Primordial Deuterium Abundance in Cosmology

• Primordial deuterium abundance is the measure of deuterium produced during Big Bang nucleosynthesis, providing insights into early universe baryon density and fundamental nuclear reaction rates.
• High-resolution quasar absorption spectroscopy yields precise D/H ratios by analyzing low-metallicity, high column density absorption systems with detailed Voigt profile fitting.
• Minimal deuterium astration in metal-poor environments ensures that observed D/H closely reflects the primordial value, enabling robust tests of cosmological models.

The primordial abundance of deuterium, (D/H)_p, is a key observable in modern cosmology, providing a direct test of Big-Bang Nucleosynthesis (BBN) and a sensitive probe of the cosmic baryon density. Deuterium is synthesized in trace quantities during the first few minutes after the Big Bang and subsequently only destroyed in stellar interiors, making the measurement of (D/H) in high-redshift, low-metallicity environments a powerful means to reconstruct physical conditions of the early universe. Progress since the 2010s has been driven by high-resolution quasar absorption spectroscopy, advances in stochastic and systematic error control, and increasingly precise laboratory determinations of key nuclear reaction rates.

1. Big-Bang Nucleosynthesis and the Sensitivity of Deuterium Production

In BBN, the synthesis of light elements is controlled by the baryon-to-photon ratio η, the neutron lifetime, and the relevant nuclear cross sections. The crucial reactions for deuterium are the formation channel p(n,γ)D and the destruction channels D(p,γ)^3He, D(d,n)^3He, and D(d,p)^3H (Coc et al., 2015). The primordial D/H ratio is exquisitely sensitive to η: over the baryon density range allowed by CMB, a small fractional change in η results in a much larger, ∼–1.6-power change in (D/H):

$$10^5\,(D/H)_p = K \left(\frac{6}{\eta_{10}}\right)^{1.6} \quad \text{with} \quad \eta_{10} = 10^{10} (n_b/n_\gamma)$$

where K depends on the adopted nuclear reaction rates and is typically K ≈ 2.5–2.6 (Cooke et al., 2013, Coc et al., 2015, Pisanti et al., 2020). For Planck's η ≈ 6.1 × 10^{-10}, current BBN codes predict (D/H)_p ≈ (2.45–2.53) × 10^{-5} (Coc et al., 2015, Pisanti et al., 2020). The predicted abundance's uncertainty is dominated by the cross sections for D(p,γ)^3He and the deuteron-deuteron reactions, for which recent laboratory and ab initio calculations have reduced theory errors to ≲2–3% (Coc et al., 2015, Pisanti et al., 2020, Cooke et al., 2015).

2. Methodologies for Empirical Determination of Primordial D/H

High-precision measurements of D/H are obtained from absorption line systems (DLAs and sub-DLAs) along quasar sightlines at z ≈ 2–4. The selection criteria for an optimal system require:

• Low metallicity ([O/H] ≲ –1.5), to minimize deuterium astration.
• High N(H I) (log N(H I) ≳ 19), to ensure the Lyα line has damping wings for robust N(H I) determination (Cooke et al., 2013, Noterdaeme et al., 2012, Pettini et al., 2012).
• Multiple unblended D I Lyman transitions, resolved at high spectral resolution (R ≳ 40 000) and high S/N (≳30–50 per pixel).

Voigt profile fitting is performed simultaneously on all H I and D I lines, with component-wise modeling of velocity structure and Doppler broadening decomposed into turbulent and thermal terms:

$b^2(m) = 2kT/m + b_\mathrm{turb}^2$

This allows the robust separation of D I (Δv = –82 km s⁻¹) from contaminating Lyα forest absorbers and the quantification of both the gas temperature and non-thermal motions (Noterdaeme et al., 2012, Cooke et al., 2016). State-of-the-art analyses employ global χ² minimization techniques, often with customized fitting software, to simultaneously model the continuum, emission lines, and all absorption features, and include systematic error budgets from continuum placement, line blending, velocity structure, and zero-level uncertainties (Pettini et al., 2012, Cooke et al., 2017, Kislitsyn et al., 23 Jan 2024).

3. Ionization Corrections and Astration

Corrections for the differential ionization of D and H are negligible in metal-poor, high-column-density DLAs due to closely matched ionization potentials and efficient charge exchange. Detailed photoionization modeling (using suites such as CLOUDY) confirms that, for log N(H I) ≳ 20, the correction to log (D/H) is IC(D/H) ≲ 0.0005 dex (≤0.1%), well below current measurement errors (Cooke et al., 2015, Kislitsyn et al., 23 Jan 2024). Even in sub-DLAs (log N(H I) ≈ 19.3–19.9), the correction remains subdominant, a conclusion supported by both analytic treatment and cosmological simulations.

Deuterium astration—the destruction of D in stars—is minimal at [O/H] ≲ –1.5. Modern chemical evolution models and cosmological zoom-in simulations (Voort et al., 2017, Dvorkin et al., 2016) demonstrate that dilution of D/H by mass loss or recycled gas is ≲ 1–2% at these low metallicities. The observed D/H thus closely tracks (D/H)_p, legitimizing the use of such systems in primordial abundance studies.

4. Observational Results and Statistical Samples

Over a dozen high-precision D/H measurements at z = 2–4 now populate the literature. Recent examples include:

QSO / System	z_abs	log N(H I)	[O/H]	D/H × 10⁵	Error (stat⊕sys)	Reference
CTQ247 (DLA)	2.621	20.45±0.10	–1.99	2.8^{+0.8}_{-0.6}	≈±0.7	(Noterdaeme et al., 2012)
SDSS J1419+0829	3.050	20.392±.003	–1.92	2.51±0.05	±0.05	(Pettini et al., 2012)
PKS1937-101 (abs3.572)	3.572	17.92	...	2.62±0.05	±0.05	(Riemer-Sørensen et al., 2017, Guarneri et al., 8 Feb 2024)
J1332+0052 (sub-DLA)	3.42	19.304±.004	–1.71	2.53±0.02	±0.014 dex (log)	(Kislitsyn et al., 23 Jan 2024)

Weighted means from strictly defined “precision” samples—employing selection on metallicity, kinematic simplicity, and unblended multi-transitions—yield:

$$(D/H)_\mathrm{p} = (2.53 \pm 0.03)\times 10^{-5} \quad \text{[1703.06656, 1308.3240]}$$

$$(D/H)_\mathrm{pr} = (2.533 \pm 0.024)\times10^{-5} \quad \text{[2401.12797]}$$

Relaxing selection yields an unweighted mean (N=15) of (D/H)_p = (2.54 ± 0.19) × 10^{-5} (Balashev et al., 2015), reflecting both intrinsic and methodological scatter.

The D/H–metallicity correlation is predicted and observed to be nearly flat for [O/H] ≲ –1, confirming negligible astration; tentative (1.4σ) evidence exists for a weak decline at higher metallicity (Cooke et al., 2016).

5. Connecting Deuterium to Cosmic Baryon Density

BBN theory relates (D/H)_p monotonically to Ω_b h². For the “precision” D/H determinations:

$$100\,\Omega_b h^2 = 2.20 \pm 0.05 \quad [1308.3240, 1703.06656]$$

$$\Omega_b h^2 = 0.02174 \pm 0.00025 \quad [1706.09512, 1801.04704]$$

These values are compared to Planck 2015/2018 CMB results:

$$\Omega_b h^2 = 0.02236 \pm 0.00015 \quad \text{[Planck 2018]}$$

The difference is marginal (≲2.2σ), with the magnitude of the tension sensitive to the adopted nuclear rates for D(p,γ)^3He. Improved laboratory measurements—such as the LUNA experiment's 3% measurement—have reduced dominant nuclear uncertainties (Pisanti et al., 2020, Coc et al., 2015). Discrepancy with CMB-inferred Ω_b h² is now at a level that warrants scrutiny of both reaction rates and potential new physics (e.g., nonstandard N_eff).

The degeneracy parameter space includes effective relativistic degrees of freedom, with joint fits yielding N_eff = 3.28 ± 0.28 (Cooke et al., 2013), compatible with the SM prediction (N_eff = 3.046), and stringent limits on neutrino asymmetry (|ξ| ≲ 0.062; 2σ).

6. Systematic Uncertainties and Model-Driven Corrections

The dominant uncertainties in current D/H measurement propagate from:

• Line blending (especially Lyα forest interlopers near D I)
• Velocity structure degeneracy and component modeling
• Continuum placement, particularly in the forest
• Oscillator strengths and zero-level corrections
• Nuclear reaction rate uncertainties (notably D(p,γ)^3He and D(d,p), D(d,n))
• Metallicity/chemical inhomogeneity (almost negligible for [O/H] ≲ –2)

Explicit error analyses using Monte Carlo, bootstrap resampling, and MCMC frameworks are now standard. For sub-DLAs (log N(H I) ≈ 19.3–19.9), and future high-precision applications, the formalism in (Cooke et al., 2015) provides readily applicable analytic corrections for the differential ionization, with recommended use of the N(N II)/N(N I) ratio for robust correction (maximum 0.1%, negligible at current precision).

7. Implications, Cosmic Evolution, and Future Prospects

The tight agreement between the primordial D/H inferred from high-redshift, metal-poor systems and standard BBN calculations anchored by CMB Ω_b h² strongly confirms the consistency of early-universe physics. The constraint on Ω_b h² from D/H approaches the precision of CMB, offering a cross-epoch test of cosmological parameters (Pisanti et al., 2020, Dvorkin et al., 2016). The observed low astration at low metallicity validates chemical evolution models with globally low star formation efficiency.

Some persistent discrepancies (e.g., the ∼2σ D/H–Ω_b h² tension, and the unresolved lithium problem) highlight the need for further reduction of nuclear uncertainties (Coc et al., 2015, Pisanti et al., 2020), a larger and even more homogeneous sample of quasar absorbers, and improved measurements of D/H and other light elements such as ^4He in diverse environments (Guarneri et al., 8 Feb 2024, Kislitsyn et al., 23 Jan 2024). The D/H–metallicity relation is established as an efficient tool to extract (D/H)_p from future data (Voort et al., 2017, Dvorkin et al., 2016).

These efforts collectively establish primordial deuterium as not only the most precise baryometer available, but also a stringent constraint on possible physics beyond the Standard Model—such as extra relativistic species, lepton asymmetry, or time-dependent baryon-to-photon ratios—across the first few minutes to several hundred thousand years after the Big Bang.