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arxiv: 2507.23354 · v2 · submitted 2025-07-31 · ✦ hep-ph · astro-ph.CO

Consistent N_{rm eff} fitting in big bang nucleosynthesis analysis

Sougata Ganguly , Tae Hyun Jung , Seokhoon Yun This is my paper

Pith reviewed 2026-05-19 02:44 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords big bang nucleosynthesisN_effentropy injectionneutrino decouplingdark radiationneutron-proton conversionprimordial abundances
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0 comments X p. Extension

The pith

BBN constraints on negative N_eff deviate when entropy injection is modeled after neutrino decoupling.

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

This paper identifies an inconsistency in how negative values of Delta N_eff are handled in big bang nucleosynthesis analyses. When negative Delta N_eff comes from entropy injection into the electromagnetic sector after neutrino decoupling, the neutrino temperature is diluted and the rates for neutrino-driven neutron to proton conversions are suppressed. Consequently, the bounds placed on N_eff from primordial element abundances differ substantially from those obtained by simply extending dark radiation models to negative deviations. Readers should care because N_eff is widely used to probe new physics in cosmology, and incorrect assumptions here can distort conclusions about the early universe.

Core claim

Under the assumption that negative Delta N_eff arises from entropy injection into the electromagnetic sector after neutrino decoupling, the resulting BBN constraints on N_eff deviate significantly from those obtained by the conventional extrapolation of dark radiation scenarios into the Delta N_eff < 0 regime. This process dilutes the neutrino density and suppresses the rate of neutrino-driven neutron-proton conversion.

What carries the argument

Entropy injection into the electromagnetic sector after neutrino decoupling, which dilutes the neutrino temperature relative to photons and suppresses neutrino-induced n-p conversion rates.

If this is right

  • The allowed range of N_eff must be restricted or neutrino reaction rates adjusted according to the physical scenario for consistent BBN analysis.
  • BBN constraints become scenario-dependent rather than universally applicable for negative Delta N_eff.
  • This affects the interpretation of cosmological observations in the presence of new physics that injects entropy post-decoupling.

Where Pith is reading between the lines

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

  • Future studies of decaying particles should use this adjusted approach to derive more accurate BBN limits.
  • The method could be extended to other post-decoupling processes affecting neutrino-photon temperature ratios.
  • It connects to the broader problem of consistently parametrizing deviations in effective degrees of freedom across different epochs.

Load-bearing premise

The entropy injection is assumed to occur after neutrino decoupling, affecting only the electromagnetic sector and thereby diluting neutrinos relative to photons while suppressing their interaction rates.

What would settle it

Precise measurements of primordial helium-4 and deuterium abundances that distinguish between the adjusted neutrino rates and the conventional negative Delta N_eff extrapolation.

Figures

Figures reproduced from arXiv: 2507.23354 by Seokhoon Yun, Sougata Ganguly, Tae Hyun Jung.

Figure 1
Figure 1. Figure 1: shows our fitting result in the Ωbh 2 – Neff plane obtained with the simplest assumption on neutrino tem￾perature for the ∆Neff < 0 region; we assume that the negative ∆Neff solely comes from the change in Tν/Tγ (the details of the assumptions are given in the next sec￾tion, and the result shown in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Primordial [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
read the original abstract

The effective number of neutrino species, $N_{\rm eff}$, serves as a key fitting parameter extensively employed in cosmological studies. In this work, we point out a fundamental inconsistency in the conventional treatment of $N_{\rm eff}$ in big bang nucleosynthesis (BBN), particularly regarding its applicability to new physics scenarios where $\Delta N_{\rm eff}$, the deviation of $N_{\rm eff}$ from the standard BBN prediction, is negative. To ensure consistent interpretation, it is imperative to either restrict the allowed range of $N_{\rm eff}$ or systematically adjust neutrino-induced reaction rates based on physically motivated assumptions. As a concrete example, we consider a simple scenario in which a negative $\Delta N_{\rm eff}$ arises from entropy injection into the electromagnetic sector due to the decay of long-lived particles after neutrino decoupling. This process dilutes the neutrino density and suppresses the rate of neutrino-driven neutron-proton conversion. Under this assumption, we demonstrate that the resulting BBN constraints on $N_{\rm eff}$ deviate significantly from those obtained by the conventional, but unphysical, extrapolation of dark radiation scenarios into the $\Delta N_{\rm eff} < 0$ regime.

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 / 1 minor

Summary. The paper claims that conventional N_eff fitting in BBN is inconsistent for negative Delta N_eff because it simply reduces total radiation density without accounting for changes to neutrino temperature or weak rates. Using the concrete example of entropy injection into the electromagnetic sector from long-lived particle decays after neutrino decoupling, the authors argue that this physically motivated scenario dilutes the neutrino-to-photon temperature ratio and suppresses neutrino-induced n-p conversion rates, leading to BBN constraints on N_eff that deviate significantly from those obtained by extrapolating dark-radiation models into the Delta N_eff < 0 regime.

Significance. If the quantitative demonstration is robust, the result would be significant for BBN analyses of new-physics scenarios that produce negative Delta N_eff, as it shows that unphysical extrapolations can bias constraints on primordial abundances and thereby affect interpretations of cosmological data.

major comments (2)
  1. [Abstract] The central claim that constraints 'deviate significantly' rests on the post-decoupling entropy-injection scenario, yet the manuscript presents this only as an illustrative example without deriving the required rescaling of the weak rates from the Boltzmann equations or from an explicit particle Lagrangian (see abstract and the discussion of the concrete scenario).
  2. To establish that the modified Hubble rate and adjusted weak rates produce quantitatively different abundance predictions, the paper must show the effect on the n-p conversion rates and the resulting shifts in Y_p or D/H; without these explicit calculations or comparison plots, the size of the reported deviation cannot be verified as robust against changes in decay lifetime, branching ratio, or injection epoch.
minor comments (1)
  1. Clarify in the introduction whether the standard N_eff = 3.046 value is held fixed or allowed to vary when comparing the two fitting procedures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We appreciate the opportunity to clarify the scope of our illustrative example and to strengthen the quantitative presentation of the results. We address each major comment below and indicate the revisions we will implement.

read point-by-point responses

  1. Referee: [Abstract] The central claim that constraints 'deviate significantly' rests on the post-decoupling entropy-injection scenario, yet the manuscript presents this only as an illustrative example without deriving the required rescaling of the weak rates from the Boltzmann equations or from an explicit particle Lagrangian (see abstract and the discussion of the concrete scenario).

    Authors: The entropy-injection scenario serves as a concrete illustrative example to demonstrate the physical inconsistency of extrapolating conventional N_eff fits into the negative Delta N_eff regime. The rescaling of the weak rates follows from the standard entropy dilution that reduces the neutrino-to-photon temperature ratio after decoupling, which directly suppresses the phase-space density entering the n-p conversion rates. This is a general consequence of post-decoupling EM entropy production and does not depend on a specific particle Lagrangian. To address the concern, we will add a concise derivation of the temperature ratio and the resulting Boltzmann-equation adjustment to the weak rates in the revised manuscript. revision: yes

  2. Referee: [—] To establish that the modified Hubble rate and adjusted weak rates produce quantitatively different abundance predictions, the paper must show the effect on the n-p conversion rates and the resulting shifts in Y_p or D/H; without these explicit calculations or comparison plots, the size of the reported deviation cannot be verified as robust against changes in decay lifetime, branching ratio, or injection epoch.

    Authors: The BBN abundance calculations in the manuscript already incorporate both the modified Hubble rate and the adjusted weak rates for the entropy-injection example, yielding the reported deviation from conventional fits. To make the quantitative impact explicit and allow verification of robustness, we will include new figures in the revised version showing the n-p conversion rates as a function of temperature for the standard and modified cases, together with the resulting shifts in Y_p and D/H for representative values of decay lifetime, branching ratio, and injection epoch. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the N_eff BBN consistency analysis

full rationale

The paper contrasts the conventional extrapolation of N_eff into the negative Delta N_eff regime (which simply reduces total radiation density) against an explicit illustrative scenario of post-neutrino-decoupling entropy injection into the EM sector from long-lived particle decay. This scenario is used to adjust both the Hubble expansion rate and the neutrino-induced n-p conversion rates, with the resulting abundance predictions computed numerically and shown to differ. No load-bearing step reduces by construction to a fitted input, self-citation chain, or ansatz smuggled from prior work; the modeling choice is stated as a concrete example rather than derived as a uniqueness theorem, and the central claim remains an independent numerical comparison against standard BBN codes. The derivation is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on standard BBN reaction network assumptions and the timing of neutrino decoupling; no new free parameters or invented entities are introduced in the abstract description.

axioms (1)
  • domain assumption Neutrino decoupling occurs before the entropy injection from long-lived particle decay
    This timing is required for the dilution to affect only the relative neutrino temperature and suppress neutrino-driven rates; invoked in the concrete example scenario.

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