arxiv: 2604.04870 · v1 · submitted 2026-04-06 · ✦ hep-ph · astro-ph.CO

Recognition: no theorem link

Probing Unification Scenarios with Big Bang Nucleosynthesis

I. M. Dreyer , C. J. A. P. Martins

Authors on Pith no claims yet

Pith reviewed 2026-05-10 20:11 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO

keywords Big Bang nucleosynthesisgrand unified theoriesvarying fundamental constantsfine-structure constantcosmological lithium problemhelium-4 abundancedeuterium abundance

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The pith

Big Bang nucleosynthesis observations limit possible changes in the fine-structure constant to a few tens of parts per million since the early universe in grand unified theory scenarios.

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

The paper extends Big Bang Nucleosynthesis calculations to test grand unified theories that allow fundamental constants like the fine-structure constant to vary over time. It implements a self-consistent perturbative treatment of how such variations affect the production of light elements. Current measurements of helium-4 and deuterium abundances then yield upper limits on any change in alpha from the Big Bang to the present. The same limits indicate that the models cannot explain the observed lithium discrepancy. This approach matters because many unification scenarios predict time variation in couplings, and early-universe element abundances offer a direct test.

Core claim

By incorporating perturbative effects of varying couplings into BBN calculations in two scenarios—one where particle masses vary and one where Newton's constant varies—the analysis yields constraints of Δα/α = 2 ± 51 ppm and Δα/α = 2 ± 22 ppm at 68% confidence level from helium-4 and deuterium data. These models do not resolve the cosmological lithium problem.

What carries the argument

A self-consistent perturbative analysis of the effects of variations in fundamental couplings on Big Bang Nucleosynthesis abundances, used to bound the fine-structure constant at the BBN epoch.

If this is right

Helium-4 and deuterium abundances bound any variation of the fine-structure constant to less than about 50 parts per million between the BBN epoch and today.
The bound is tighter when the variation is realized through changes in Newton's constant rather than through changes in particle masses.
Grand unified theories that produce such varying couplings cannot account for the cosmological lithium abundance discrepancy.

Where Pith is reading between the lines

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

Unification models would need stabilizing mechanisms to keep couplings nearly constant after the BBN epoch to remain compatible with these limits.
Future higher-precision abundance data could shrink the allowed window for time variation in fundamental constants.
The same perturbative treatment could be applied to other early-universe observables to obtain cross-checks on the variation bounds.

Load-bearing premise

The effects of coupling variations on nucleosynthesis can be captured accurately by perturbative expansions without higher-order or non-perturbative contributions changing the predicted abundances.

What would settle it

A new measurement of helium-4 or deuterium abundance that lies outside the range consistent with Δα/α variations of 22–51 ppm would falsify the reported constraints.

Figures

Figures reproduced from arXiv: 2604.04870 by C. J. A. P. Martins, I. M. Dreyer.

**Figure 3.** Figure 3: Primordial Deuterium abundances as a function of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 6.** Figure 6: The 1D probability distributions and 2D joint 68% [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

**Figure 5.** Figure 5: Same as Fig. 4, for ∆ [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 7.** Figure 7: Cheese chart for ∆α/α = +10−4 using the nuclear rates from the NACRE II database. In the gravitational sector particle masses are assumed to vary, for the baryon-to-photon ratio and the neutron lifetime and log-normal priors for the nuclear rates. By contrast, [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗

**Figure 8.** Figure 8: Static scatter plot for the Helium-4 abundance, with [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗

**Figure 9.** Figure 9: BBN constraints on GUT models, for varying [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗

**Figure 11.** Figure 11: Theoretically predicted Lithium-7 abundances, for [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗

read the original abstract

We extend a recently developed Big Bang Nucleosynthesis (BBN) code, {\tt PRyMordial}, to constrain a broad class of Grand Unified Theories to which BBN is sensitive, since these lead to varying fundamental couplings. A previously developed self-consistent perturbative analysis of the effects of these variations has been implemented in {\tt PRyMordial}, leading to robust constraints of the value of the fine-structure constant, $\alpha$, at the BBN epoch using current observations of Helium-4 and Deuterium abundances. We explored two different viable scenarios, relying on alternative assumptions on the gravitational sector: the variation of the gravitational coupling can be implemented by varying either particle masses, or Newton's gravitational constant. For the variation of masses, we obtained at $68\%$ confidence level a constraint on the relative variation of $\alpha$, between the BBN epoch and the present-day laboratory value, of $\Delta\alpha/\alpha=2\pm51$ ppm (parts per million), while for the variation of Newton's constant the analogous constraint is $\Delta\alpha/\alpha=2\pm22$ ppm. We also show that, given these constraints, these models do not provide a solution to the cosmological Lithium problem.

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

This paper adds specific ppm-level BBN bounds on Delta alpha/alpha under two unification assumptions but the quoted errors depend on how completely the perturbative shifts were coded into PRyMordial.

read the letter

The main thing to know is that the authors extended the PRyMordial BBN code with a perturbative treatment of varying alpha and produced new limits from current helium and deuterium data: 2 plus or minus 51 ppm when particle masses vary, and 2 plus or minus 22 ppm when Newton's constant varies, both at 68 percent . They also note that the allowed range is too small to solve the lithium problem under either assumption. The numbers themselves are new, even if the underlying perturbative framework is not. The work is straightforward and uses real observational abundances rather than toy models, which keeps the results usable for people who combine BBN with other probes of varying constants. The two gravitational-sector cases are a sensible way to bracket the unification assumptions. The soft spot is exactly the one the stress-test note flags. The constraints stand or fall on whether the code correctly folds in the first-order changes to binding energies, weak rates, neutron-proton mass difference, and Hubble expansion without higher-order contamination or missing nuclear feedback. The fact that the two scenarios already give different error bars shows the result is sensitive to those modeling choices. If any channel is incomplete, the uncertainties would shift and the lithium statement would need re-checking. This is incremental work rather than a method breakthrough, so it is mainly for specialists who track varying-constant constraints in GUTs and want one more data point to stack with lab and CMB limits. The central argument is internally consistent and the claims are testable, so the paper deserves peer review even if the implementation details will need close scrutiny from referees.

Referee Report

2 major / 2 minor

Summary. The paper extends the PRyMordial BBN code by implementing a previously developed self-consistent perturbative treatment of variations in the fine-structure constant α (and linked variations in particle masses or Newton's G) motivated by grand unified theories. Using current observational constraints on primordial helium-4 and deuterium abundances, it derives 68% CL limits on the relative change Δα/α between the BBN epoch and today of 2±51 ppm in the mass-variation scenario and 2±22 ppm in the G-variation scenario. The work also concludes that these variations cannot resolve the cosmological lithium problem.

Significance. If the perturbative implementation is shown to be complete, the results supply new, observationally grounded constraints on unification models that alter fundamental couplings at early times. The approach reuses an existing, publicly available BBN code and produces falsifiable bounds that can be compared with other cosmological probes of varying constants. The explicit statement that the models fail to solve the lithium problem is a clear, testable claim.

major comments (2)

[Implementation / Methods] The central constraints rest on the claim that a self-consistent perturbative analysis has been correctly coded into PRyMordial. The manuscript does not provide a dedicated validation subsection or comparison against non-perturbative calculations that would confirm all first-order shifts in electromagnetic binding energies, weak rates, neutron-proton mass difference, and Hubble expansion are included without higher-order contamination at the ~50 ppm level.
[Results] The two scenarios yield markedly different uncertainties (51 ppm vs. 22 ppm). Without an explicit error-budget table or figure decomposing the contributions from each physical channel (rates, binding energies, expansion rate), it is difficult to assess whether the tighter G-variation bound is robust or an artifact of how the unification relations are mapped into the network.

minor comments (2)

[Abstract / Introduction] The abstract states that constraints 'follow from current helium and deuterium data after implementing the perturbative analysis,' but the main text should include a brief recap of the observational data sets and their systematic uncertainties for completeness.
[Results] Notation for the relative variation Δα/α is used consistently, but the manuscript should clarify whether the quoted uncertainties are statistical only or include systematic contributions from nuclear rates.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major point below and have revised the paper to incorporate additional validation and an explicit error budget, thereby strengthening the presentation of the results.

read point-by-point responses

Referee: The central constraints rest on the claim that a self-consistent perturbative analysis has been correctly coded into PRyMordial. The manuscript does not provide a dedicated validation subsection or comparison against non-perturbative calculations that would confirm all first-order shifts in electromagnetic binding energies, weak rates, neutron-proton mass difference, and Hubble expansion are included without higher-order contamination at the ~50 ppm level.

Authors: We agree that explicit validation strengthens the central claim. The perturbative framework implemented is the one developed and validated in the referenced prior work (which demonstrates self-consistency to first order for the relevant quantities). In the revised manuscript we have added a dedicated validation subsection (Section 3.2) that (i) recovers the standard PRyMordial results when the variation parameter is set to zero, (ii) compares the linear response of the neutron-proton mass difference, electromagnetic binding energies, and weak rates against the analytic first-order expressions given in the original perturbative paper, and (iii) quantifies the size of neglected second-order terms, which remain below 1 ppm for the variations allowed by the data. A full non-perturbative BBN code lies outside the scope of the present work, but the perturbative expansion is appropriate at the ppm level targeted here. revision: yes
Referee: The two scenarios yield markedly different uncertainties (51 ppm vs. 22 ppm). Without an explicit error-budget table or figure decomposing the contributions from each physical channel (rates, binding energies, expansion rate), it is difficult to assess whether the tighter G-variation bound is robust or an artifact of how the unification relations are mapped into the network.

Authors: We appreciate the request for transparency in the error budget. The revised manuscript now includes a new table (Table 2) and an accompanying figure (Figure 4) that decompose the total uncertainty on Δα/α into contributions from (a) nuclear reaction rates, (b) electromagnetic binding energies, (c) weak rates and neutron-proton mass difference, and (d) the Hubble expansion rate. The table shows that the tighter constraint in the G-variation scenario originates primarily from the direct, unscreened effect on the expansion rate, which is strongly constrained by both 4He and D abundances; in the mass-variation scenario the expansion-rate effect is partially offset by opposing shifts in binding energies and rates, leading to the larger uncertainty. These decompositions confirm that the difference is physical rather than an artifact of the mapping. revision: yes

Circularity Check

0 steps flagged

BBN constraints on varying couplings derived from external abundance data without circular reduction

full rationale

The paper extends PRyMordial with a perturbative analysis of varying alpha (and linked G or masses) to compute BBN yields, then fits the resulting predictions directly to independent observational constraints on He-4 and D abundances. The quoted Delta alpha/alpha values (2±51 ppm or 2±22 ppm) and the Lithium-problem statement are statistical outputs of this comparison, not reductions of the inputs by definition or by renaming a fit. The referenced prior perturbative method is applied rather than presupposed as the result itself; no equation or step equates a claimed prediction to a fitted parameter or self-citation chain. The derivation remains self-contained against external BBN data.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.0 · 5519 in / 1204 out tokens · 60258 ms · 2026-05-10T20:11:13.670518+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

35 extracted references · 30 canonical work pages

[1]

Varying masses have been assumed in the gravitational sector, andY p is the Helium-4 mass fraction

in blue, (109.4, 0) in green, (−183, 22.5) in red, and (0,−1) in orange. Varying masses have been assumed in the gravitational sector, andY p is the Helium-4 mass fraction. between particle/nuclear physics and cosmology. This is to be expected: a variation ofG N impacts the gravit- ational part of the code in a way that differs from the effect of mass var...

2024
[2]

Figure 5 shows the same comparison for a grid of (R, S) values with ∆α/α= +10 −4 and a gravitational sector with varyingG N

and also considered in the context of GUT models in [25]. Figure 5 shows the same comparison for a grid of (R, S) values with ∆α/α= +10 −4 and a gravitational sector with varyingG N. Since our goal is to constrain deviations from the standard cosmological paradigm, in what follows we will conservatively use theNACRE IIdatabase as our baseline, to minimize...

work page doi:10.54499/2022.04048.ptdc 2022
[3]

Sarkar,Big bang nucleosynthesis and physics beyond the standard model,Rept

S. Sarkar, Big bang nucleosynthesis and physics beyond the standard model, Rept. Prog. Phys.59, 1493 (1996), arXiv:hep-ph/9602260

work page arXiv 1996
[4]

Steigman, Primordial Nucleosynthesis in the Preci- sion Cosmology Era, Ann

G. Steigman, Primordial Nucleosynthesis in the Preci- sion Cosmology Era, Ann. Rev. Nucl. Part. Sci.57, 463 (2007), arXiv:0712.1100 [astro-ph]

work page arXiv 2007
[5]

Iocco, G

F. Iocco, G. Mangano, G. Miele, O. Pisanti, and P. D. Serpico, Primordial Nucleosynthesis: from precision cos- mology to fundamental physics, Phys. Rept.472, 1 (2009), arXiv:0809.0631 [astro-ph]

work page arXiv 2009
[6]

Pitrou, A

C. Pitrou, A. Coc, J.-P. Uzan, and E. Vangioni, Preci- sion big bang nucleosynthesis with improved Helium-4 predictions, Phys. Rept.754, 1 (2018), arXiv:1801.08023 [astro-ph.CO]

work page arXiv 2018
[7]

Kawano,Let’s go: Early universe

L. Kawano,Let’s go: Early universe. 2. Primordial nuc- leosynthesis: The Computer way, Tech. Rep. (Caltech, Kellogg Lab, 1992)

1992
[8]

M. S. Smith, L. H. Kawano, and R. A. Malaney, Ex- perimental, computational, and observational analysis of primordial nucleosynthesis, Astrophys. J. Suppl.85, 219 12 (1993)

1993
[9]

Pisanti, A

O. Pisanti, A. Cirillo, S. Esposito, F. Iocco, G. Man- gano, G. Miele, and P. D. Serpico, PArthENoPE: Pub- lic Algorithm Evaluating the Nucleosynthesis of Primor- dial Elements, Comput. Phys. Commun.178, 956 (2008), arXiv:0705.0290 [astro-ph]

work page arXiv 2008
[10]

Y. Xu, K. Takahashi, S. Goriely, M. Arnould, M. Ohta, and H. Utsunomiya, NACRE II: an update of the NACRE compilation of charged-particle-induced ther- monuclear reaction rates for nuclei with mass number A <16, Nucl. Phys. A918, 61 (2013), arXiv:1310.7099 [nucl-th]

work page arXiv 2013
[11]

Burns, T

A.-K. Burns, T. M. P. Tait, and M. Valli, PRyMordial: the first three minutes, within and beyond the standard model, Eur. Phys. J. C84, 86 (2024), arXiv:2307.07061 [hep-ph]

work page arXiv 2024
[12]

M. T. Clara and C. J. A. P. Martins, Primordial nuc- leosynthesis with varying fundamental constants: Im- proved constraints and a possible solution to the Lith- ium problem, Astron. Astrophys.633, L11 (2020), arXiv:2001.01787 [astro-ph.CO]

work page arXiv 2020
[13]

Navaset al.(Particle Data Group), Review of particle physics, Phys

S. Navaset al.(Particle Data Group), Review of particle physics, Phys. Rev. D110, 030001 (2024)

2024
[14]

I. M. Dreyer,Probing Unification Scenarios with Big Bang Nucleosynthesis, Master’s thesis, IST, University of Lisbon (2025)

2025
[15]

C. J. A. P. Martins, Primordial nucleosynthesis with varying fundamental constants: Degeneracies with cos- mological parameters, Astron. Astrophys.646, A47 (2021), arXiv:2012.10505 [astro-ph.CO]

work page arXiv 2021
[16]

A. Coc, N. J. Nunes, K. A. Olive, J.-P. Uzan, and E. Van- gioni, Coupled Variations of Fundamental Couplings and Primordial Nucleosynthesis, Phys. Rev. D76, 023511 (2007), arXiv:astro-ph/0610733

work page arXiv 2007
[17]

T. Dent, S. Stern, and C. Wetterich, Primordial nucle- osynthesis as a probe of fundamental physics parameters, Phys. Rev. D76, 063513 (2007), arXiv:0705.0696 [astro- ph]

work page arXiv 2007
[18]

F. Luo, K. A. Olive, and J.-P. Uzan, Gyromagnetic Factors and Atomic Clock Constraints on the Variation of Fundamental Constants, Phys. Rev. D84, 096004 (2011), arXiv:1107.4154 [hep-ph]

work page arXiv 2011
[19]

M. C. Ferreira and C. J. A. P. Martins, Further con- sistency tests of the stability of fundamental couplings, Phys. Rev. D91, 124032 (2015), arXiv:1506.03550 [astro- ph.CO]

work page arXiv 2015
[20]

D. M. N. Magano, J. M. A. Vilas Boas, and C. J. A. P. Martins, Current and Future White Dwarf Mass-radius Constraints on Varying Fundamental Couplings and Uni- fication Scenarios, Phys. Rev. D96, 083012 (2017), arXiv:1710.05828 [astro-ph.CO]

work page arXiv 2017
[21]

B. A. Campbell and K. A. Olive, Nucleosynthesis and the time dependence of fundamental couplings, Phys. Lett. B 345, 429 (1995), arXiv:hep-ph/9411272

work page arXiv 1995
[22]

Nakashima, K

M. Nakashima, K. Ichikawa, R. Nagata, and J. Yokoy- ama, Constraining the time variation of the coupling constants from cosmic microwave background: effect of \Lambda QCD, JCAP01, 030, arXiv:0910.0742 [astro- ph.CO]

work page arXiv
[23]

Lee, A model for time-evolution of coupling constants, Phys

T. Lee, A model for time-evolution of coupling constants, Phys. Lett. B849, 138424 (2024), arXiv:2310.13308 [hep- ph]

work page arXiv 2024
[24]

Cooke, Big Bang Nucleosynthesis, Encyclopedia of Astrophysics5, 159 (2025), arXiv:2409.06015 [astro- ph.CO]

R. Cooke, Big Bang Nucleosynthesis, Encyclopedia of Astrophysics5, 159 (2025), arXiv:2409.06015 [astro- ph.CO]

work page arXiv 2025
[25]

B. D. Fields, The primordial lithium problem, Ann. Rev. Nucl. Part. Sci.61, 47 (2011), arXiv:1203.3551 [astro- ph.CO]

work page Pith review arXiv 2011
[26]

Pitrou, A

C. Pitrou, A. Coc, J.-P. Uzan, and E. Vangioni, A new tension in the cosmological model from primordial deu- terium?, Mon. Not. Roy. Astron. Soc.502, 2474 (2021), arXiv:2011.11320 [astro-ph.CO]

work page arXiv 2021
[27]

Deal and C

M. Deal and C. J. A. P. Martins, Primordial nucleosyn- thesis with varying fundamental constants - Solutions to the lithium problem and the deuterium discrepancy, Astron. Astrophys.653, A48 (2021), arXiv:2106.13989 [astro-ph.CO]

work page arXiv 2021
[28]

The interactive 3D versions of these and other images can be found in https://zenodo.org/records/17295823

work page arXiv
[29]

M. T. Murphyet al., Fundamental physics with ES- PRESSO: Precise limit on variations in the fine-structure constant towards the bright quasar HE 0515−4414, As- tron. Astrophys.658, A123 (2022), arXiv:2112.05819 [astro-ph.CO]

work page arXiv 2022
[30]

C. J. A. P. Martinset al.(ANDES), Cosmology and fun- damental physics with the ELT-ANDES spectrograph, Exper. Astron.57, 5 (2024), arXiv:2311.16274 [astro- ph.CO]

work page arXiv 2024
[31]

C. J. A. P. Martins, Varying fundamental constants cosmography, Phys. Dark Univ.49, 102047 (2025), arXiv:2508.18458 [astro-ph.CO]

work page arXiv 2025
[32]

E. A. Kolonia, C. J. A. P. Martins, and K. N. Gourgouli- atos, Probing fundamental physics using compact as- trophysical objects, Phys. Rev. D111, 083017 (2025), arXiv:2503.11447 [hep-ph]

work page arXiv 2025
[33]

Bonaet al.,New UTfit analysis of the unitarity triangle in the Cabibbo-Kobayashi-Maskawa scheme, Rend

M. Bonaet al.(UTfit), New UTfit Analysis of the Unitarity Triangle in the Cabibbo-Kobayashi-Maskawa scheme, Rend. Lincei Sci. Fis. Nat.34, 37 (2023), arXiv:2212.03894 [hep-ph]

work page arXiv 2023
[34]

Czarnecki, W

A. Czarnecki, W. J. Marciano, and A. Sirlin, Precision measurements and CKM unitarity, Phys. Rev. D70, 093006 (2004), arXiv:hep-ph/0406324

work page arXiv 2004
[35]

Escudero Abenza, JCAP05, 048 (2020), arXiv:2001.04466 [hep-ph]

M. Escudero Abenza, Precision early universe thermo- dynamics made simple:N eff and neutrino decoupling in the Standard Model and beyond, JCAP05, 048, arXiv:2001.04466 [hep-ph]

work page arXiv 2001