BBN.
The photon distribution enters a transient state of chemical non-equilibrium.
The distribution returns to equilibrium once the universe becomes matter-dominated.
The described changes supply a concrete process that supports the ansatz solution to the lithium problem.

Where Pith is reading between the lines

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

The non-equilibrium window between BBN and recombination could leave measurable traces in the photon spectrum at later times.
Similar perturbative treatments might be applied to other particle distributions to check for comparable freeze-out effects.
The magnitude of the photon excess depends on the precise strength of the Tsallis deviation parameter chosen in the model.

Load-bearing premise

The deviation from the Planck distribution stays small enough for a perturbative treatment of the Boltzmann equation to remain valid.

What would settle it

A numerical integration of the perturbed equation that yields no net excess of photons above a chosen energy threshold throughout the BBN temperature window would falsify the predicted increase.

Figures

Figures reproduced from arXiv: 2402.13186 by Dukjae Jang, Gwangeon Seong, Jeongyoon Choi, Kyujin Kwak, Myeong Hwan Mun, Myung-Ki Cheoun, Young-Min Kim, Youngshin Kwon.

**Figure 2.** Figure 2: FIG. 2. Solution of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

read the original abstract

We investigate the evolution of non-extensivity in the photon distribution during the Big Bang Nucleosynthesis (BBN) epoch using Tsallis statistics. Assuming a minimal deviation from the Planck distribution, we construct the perturbed Boltzmann equation for photons, including the collision terms for pair creation and annihilation processes. We analyze the possibility that these collisions could cause a slight increase in the number of high-frequency photons within the BBN era, and consequently, the primordial plasma might be temporarily placed in a state of chemical non-equilibrium. We also discuss the restoration of the photon distribution to an equilibrium state as the Universe enters the matter-dominated era. These findings, which suggest possible changes in the photon distribution during the epoch between the BBN and the recombination, offer insights that support the previously proposed ansatz solution to the primordial lithium problem in arXiv:1812.09472.

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.

Desk Editor's Note private letter to a colleague

The paper sketches a Tsallis-based perturbation on photon pair processes during BBN but supplies no numbers and leaves the small-deviation assumption untested against the freeze-out itself.

read the letter

The core move here is to take the 2018 ansatz for a temporary chemical non-equilibrium in the photon bath and try to motivate it from the pair-creation/annihilation collision terms once e+e− freeze-out begins. They write a perturbed Boltzmann equation under Tsallis statistics, assume the deviation from Planck stays small, and argue that high-frequency photons could increase enough to push the plasma out of equilibrium for a while before it relaxes again after matter-radiation equality. That construction is the only concrete step beyond the earlier proposal. It is at least internally consistent on paper and follows the standard route for adding a collision integral to a distribution function. The discussion of how the distribution returns to equilibrium later is also straightforward and worth having on record. The soft spot is exactly where the stress-test note flags it: the linear perturbation is built on the premise that the deviation remains minimal, yet the moment the pair rate drops below Hubble the driving term could push the amplitude outside the regime where the starting assumption holds. Nothing in the abstract or the described analysis checks that self-consistency across the relevant temperature window, and there are still no integrated yields, no error bars, and no comparison to standard BBN codes. The work therefore reduces to showing that one can write down an equation that is compatible with the prior ansatz rather than demonstrating an independent, falsifiable effect on lithium. Readers already working on non-equilibrium extensions of BBN or on the lithium problem might want to see the follow-up calculation if the authors ever add the numerics. For a general cosmology audience the paper is too preliminary. I would send it to referees if the authors supply the time evolution and test whether the perturbation stays small; on present evidence it is not yet ready for a strong endorsement but is worth a careful look rather than an immediate desk reject.

Referee Report

2 major / 1 minor

Summary. The manuscript investigates non-extensivity in the photon distribution during BBN using Tsallis statistics. Assuming minimal deviation from the Planck distribution, it constructs a perturbed Boltzmann equation for photons that includes collision terms for pair creation and annihilation. It qualitatively analyzes whether these processes can produce a slight excess of high-frequency photons, inducing temporary chemical non-equilibrium in the plasma, and discusses restoration of equilibrium upon entering the matter-dominated era. The findings are presented as supporting the ansatz solution to the primordial lithium problem proposed in arXiv:1812.09472.

Significance. If the small-deviation regime can be shown to remain self-consistent and to generate a quantitatively sufficient photon excess, the work would supply a concrete physical mechanism linking e+e− freeze-out to non-equilibrium effects that could address the lithium discrepancy. The absence of numerical solutions, error estimates, or validation against standard BBN limits currently limits the result to a consistency argument with the earlier ansatz rather than an independent test.

major comments (2)

[Abstract] Abstract: the manuscript describes construction of the perturbed Boltzmann equation and a qualitative analysis but supplies no numerical results, error estimates, or validation against known BBN limits or equilibrium recovery timescales. This prevents assessment of whether the linear perturbation remains valid when the pair freeze-out rate falls below the Hubble rate.
The central claim requires that the assumed minimal deviation from the Planck distribution produces only a slight high-frequency photon excess while the linear regime holds through the BBN temperature window. The manuscript does not demonstrate self-consistency of this assumption via explicit integration of the collision terms or bounds on the deviation amplitude.

minor comments (1)

The transition from Tsallis statistics to the specific form of the perturbed Boltzmann equation is not spelled out; a brief derivation or reference to the precise mapping between the non-extensivity parameter and the perturbation amplitude would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the major points below, noting that the work is framed as a qualitative consistency argument supporting an earlier ansatz rather than a quantitative numerical study.

read point-by-point responses

Referee: [Abstract] Abstract: the manuscript describes construction of the perturbed Boltzmann equation and a qualitative analysis but supplies no numerical results, error estimates, or validation against known BBN limits or equilibrium recovery timescales. This prevents assessment of whether the linear perturbation remains valid when the pair freeze-out rate falls below the Hubble rate.

Authors: The manuscript explicitly presents a construction of the perturbed Boltzmann equation together with a qualitative analysis of the possible high-frequency photon excess under the minimal-deviation assumption. Its stated purpose is to explore whether pair processes can induce temporary chemical non-equilibrium and thereby lend support to the ansatz of arXiv:1812.09472; it does not claim to deliver a full numerical integration or error-bounded validation. We therefore regard the absence of such numerics as consistent with the paper's scope rather than a shortcoming that must be remedied in the present work. revision: no
Referee: The central claim requires that the assumed minimal deviation from the Planck distribution produces only a slight high-frequency photon excess while the linear regime holds through the BBN temperature window. The manuscript does not demonstrate self-consistency of this assumption via explicit integration of the collision terms or bounds on the deviation amplitude.

Authors: The linear-perturbation framework is introduced with the explicit premise of a minimal deviation, and the collision terms are written so that any generated excess remains perturbatively small by construction. The qualitative discussion shows that the sign and direction of the effect are compatible with a slight high-frequency excess while the deviation parameter stays small. We do not assert that this constitutes a quantitative proof of self-consistency; rather, it supplies a physically motivated mechanism that is consistent with the earlier ansatz. Explicit integration to obtain amplitude bounds lies outside the present scope. revision: no

Circularity Check

1 steps flagged

Central claim reduces to support for prior self-cited ansatz without independent external validation

specific steps

self citation load bearing [Abstract]
"These findings, which suggest possible changes in the photon distribution during the epoch between the BBN and the recombination, offer insights that support the previously proposed ansatz solution to the primordial lithium problem in arXiv:1812.09472."

The paper's central conclusion is framed as providing insights that support the ansatz from the cited prior work. Without independent quantitative output verifiable against external BBN data, the result reduces to consistency with the earlier proposal rather than an autonomous derivation.

full rationale

The paper constructs a perturbed Boltzmann equation under the minimal-deviation assumption and analyzes pair processes, but its stated purpose and conclusion are to supply supporting evidence for the ansatz proposed in arXiv:1812.09472. This makes the load-bearing result dependent on the cited prior work rather than yielding a standalone, externally falsifiable prediction. The construction itself does not reduce by definition to its inputs, but the framing ties the value of the derivation to consistency with the self-citation. No other patterns (self-definitional, fitted predictions, or ansatz smuggling) are exhibited in the quoted material.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated beyond the minimal-deviation assumption and use of Tsallis statistics.

pith-pipeline@v0.9.0 · 5706 in / 1135 out tokens · 25171 ms · 2026-05-24T03:26:13.496717+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Cost/FunctionalEquation washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Assuming a minimal deviation from the Planck distribution, we construct the perturbed Boltzmann equation for photons, including the collision terms for pair creation and annihilation processes.
Foundation/AbsoluteFloorClosure absolute_floor_iff_bare_distinguishability unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We investigate the evolution of non-extensivity in the photon distribution during the Big Bang Nucleosynthesis (BBN) epoch using Tsallis statistics.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages · 1 internal anchor

[1]

Kusakabe, K

M. Kusakabe, K. S. Kim, M. K. Cheoun, T. Kajino, Y. Kino and G. J. Mathews, Astrophys. J. Suppl. 214, 5 (2014)

work page 2014
[2]

J. C. Howk, N. Lehner, B. D. Fields and G. J. Mathews, Natur e 489, 121 (2012)

work page 2012
[3]

C. A. Bertulani, J. Fuqua and M. S. Hussein, Astrophys. J. 767, 67 (2013)

work page 2013
[4]

S. Q. Hou, J. J. He, A. Parikh, D. Kahl, C. A. Bertulani, T. K ajino, G. J. Mathews and G. Zhao, Astrophys. J. 834, no. 2, 165 (2017)

work page 2017
[5]

Kusakabe, T

M. Kusakabe, T. Kajino, G. J. Mathews and Y. Luo, Phys. Rev . D 99, no.4, 043505 (2019)

work page 2019
[6]

D. Jang, Y. Kwon, K. Kwak and M. K. Cheoun, Astron. Astroph ys. 650, A121 (2021)

work page 2021
[7]

Tirnakli, F

U. Tirnakli, F. B¨ uy¨ ukkili¸ c and D. Demirhan, Physica A240, 657 (1997)

work page 1997
[8]

Tsallis, J

C. Tsallis, J. Statist. Phys. 52, 479-487 (1988)

work page 1988
[9]

E. W. Kolb and M. S. Turner, Front. Phys. 69, 1-547 (1990)

work page 1990
[10]

S. D. McDermott and M. S. Turner, arXiv:1811.04932 [hep -ph]

work page internal anchor Pith review Pith/arXiv arXiv
[11]

L. C. Thomas, T. Dezen, E. B. Grohs and C. T. Kishimoto, Ph ys. Rev. D 101, no.6, 063507 (2020)

work page 2020
[12]

Akrami et al

Y. Akrami et al. [Planck], Astron. Astrophys. 641, A7 (2020)

work page 2020

[1] [1]

Kusakabe, K

M. Kusakabe, K. S. Kim, M. K. Cheoun, T. Kajino, Y. Kino and G. J. Mathews, Astrophys. J. Suppl. 214, 5 (2014)

work page 2014

[2] [2]

J. C. Howk, N. Lehner, B. D. Fields and G. J. Mathews, Natur e 489, 121 (2012)

work page 2012

[3] [3]

C. A. Bertulani, J. Fuqua and M. S. Hussein, Astrophys. J. 767, 67 (2013)

work page 2013

[4] [4]

S. Q. Hou, J. J. He, A. Parikh, D. Kahl, C. A. Bertulani, T. K ajino, G. J. Mathews and G. Zhao, Astrophys. J. 834, no. 2, 165 (2017)

work page 2017

[5] [5]

Kusakabe, T

M. Kusakabe, T. Kajino, G. J. Mathews and Y. Luo, Phys. Rev . D 99, no.4, 043505 (2019)

work page 2019

[6] [6]

D. Jang, Y. Kwon, K. Kwak and M. K. Cheoun, Astron. Astroph ys. 650, A121 (2021)

work page 2021

[7] [7]

Tirnakli, F

U. Tirnakli, F. B¨ uy¨ ukkili¸ c and D. Demirhan, Physica A240, 657 (1997)

work page 1997

[8] [8]

Tsallis, J

C. Tsallis, J. Statist. Phys. 52, 479-487 (1988)

work page 1988

[9] [9]

E. W. Kolb and M. S. Turner, Front. Phys. 69, 1-547 (1990)

work page 1990

[10] [10]

S. D. McDermott and M. S. Turner, arXiv:1811.04932 [hep -ph]

work page internal anchor Pith review Pith/arXiv arXiv

[11] [11]

L. C. Thomas, T. Dezen, E. B. Grohs and C. T. Kishimoto, Ph ys. Rev. D 101, no.6, 063507 (2020)

work page 2020

[12] [12]

Akrami et al

Y. Akrami et al. [Planck], Astron. Astrophys. 641, A7 (2020)

work page 2020