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

Anne-Katherine Burns

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}

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 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 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 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}
Paper Structure (37 sections, 16 equations, 36 figures, 11 tables)

This paper contains 37 sections, 16 equations, 36 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Cosmological Observations
  3. A New Measurement of $Y_p$ from the LBT
  4. EMPRESS Result for $Y_p$
  5. Observation of Deuterium
  6. Observation of Lithium-7
  7. Observation of $N_{\rm{eff}}$: A new value determined using LBT data
  8. Theoretical Framework and Numerical Methods
  9. n/p
  10. Expansion rate of the Universe
  11. Baryon Abundance
  12. Thermo-nuclear Reaction Rates
  13. Sensitivity Analysis: Fundamental Physics Parameters
  14. Neutron lifetime, $\tau_{n}$
  15. Neutron-proton mass difference, Q
  16. ...and 22 more sections

Figures (36)

  • Figure 1: Schematic overview of the BBN calculation as implemented in https://github.com/vallima/PRyMordial. The three computational stages: background thermodynamics , neutron--proton interconversion rates and the nuclear reaction network are shown along with their three outputs: $N_\text{eff}$, the relic neutrino abundance, and the final light-element abundances. Each colored circle represents a fundamental input parameter varied in this analysis. The symbols described in the legend indicates whether a given quantity depends on the photon temperature, neutrino temperature, or scale factor. Arrows trace how each input propagates through the calculation.
  • Figure 2: Predicted $Y_p$ as a function of $\tau_n$/$\tau_n^{\rm SM}$ calculated using PRIMAT (blue) and NACRE-II (red) reaction rates.
  • Figure 3: Predicted $D/H \times 10^5$ as a function of $\tau_n$/$\tau_n^{\rm SM}$ calculated using PRIMAT (blue) and NACRE-II (red) reaction rates.
  • Figure 4: Predicted $Y_p$ as a function of $Q$/$Q^{\rm SM}$ calculated using PRIMAT (blue) and NACRE-II (red) reaction rates using the $\tau_n$ weak rate normalization.
  • Figure 5: Predicted $D/H \times 10^5$ as a function of $Q$/$Q^{\rm SM}$ calculated using PRIMAT (blue) and NACRE-II (red) reaction rates using the $\tau_n$ weak rate normalization.
  • ...and 31 more figures