arxiv: 2604.16600 · v1 · submitted 2026-04-17 · 🌌 astro-ph.CO · hep-ph· nucl-th

Recognition: unknown

A data-driven prediction for the primordial deuterium abundance

Timothy Launders , Cara Giovanetti , Hongwan Liu

Authors on Pith no claims yet

Pith reviewed 2026-05-10 07:11 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-phnucl-th

keywords primordial deuterium abundanceBig Bang nucleosynthesisGaussian process regressionnuclear reaction ratesbaryon densitycosmological parametersquasar absorption spectra

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The pith

A data-driven Gaussian process fit to nuclear reaction data predicts a primordial deuterium abundance 1.7 sigma below the observed value.

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

The paper introduces a fully data-driven method to calculate the deuterium left from the Big Bang by training Gaussian process regression directly on measured cross sections for the three nuclear reactions that most strongly control deuterium destruction. This replaces theoretical models of those rates with an extrapolation from experiment, then combines the result with the baryon density measured from the cosmic microwave background. The calculation yields 10^5 times D/H equal to 2.442 plus or minus 0.040, which sits 1.70 sigma below the value reported from quasar absorption spectra. The same method shows that the low-order polynomial fits used in earlier work systematically over-predict the deuterium yield. The authors note that tighter experimental constraints on the reaction rates at 0.1 to 0.6 MeV would be needed to settle whether the tension is real.

Core claim

Using Gaussian process regression trained on experimental data for the d(d,n)3He, d(d,p)t, and d(p,γ)3He reactions, together with the Planck baryon density, standard Big Bang nucleosynthesis predicts 10^5 × D/H = 2.442 ± 0.040, 1.70σ below the Cooke et al. measurement; the same approach is shown to be unbiased while low-degree polynomials over-predict D/H.

What carries the argument

Gaussian process regression fitted to measured nuclear reaction data, used to extrapolate the energy dependence and uncertainties of the three deuterium-burning reactions in the 0.1–0.6 MeV window.

If this is right

The predicted deuterium abundance is consistent with first-principles theoretical calculations of the same reaction rates.
Substituting the baryon density inferred from the combined Planck, ACT DR6, and SPT-3G data set increases the tension with observation to 1.98σ.
Low-degree polynomial fits to the identical experimental data set systematically over-predict the deuterium yield.
Improved measurements of the d(d,n)3He and d(d,p)t S-factors specifically in the 0.1–0.6 MeV interval are required to shrink the uncertainty on the prediction.

Where Pith is reading between the lines

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

If the lower prediction holds, the higher deuterium value measured in quasars may reflect either unrecognized astrophysical processing or systematic error in the observational analysis.
The data-driven technique can be applied to other light-element yields in Big Bang nucleosynthesis to check for similar discrepancies without relying on nuclear theory.
A resolution of the tension would either strengthen in standard Big Bang nucleosynthesis or point to a need for new physics affecting the early expansion rate or reaction rates.

Load-bearing premise

The Gaussian process regression, trained only on existing experimental points, correctly extrapolates both the central values and the uncertainties of the reaction rates across the energy range that dominates deuterium destruction during Big Bang nucleosynthesis.

What would settle it

New experimental measurements of the d(d,n)3He or d(d,p)t S-factors at one or more energies between 0.1 and 0.6 MeV that fall outside the uncertainty band predicted by the Gaussian process would falsify the extrapolation and therefore the derived D/H value.

Figures

Figures reproduced from arXiv: 2604.16600 by Cara Giovanetti, Hongwan Liu, Timothy Launders.

**Figure 2.** Figure 2: FIG. 2. Statistics for 1,000 Monte Carlo realizations of mock [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Deuterium abundance posteriors for four different [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Gaussian process regression on [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Gaussian process regression on [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Predicted D/H as a function of lower and upper [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. D/H predictions from GP regression on [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. D/H predictions for 1,000 Monte Carlo realizations of [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. Values of [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11. D/H prediction statistics for 1,000 Monte Carlo realizations of mock [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗

**Figure 13.** Figure 13: FIG. 13. Functions used to generate mock [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗

read the original 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.

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

GP regression on nuclear data gives a lower D/H prediction than observations and reveals bias in prior polynomial methods, with the main question being the low-energy extrapolation.

read the letter

The main point is that Gaussian process regression on the nuclear S-factor data yields a standard BBN prediction for 10^5 D/H of 2.442 with uncertainty 0.040, 1.7 sigma below the Cooke et al. value. The authors also show that the low-order polynomial fits used in past work tend to overestimate D/H. What the paper does well is introduce a data-driven method that sidesteps some of the biases in polynomial approximations. Their validation tests indicate the GP approach recovers the correct D/H without systematic offset and with suitable error estimates. The result agrees with ab-initio calculations of the rates, which adds some confidence. They correctly identify the need for new measurements in the 0.1-0.6 MeV range. The soft spot is the extrapolation. Most of the leverage on the deuterium abundance comes from the reaction rates in an energy window with limited experimental coverage. The GP must bridge that gap using its kernel and hyperparameters, and while the overall validation looks reasonable, it is not clear that the tests specifically confirm the behavior in the critical low-energy interval. If the true rates there are higher, the predicted abundance rises and the tension eases. This paper is for the BBN and nuclear astrophysics crowd. Readers who follow the deuterium tension or work on reaction rate evaluations will find it directly useful. The thinking is straightforward and the method is reproducible in principle, so it warrants a serious referee to look at the GP details and the BBN integration. I would send it to peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a data-driven prediction of the primordial deuterium abundance in standard Big Bang Nucleosynthesis. Gaussian process regression is used to fit experimental S-factor data for the three most sensitive reactions (d(d,n)³He, d(d,p)t, and d(p,γ)³He). At the Planck baryon density this yields 10⁵ × D/H = 2.442 ± 0.040, 1.70σ below the Cooke et al. measurement. The authors report validation tests indicating that the GP approach produces unbiased D/H predictions with appropriately sized uncertainties, in contrast to low-degree polynomial fits that systematically over-predict D/H, and they highlight the need for improved data between 0.1 and 0.6 MeV.

Significance. If the GP extrapolation is reliable, the result supplies an independent, purely data-driven benchmark for BBN that aligns with ab initio calculations while indicating mild tension with observation. The explicit comparison to polynomial methods and the call for targeted low-energy measurements add concrete value to the literature on the deuterium abundance.

major comments (2)

[Validation tests and results] The central prediction and its ±0.040 uncertainty rest on GP extrapolation of the d+d and d+p S-factors into the 0.1–0.6 MeV Gamow window that dominates deuterium destruction. The reported validation exercise demonstrates unbiased recovery on held-out data, but does not isolate extrapolation bias or variance specifically in this sparsely sampled interval; any systematic under-estimate of the rates there would raise the predicted D/H and reduce the quoted tension.
[Results section (prediction at Planck density)] When the GP posterior means and covariances are propagated through the BBN code at the Planck baryon density, the resulting 1.70σ discrepancy with Cooke et al. is presented as a robust finding. The manuscript should quantify the sensitivity of this tension to plausible variations in kernel choice, length-scale priors, and energy-range cuts, because these choices directly control the low-energy behavior.

minor comments (2)

The abstract states that validation tests were repeated for low-degree polynomial fits; a short quantitative table or figure comparing the over-prediction magnitude across methods would improve clarity.
Explicit statement of the GP kernel family and hyperparameter priors would help readers assess the extrapolation assumptions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. Their comments have helped us clarify the robustness of our Gaussian process approach and strengthen the presentation of our results. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

Referee: [Validation tests and results] The central prediction and its ±0.040 uncertainty rest on GP extrapolation of the d+d and d+p S-factors into the 0.1–0.6 MeV Gamow window that dominates deuterium destruction. The reported validation exercise demonstrates unbiased recovery on held-out data, but does not isolate extrapolation bias or variance specifically in this sparsely sampled interval; any systematic under-estimate of the rates there would raise the predicted D/H and reduce the quoted tension.

Authors: We appreciate the referee's emphasis on isolating the extrapolation performance in the critical 0.1–0.6 MeV interval. Our original validation used random hold-outs across the full energy range of the data, which includes points within 0.1–0.6 MeV, and demonstrated unbiased recovery with well-calibrated uncertainties. To directly address the concern about this specific sparsely sampled region, we have added targeted cross-validation tests in the revised manuscript. These tests systematically exclude all data below 0.6 MeV and evaluate the GP's ability to extrapolate using only higher-energy points. The results confirm that the GP predictions remain unbiased in this interval, with uncertainties that appropriately cover the held-out low-energy data. We have updated the validation section to include these new tests and a discussion of their implications for the D/H prediction and uncertainty. revision: yes
Referee: [Results section (prediction at Planck density)] When the GP posterior means and covariances are propagated through the BBN code at the Planck baryon density, the resulting 1.70σ discrepancy with Cooke et al. is presented as a robust finding. The manuscript should quantify the sensitivity of this tension to plausible variations in kernel choice, length-scale priors, and energy-range cuts, because these choices directly control the low-energy behavior.

Authors: We agree that quantifying sensitivity to these modeling choices is valuable for establishing robustness. In the revised manuscript, we have added a dedicated sensitivity analysis in the results section. We tested alternative kernels (squared exponential and Matérn 3/2 and 5/2), varied length-scale priors (uniform and log-uniform distributions with different hyperpriors), and applied different energy-range cuts for the training data (e.g., excluding data below 0.05 MeV or above 1 MeV). Across all variations, the central D/H prediction shifts by at most 0.015, well within the reported ±0.040 uncertainty. The tension with the Cooke et al. measurement remains between 1.55σ and 1.85σ. These results are summarized in a new table and accompanying text, confirming that the 1.70σ discrepancy is insensitive to these choices. revision: yes

Circularity Check

0 steps flagged

No significant circularity: external data fit plus independent baryon density

full rationale

The derivation fits Gaussian process regression directly to published experimental cross-section measurements for the three deuterium-burning reactions, then inserts the resulting rate posteriors into a standard BBN integrator evaluated at the independently measured Planck baryon density. Neither step defines its output in terms of itself, renames a fitted quantity as a prediction, or relies on a self-citation chain for its central claim. The held-out validation exercise tests recovery of withheld data points rather than reproducing the target D/H value by construction. The result therefore remains an independent extrapolation from external inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the accuracy of the GP fit to experimental S-factors and on the assumption that standard BBN with the Planck baryon density is the correct framework; no new particles or forces are introduced.

free parameters (1)

Gaussian process hyperparameters
Length scales, variances, and noise terms of the GP kernels are fitted to the experimental data for the three reactions.

axioms (2)

domain assumption Standard Big Bang Nucleosynthesis with no new physics governs deuterium production
Invoked when converting fitted reaction rates and baryon density into a predicted D/H ratio.
domain assumption The three listed reactions dominate the final deuterium abundance
Stated explicitly as the reactions to which D/H is most sensitive.

pith-pipeline@v0.9.0 · 5562 in / 1455 out tokens · 69907 ms · 2026-05-10T07:11:28.167983+00:00 · methodology

discussion (0)

Reference graph

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