A data-driven prediction for the primordial deuterium abundance

Abstract

We predict the primordial deuterium abundance using a novel, fully data-driven approach, where we use Gaussian process regression to fit experimental nuclear reaction data for $d$,($d$,$n$)$^3$He, $d$,($d$,$p$)$t$, and $d$($p$,$\gamma$)$^3$He, three reactions to which the primordial deuterium abundance is most sensitive. Using the Planck determination of the baryon density, we predict $10^5\times\mathrm{D/H} = 2.442\pm0.040$ in standard Big Bang Nucleosynthesis, $1.70\sigma$ below the Cooke et al. measurement. Our result is consistent with predictions relying on first principles calculations of the deuterium burning cross sections. With the inferred baryon density from a combined fit to Planck, ACT DR6, and SPT-3G D1, this discrepancy worsens to $1.98\sigma$. We validate our approach and confirm that Gaussian processes make unbiased D/H predictions with appropriately-sized uncertainties. We repeat our validation tests for low-degree polynomial fits, a technique used in previous analyses, and find that they systematically over-predict D/H. Our results highlight the need for improved measurements of the $d$,($d$,$n$)$^3$He and $d$,($d$,$p$)$t$ S-factors at energies between 0.1 and 0.6 MeV.