Inside the Black Box of Big Bang Nucleosynthesis: Parameter Sensitivity Studies in Light of new LBT Data

Abstract: In this study we present a comprehensive sensitivity atlas for Big Bang Nucleosynthesis (BBN) in which we quantify the dependence of the primordial abundances of helium-4, deuterium, and lithium-7 as well as $N_{\rm{eff}}$ on variations in 14 fundamental particle physics and cosmological parameters and 63 thermonuclear reaction rates. We use the publicly available BBN code \faGithub \href{https://github.com/vallima/PRyMordial}{\,\texttt{PRyMordial}} to compute each sensitivity using two nuclear reaction rate compilations and two weak-rate normalization schemes, and provide a model independent reference applicable to Beyond the Standard Model (BSM) models in which MeV scale physics is modified. In addition, we rank each parameter's contribution to the theoretical uncertainty budget. We compare our predictions against the latest observational determinations of the primordial abundances, including a recent LBT measurement of the helium-4 abundance \cite{Aver:2026dxv} which roughly halves the observational uncertainty relative to previous determinations. We present these results both fixing $ΔN_{\rm eff}$ at its Standard Model (SM) value, and allowing it to be a free parameter using the latest uncertainty from the combined CMB+BAO+BBN 2026 value \cite{Goldstein:2026iuu}. When $ΔN_{\rm eff}$ is allowed to be a free parameter, it dominates the theoretical uncertainty of the helium-4 abundance, highlighting the importance of upcoming observations from the Simons Observatory \cite{SimonsObservatory:2025wwn}. As illustrative applications, we examine the deuterium tension and the lithium problem in light of our sensitivity analysis. The full set of numerical results and figures is publicly available on GitHub \faGithub \href{https://github.com/Anne-KatherineBurns/bbn-sensitivity-atlas}{\,\texttt{bbn-sensitivity-atlas}

• The paper provides a comprehensive sensitivity atlas for BBN by varying 77 fundamental and nuclear parameters, revealing their effects on light-element abundances and Nₑff.
• It employs updated nuclear reaction rates, dual normalization schemes, and linear error propagation, reconciling theoretical predictions with high-precision LBT helium observations.
• Results highlight key uncertainties from neutron lifetime, n-p mass difference, and nuclear cross-sections, guiding future probes into beyond Standard Model physics.

Inside the Black Box of BBN: Parameter Sensitivity in Light of new LBT Data

Introduction

This work presents a rigorous, comprehensive sensitivity atlas for Big Bang Nucleosynthesis (BBN), quantifying the response of primordial helium-4 ($Y_p$), deuterium (D/H), lithium-7 ($^7$Li/H), and the effective number of neutrino species ($N_{\rm eff}$) to all relevant input parameters: 14 fundamental constants and cosmological parameters as well as 63 thermonuclear reaction rates. The analysis leverages the PRyMordial (Burns et al., 2023) numerical framework, systematically studying both the impact of parameter variations and the theoretical uncertainty budgets with updated nuclear networks and weak-interaction schemes. Central to the study is the utilization of new high-precision LBT $Y_p$ observations, which halve the $Y_p$ observational error and motivate a re-examination of error budgets.

Implementation and Methodology

The BBN calculation is structured into three computational stages: background thermodynamics (including neutrino decoupling and expansion history), neutron-proton interconversion (weak interaction rates), and nuclear reaction networks, producing in tandem the predicted light-element abundances and $N_{\rm eff}$.

Figure 1: Schematic overview of the BBN pipeline in PRyMordial, with colored nodes indicating varied input parameters and arrows tracing sensitivity pathways.

Parameter response functions and theoretical uncertainties are evaluated in a strictly uniform framework. Each parameter is varied independently, and results are reported for both the PRIMAT [Pitrou:2018cgg] and NACRE-II [Xu:2013fha] reaction rate compilations, using both weak-norm parameterizations (fundamental and $\tau_n$ normalization). Sensitivities are tabulated as local logarithmic derivatives or absolute derivatives with respect to non-standard parameters. Uncertainties are propagated via linear error analysis, providing transparency in the decomposition of the total theory error.

Observational Anchors

Helium-4 ($Y_p$): The new LBT emission-line survey yields $Y_p = 0.2458 \pm 0.0013$ [Aver:2026dxv], a $\sim2\times$ improvement over prior constraints and in excellent agreement with Standard Model (SM) predictions.

Deuterium: Current observations yield $D/H = (2.508 \pm 0.029) \times 10^{-5}$ [PDG2025], with a (model-dependent) mild tension with SM BBN depending on nuclear rates.

Lithium-7: The old "lithium problem" persists: the inferred primordial $^7$Li/H underpredicts the SBBN value by $\sim$3--4$\sigma$; all parameter sensitivities/uncertainties for $^7$Li/H are presented, though no nuclear/astrophysical solution emerges within 1$\sigma$.

Neff: The latest joint CMB+BAO+BBN result is $N_{\rm eff} = 2.990 \pm 0.070$ [Goldstein:2026iuu], reducing the error bar by nearly a factor of two.

Parameter Sensitivity Overview

Fundamental parameter variations propagate into the light-element and $N_{\rm eff}$ predictions through several mechanisms:

• Neutron lifetime ($\tau_n$): Dominates $Y_p$ and D/H uncertainties in the $\tau_n$ normalization. Increasing $\tau_n$ shifts weak freezeout to higher temperatures, raising $n/p$ at BBN and increasing both $Y_p$ and D/H.

Figure 2: $Y_p$ variation as a function of $\tau_n/\tau_n^{\rm SM}$, for both PRIMAT and NACRE-II rates; $Y_p$ increases approximately linearly with $\tau_n$.

• n-p Mass Difference ($Q$): Qualitatively different impact depending on weak-rate normalization; in the fundamental normalization, increasing $Q$ reduces final element yields (all $d\ln Y/d\ln Q < 0$), while in $\tau_n$ normalization the sign flips.

Figure 3: $Y_p$ vs $Q/Q^{\rm SM}$, $\tau_n$ normalization: $Y_p$ increases with $Q$; fundamental normalization: $Y_p$ decreases with $Q$.

• Fine structure constant ($\alpha_{EM}$): Shifts weak rates and QED corrections, weakly increasing $Y_p$ and D/H with $\alpha_{EM}$, and raises $N_{\rm eff}$ by increasing the coupling at neutrino decoupling.

Figure 4: $Y_p$ as a function of $\alpha_{EM}/\alpha_{EM}^{\rm SM}$. The effect is subdominant but non-negligible in the precision regime.

• Gravitational constant ($G_N$): Affects both expansion rate and baryon-to-photon conversion. Increasing $G_N$ increases $Y_p$ and D/H (via earlier weak decoupling and less time for nuclear burning).

Figure 5: $Y_p$ as a function of $G_N/G_N^{\rm SM}$, for both nuclear libraries; the slope quantifies the sensitivity to new gravitational physics.

• Neutrino sector ($\Delta N_{\rm eff}$, $\xi_\nu$): Raising $\Delta N_{\rm eff}$, with variance taken from combined CMB+BAO+BBN, increases $Y_p$ sharply, dominating the $Y_p$ theory error budget if left free.

Figure 6: $Y_p$ as a function of $\Delta N_{\rm eff}$. Current errors on $\Delta N_{\rm eff}$ directly translate to an $\mathcal{O}($0.001$) uncertainty in$Y_p$.</p></p> <ul> <li><strong>Baryon abundance ($\Omega_b h^2$):</strong> Controls D/H and$^7$$Li/H linearly.</li> </ul> <p><strong>Nuclear rate uncertainties</strong>: D/H and$$^7$$Li/H retain significant rate-limited uncertainties, with the dominant rates being$$d(p,\gamma)^3$He,$d(d,n)^3$He, and$^3$He($^4$He,$\gamma$)$^7$$Be. <img src="https://emergentmind-storage-cdn-c7atfsgud9cecchk.z01.azurefd.net/paper-images/2603-22414/all12_sigma_compare.png" alt="Figure 7" title="" class="markdown-image" loading="lazy"> <p class="figure-caption">Figure 7: D/H is strongly sensitive to$$d(p,\gamma)^3$He and$d(d,n)^3$He,$^7$Li/H to$^3$He+$^4$He$\rightarrow$$^7$Be;$Y_p$$is insensitive to nuclear rates at this level.</p></p> <h2 class='paper-heading' id='uncertainty-budgets-and-ranking'>Uncertainty Budgets and Ranking</h2> <p>For SM input parameters (fixed$$N_{\rm eff}$),$Y_p$errors are dominated by$\tau_n$(weak-norm) or$g_A$/$V_{ud}$(fundamental norm); D/H errors switch from$\Omega_b h^2$dominance (PRIMAT rates) to$d(d,n)^3$He (NACRE-II);$^7$$Li/H is always nuclear-limited.</p> <p>When allowing$$\Delta N_{\rm eff}$$to float with the latest uncertainty, it accounts for$$>90\%$of the total$Y_p$$error, entirely setting the precision frontier for BBN-based physics searches. D/H is increasingly limited by nuclear physics, signaling the need for improved rate measurements to exploit future high-precision deuterium observations.</p> <h2 class='paper-heading' id='numerical-results-and-theory-data-comparison'>Numerical Results and Theory-Data Comparison</h2> <p>The theoretical predictions for primordial abundances, comparing the two nuclear rate sets and normalization schemes, confirm:</p> <ul> <li><strong>Excellent agreement for$$Y_p$$</strong> with new LBT and CMB+BAO+BBN values. Observational errors and theoretical systematics are now at parity for the first time, greatly tightening constraints on new physics in MeV-scale cosmology.</li> <li><strong>Mild D/H tension</strong> remains (for PRIMAT rates), but can be alleviated by modest, physically plausible shifts in nuclear rates or baryon density (though CMB-concordance discourages the latter).</li> <li><strong>No nuclear fix for the lithium problem</strong> is found at$$1\sigma$$. Resolving the discrepancy with nuclear rate variations would require several jointly$$>3\sigma$$shifts in key reactions, disfavored by existing experimental data.</li> </ul> <h2 class='paper-heading' id='implications-and-prospects'>Implications and Prospects</h2> <p><strong>Practically:</strong> This atlas provides definitive guidance for where theory and experiment must focus to further sharpen BBN as a probe of MeV-scale and <a href="https://www.emergentmind.com/topics/branch-solve-merge-bsm" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">BSM</a> physics. The principal leverage for$$Y_p$comes from n/p ratio parameters ($\tau_n$,$g_A$,$V_{ud}$,$Q$$), for D/H from both baryon density and select nuclear rates, and for$$N_{\rm eff}$$all improvement hinges on future CMB experiments (e.g., <a href="https://www.emergentmind.com/topics/simons-observatory-so" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Simons Observatory</a> [SimonsObservatory:2025wwn]).</p> <p><strong>Theoretically:</strong> The decoupling of parameter sensitivities (independent local variations) supports rapid mapping of any BSM scenario with arbitrary shifts to couplings or rates—crucially, the sign and magnitude of each response function are tabulated; full covariance propagation is supported for correlated parameter scenarios.</p> <p><strong>Speculation:</strong> As observational$$Y_p$errors continue to decline and constraints on$\Delta N_{\rm eff}$$tighten, the next generation of BBN tests will have capacity to constrain new light degrees of freedom, neutrino-neutrino interactions, gravitational/expansion physics, and even subtle time-variation in standard constants at the$$10^{-4}$–$10^{-3}$ level. D/H&#39;s ultimate utility is limited by laboratory nuclear cross-sections, making additional measurements of $d(p,\gamma)^3$He and$d(d,n)^3$$He vital.</p> <h2 class='paper-heading' id='conclusion'>Conclusion</h2> <p>This comprehensive and uniform BBN sensitivity atlas provides the research community with an authoritative guide to the local response and uncertainty propagation of all relevant SM and nuclear input parameters, in direct connection with the latest observational and cosmological constraints. The results enable rapid assessment of BSM impacts, identify current limiting theoretical and experimental contributions, and chart the critical path for further progress. Full data and numerical results are released with the paper.</p> <hr> <p><strong>References:</strong></p> <ul> <li>(2603.22414) (this paper)</li> <li>PRyMordial BBN code: (<a href="/papers/2307.07061" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Burns et al., 2023</a>)</li> <li>Nuclear rate networks: [Pitrou:2018cgg], [Xu:2013fha]</li> <li>Latest LBT$$Y_p$$results: [Aver:2026dxv]</li> <li>Combined CMB+BAO+BBN$$N_{\rm eff}$ constraint: [Goldstein:2026iuu]

Simons Observatory forecasts: [SimonsObservatory:2025wwn]