Big Bang Nucleosynthesis and the Light Elements

Yeh, Tsung-Han et al.  The LBT Y_p Project V: Cosmological Implications of a New Determination of Primordial ⁴He.  Feb 2, 2026.  The fifth paper in the LBT Y_p project, a cosmology analysis of a new measurement of primordial helium-4, the helium made in the early universe.  A preprint (draft of 2 February 2026), and Table 2's caption still carries the authors' editing marker, so check the published version before relying on that table.  The article uses its Table 1 for the two separate baryon-density values, one from deuterium and one from the microwave background.

1. 1a.

   Table 1:  With N_ν = 3 and marginalised over Y_p.  BBN+D, using deuterium and laboratory nuclear rates with no CMB input: η₁₀ = 6.096 ± 0.119, Ω_bh² = 0.02227 ± 0.00043.  CMB-only, with no light-element input: η₁₀ = 6.104 ± 0.055, Ω_bh² = 0.02230 ± 0.00020.  The 0.13 percent and 0.06σ figures are arithmetic on those two published rows. ↩ ↩ ↩ ↩

2. 1b.

   Section Abstract:  “For Standard BBN, where the number of light neutrino species is fixed at N_ν = 3, the single free parameter is the cosmic baryon density; the CMB measures this independently, with results consistent with each other. … Our results demonstrate consistency with the Standard Model of particle physics, and with the standard cosmology that links BBN at ∼1 sec and the CMB at ∼400,000 yr.” ↩

3. 1c.

   Section Abstract:  With the neutrino count left free:  “N_ν = 2.925 ± 0.082, and for N_ν ≥ 3, ΔN_ν = N_ν − 3 ≤ 0.125 (95% CL) during BBN and the CMB.”  Table 2:  From the light elements alone (BBN+Y_p+D), Table 2 gives N_ν = 2.941 ± 0.092.  Their comment on that agreement:  “points further to the lack of new physics affecting this number.” ↩ ↩

4. 1d.

   Their adopted deuterium value:  “Based on 12 objects … (D/H)_p = (2.513 ± 0.028) × 10⁻⁵.” ↩

5. 1e.

   Their CMB+BBN predicted abundances, Eqs. 19-22: Y_p = 0.2467 ± 0.0002; D/H = (2.506 ± 0.083) × 10⁻⁵; ³He/H = (10.45 ± 0.87) × 10⁻⁶; ⁷Li/H = (4.95 ± 0.70) × 10⁻¹⁰. ↩ ↩ ↩

Launders, Timothy et al.  “A data-driven prediction for the primordial deuterium abundance.”  arXiv.  Apr 17, 2026.  A 2026 preprint by three physicists at Boston University, Lawrence Berkeley National Laboratory and the University of California, Berkeley.  They fit experimental data on three nuclear reactions that make deuterium, using Gaussian-process regression, a curve-fitting method that does not assume a fixed shape, and predict the primordial deuterium abundance from the fit.  Their prediction sits 1.70σ below the Cooke et al. measurement, and 1.98σ below when the baryon density comes from a combined fit to Planck, ACT DR6 and SPT-3G D1 data.  The article uses it as the competing analysis that brings the disagreement to about 2σ. ↩

1. 2a.

   Section Abstract:  “Using the Planck determination of the baryon density, we predict 10⁵ × D/H = 2.442 ± 0.040 in standard Big Bang Nucleosynthesis, 1.70σ below the Cooke et al. measurement. … With the inferred baryon density from a combined fit to Planck, ACT DR6, and SPT-3G D1, this discrepancy worsens to 1.98σ. … 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)³He and d(d,p)t S-factors at energies between 0.1 and 0.6 MeV.”  Their Table II, all at the same Planck baryon density, gives Gaussian process 2.442 ± 0.040 (1.70σ), PRIMAT 2.444 ± 0.037 (1.74σ), PArthENoPE 2.512 ± 0.042 (0.29σ), PRyMordial/YOF 2.520 ± 0.104 (0.06σ), against Cooke's measured 2.527 ± 0.030.  The paper's Table I misprints Planck's baryon density as 100ω_b = 2.337 ± 0.015; the correct Planck value is 2.237, and their own text is inconsistent with the misprint. ↩ ↩ ↩ ↩ ↩

Camphuis, E. et al.  “SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G Main field.”  Physical Review D 113:083504.  2026.  A collaboration paper from the SPT-3G team, which measures the cosmic microwave background from 4 percent of the sky with the South Pole Telescope's current camera.  It reports the temperature and polarization power spectra and the standard cosmological parameters from those measurements.  The article uses its table of cosmological values, including the baryon density (the amount of ordinary matter, written 100 Ω_bh² in the table), to show how far the three leading microwave-background experiments disagree with each other.

1. 3a.

   Page 7:  In the ΛCDM parameter table, row "100 Ω_bh²": Planck 2.238 ± 0.014; SPT-3G D1 2.221 ± 0.020; ACT DR6 2.257 ± 0.016; SPT+ACT 2.247 ± 0.013; SPT+Planck 2.230 ± 0.011; CMB-SPA 2.2398 ± 0.0095.  The three leading experiments span 1.6 percent, and SPT and ACT differ from each other by about 1.4σ. ↩ ↩ ↩

Fields, B. D. et al.  “24. Big-Bang Nucleosynthesis.”  International Journal of Modern Physics A 41:2630011.  Edited by F. Takahashi et al.  2026.  A review of Big Bang nucleosynthesis in the Particle Data Group's Review of Particle Physics, revised in August 2025 and printed in the journal's 2026 volume.  The 2025 and 2026 editions carry the same review text; the 2024 edition, the August 2023 revision, has different numbers.  The article uses its figures for the measured deuterium ratio, the helium-3 and lithium-7 problems, and the claim that the standard theory has a single free parameter.

1. 4a.

   Section 24.3:  On helium-3:  “The primordial abundance of ³He has the poorest observational determination of all of the light nuclides.  The only data available come from the Solar system and from solar-metallicity HII regions in the Galaxy.  Therefore, inferring the primordial ³He abundance is problematic, compounded by the fact that stellar nucleosynthesis models for ³He are in conflict with observations.  Consequently, we consider it inappropriate to use ³He (and also D+³He) as a cosmological probe.” ↩ ↩ ↩

2. 4b.

   Section 24.3:  The recommended value is.  “D/H|_p × 10⁶ = 25.08 (±0.29),”.  a weighted mean of twelve quasar-absorber systems listed in Table 24.1, with the uncertainty inflated by S = 1.08 because χ²/(N−1) = 1.160.  On the trend:  “The observed D/H ratio exhibits no correlation with metallicity, redshift, or the neutral hydrogen column density N(HI) … integrated along the line of sight through the absorber.  The metallicities of these absorption systems range from (0.001 − 0.03)× the Solar value, and the level of deuterium astration is estimated to be between 0.1% and 1%.”  Also:  “despite nearly three decades of observational effort, only 12 high-precision determinations are currently available.” ↩ ↩ ↩ ↩ ↩

3. 4c.

   Section 24.5:  “As shown in Fig. 24.1, stellar Li/H measurements are inconsistent with the D/H (and CMB) constraints, given the quoted error budgets.  For example, the primordial value from [45] Li/H|_p = (4.72 ± 0.7) × 10⁻¹⁰ exceeds the prediction of eq. 24.4 by a factor of 3.3, corresponding to a 4.4σ discrepancy.”  The review's wording swaps the labels "primordial value" and "prediction"; the substance is that theory gives 4.72 and stars give 1.45. ↩ ↩ ↩ ↩ ↩

4. 4d.

   Section 24.2:  “This resulted in departure from chemical equilibrium (freeze-out) at T_fr ∼ (g_*G_N/G⁴_F)^1/6 ≃ 1 MeV.  The neutron fraction at this time, n/p = e^−Q/T~fr~ ≃ 1/6, is thus sensitive to every known physical interaction, since Q is determined by both strong and electromagnetic interactions while T_fr depends on the weak as well as gravitational interactions.”  “After freeze-out, the neutrons were free to β-decay, so the neutron fraction dropped to n/p ≃ 1/7 by the time nuclear reactions began.”  The deuterium bottleneck breaks when.  “the number of photons per baryon above the deuterium photo-dissociation threshold, falls below unity at T ≃ 0.1 MeV.” ↩ ↩ ↩

5. 4e.

   Section 24.2:  “Heavier nuclei do not form in any significant quantity both because of the absence of stable nuclei with mass number 5 or 8 (which impedes nucleosynthesis via n⁴He, p⁴He or ⁴He⁴He reactions), and the large Coulomb barriers for reactions such as ³He(⁴He, γ)⁷Li and ³He(⁴He, γ)⁷Be.  Hence the primordial mass fraction of ⁴He, Y_p ≡ ρ(⁴He)/ρ_b, can be estimated by the simple counting argument Y_p = 2(n/p)/(1 + n/p) ≃ 0.25 … There is little sensitivity here to the actual nuclear reaction rates for the production of ⁴He.” ↩ ↩

6. 4f.

   Section 24.4:  “We now use the observed light element abundances to test the theory.  We first consider standard BBN, which is based on Standard Model physics alone, so N_ν = 3 and the only free parameter is the baryon-to-photon ratio η. … Thus, any abundance measurement determines η, and additional measurements overconstrain the theory and thereby provide a consistency check.”  And later:  “Within the context of the Standard Model, BBN then becomes a zero-parameter theory, and the light element abundances are completely determined to within the uncertainties in η_CMB and the BBN theoretical errors.” ↩

7. 4g.

   Section 24.4:  “One can determine η from the amplitudes of the acoustic peaks in the CMB angular power spectrum, making it possible to compare two measures of η using very different physics, at two widely separated epochs.  In the standard cosmology, there is no change in η between BBN and CMB decoupling, thus, a comparison of η_BBN and η_CMB is a key test.  Agreement would endorse the standard picture, while disagreement could point to new physics during/between the BBN and CMB epochs.” ↩

8. 4h.

   Section 24.4:  Eq. 24.6:  “(Ω_bh²)_SBBN = 0.02205 ± 0.00043.”  The Planck value without BBN theory:  “Without BBN theory, the Planck TT, TE, EE + lowE data plus lensing give Ω_bh² = 0.02230 ± 0.00021, corresponding to η₁₀ = 6.104 ± 0.058.”  Combined:  “η₁₀ = 6.115 ± 0.038 and Ω_bh² = 0.02233 ± 0.00014.” ↩ ↩

9. 4i.

   Section 24.4:  “Very recently, the Atacama Cosmology Telescope and South Pole Telescope have each released new cosmological parameters arising from their most recent data, reporting N_eff = 2.86 ± 0.13 and N_eff = 2.83 ± 0.13, respectively.”  The BBN-only value in the same section is.  “N_ν = 2.898 ± 0.141.” ↩

10. 4j.

    Section 24.4:  “small corrections for non-equilibrium neutrino heating are included in the thermal evolution and lead to an effective N_ν = 3.044 compared to assuming instantaneous neutrino freezeout.”  Also useful:  “The computed ⁴He abundance scales as ΔY_p ≃ 0.013ΔN_ν.”  Other reviews quote 3.043, 3.045 or 3.046 for the same quantity; this article uses the PDG's 3.044. ↩ ↩

11. 4k.

    Section 24.3:  “In contrast, within the Milky Way, DI/HI measurements show an anti-correlation with metal abundance, suggesting that a fraction of interstellar deuterium is depleted onto dust grains.  However, in the absorbers where deuterium is measured, the dust content is small, as implied by Solar proportions of the abundances of refractory and non-refractory elements.  Thus, the neutral atomic ratio DI/HI ≡ D/H should match the underlying isotope ratio, and be truly representative of the primordial value D/H|_p.” ↩ ↩

12. 4l.

    Section 24.3:  “BBN is the only significant source of deuterium, which is entirely destroyed when cycled through stars.  Thus, any detection of D provides a lower limit to the primordial abundance D/H|_p, and correspondingly, an upper limit on the baryon-to-photon ratio η₁₀.” ↩

13. 4m.

    Section 24.3:  “systematic effects dominate the uncertainties in the abundance determination.  A major step forward has been the inclusion of the He λ10830 infrared emission line which shows a strong dependence on the electron density and is thus useful to break the degeneracy with the temperature.” ↩

14. 4n.

    Section 24.3:  Table 24.2 and the surrounding text:  “Y_p = 0.245 ± 0.003.”  Their caution:  “The central value is close to the mean/weighted average of the values in Table 24.2, however we caution that combining these partially overlapping data sets is not straightforward.  The uncertainty reflects the combined statistical and systematic errors, with the latter, estimated to be ±0.002, being dominant.” ↩ ↩

15. 4o.

    Section 24.4:  “The CMB damping tail is sensitive to the primordial ⁴He abundance independently of both BBN and local ⁴He measurements.  The Planck analysis using TT, TE, EE+lowE and lensing but not the BBN Y_p(η) relation gives a ⁴He mass fraction 0.239 (+0.024/−0.025) … both at 95% CL.  This is consistent with the HII region helium abundance determination. … This concordance represents a successful CMB-only test of BBN.”  The printed PDF contains a typographical error in the second helium figure; it is not reproduced here. ↩

16. 4p.

    Section 24.3:  “Observations have long shown that ⁷Li does not vary significantly among halo dwarfs with metallicities ≲ 1/30 of Solar — the Spite plateau.  However, more recent observations show an increase in Li depletion in metal-poor stars.  The reason for this increased scatter at low metallicity remains unknown and prevents a reliable derivation of the primordial ⁷Li abundance by extrapolation to zero metallicity.  To estimate the primordial ⁷Li abundance, we restrict the analysis to stars with metallicities in the range −3.5 < [Fe/H] < −1.5, where no scatter beyond the observational uncertainties is observed.”  The recommended value is.  “Li/H|_p = (1.45 ± 0.25) × 10⁻¹⁰.” ↩ ↩

17. 4q.

    Section 24.3:  “Strictly speaking, the inferred primordial ⁷Li abundance should be regarded as a lower bound rather than a direct measurement.  This is because ⁷Li in Population II stars may have been partially destroyed through mixing of the outer stellar layers with the hotter interior.  Such processes are constrained by the lack of significant scatter in ⁷Li as a function of T_eff, yet a significant depletion may still have occurred.” ↩

18. 4r.

    Section 24.5:  “The universality of this problem is underscored by the fact that stars accreted into the Milky Way billions of years ago from external galaxies exhibit the same Li abundances as native stars.” ↩

19. 4s.

    Section 24.5:  “Nuclear inputs (cross sections) for BBN reactions are constrained by extensive laboratory measurements; to increase ⁷Be destruction requires enhancement of otherwise subdominant processes that can be attained by missed resonances in a few reactions such as ⁷Be(d, p)2α if the compound nuclear state properties are particularly favorable.  However, experimental searches have now closed off these possibilities, making a nuclear fix increasingly unlikely.” ↩

20. 4t.

    Section 24.5:  “Nucleosynthesis models in which the baryon-to-photon ratio is inhomogeneous can alter abundances for a given η_BBN, but will overproduce ⁷Li.  Entropy generation by some non-standard process could have decreased η between the BBN era and CMB decoupling, however the lack of spectral distortions in the CMB rules out any significant energy injection up to a redshift z ∼ 10⁷.”  On particle injection:  “This introduces a tension between Li/H reduction and D/H enhancement that becomes increasingly restrictive with the increasing precision of deuterium observations.  Indeed, this now forces particle injection scenarios to make very small ⁷Li perturbations — far short of the level needed.  An exception is a recent model wherein MeV-scale decays by construction avoid ⁴He dissociation and associated D/H overproduction, instead borrowing neutrons by dissociating only deuterons.” ↩ ↩ ↩

21. 4u.

    Section 24.5:  “Alternatively, lithium may be destroyed in situ within stars over their lifetimes.  Depletion mechanisms include diffusion, rotational mixing, and pre-main-sequence burning.  While these effects are real, reducing Li to the required levels generally demands some degree of fine-tuned stellar parameters or ad hoc mechanisms.  Diffusive models, for instance, predict both a dispersion in Li abundances and a downturn at the hot end of the Spite plateau.  Additional turbulence must then be invoked to suppress diffusion and restore the observed uniformity.” ↩ ↩

22. 4v.

    Section 24.5:  “Large surveys provide new insight.  The GALAH project, which measured Li abundances for over 100,000 field stars, finds that warm stars with −1.0 ≤ [Fe/H] ≤ −0.5 form a plateau consistent with BBN predictions.  This suggests that more metal-poor stars—now evolved beyond observability—may once have had higher Li abundances as well.”  The same section records the counter-evidence:  “Finally, interstellar lithium measurements in low-metallicity systems provide a stellar depletion-free probe.  In the Small Magellanic Cloud, interstellar Li/H has been measured at levels consistent with Galactic halo stars.” ↩ ↩

23. 4w.

    Section 24.4:  Immediately after Eq. 24.6:  “First of all Ω_b ≪ 1, i.e., baryons cannot close the Universe.  Furthermore, the cosmic density of (optically) luminous matter is Ω_lum ≃ 0.0024h⁻¹, so that Ω_b ≫ Ω_lum: most baryons are optically dark, probably in the form of a diffuse intergalactic medium.  Finally, given that Ω_m ∼ 0.3 … we infer that most matter in the Universe is not only dark, but also takes some non-baryonic (more precisely, non-nucleonic) form.” ↩

24. 4x.

    Section 24.4:  “Despite the lithium problem, the overall concordance remains remarkable: using only well-established microphysics we can extrapolate back to t ∼ 1 s to predict light element abundances spanning nine orders of magnitude, in approximate agreement with observation.  This is a major success for the standard cosmology, and inspires confidence in extrapolation back to such early times.”  The same section is explicit about the exclusion:  “While the η ranges spanned by the boxes in Fig 24.1 do not all overlap, they are all within a factor ∼2 of each other. … If however we exclude the lithium constraint because its inferred abundance suffers from systematic uncertainties, then D/H and ⁴He are in agreement.”  The abstract adds the range being covered:  “these abundances span nine orders of magnitude — from ⁴He/H ∼ 0.08 down to ⁷Li/H ∼ 10⁻¹⁰.” ↩ ↩

Aver, Erik et al.  The LBT Y_p Project IV: A New Value of the Primordial Helium Abundance.  Feb 2, 2026.  A preprint, not yet a journal article, with an arXiv draft dated 2 February 2026.  It is part IV of the LBT (Large Binocular Telescope) helium project.  It measures 54 metal-poor glowing gas clouds, keeps 15 of the cleanest low-metallicity ones, and takes their weighted average to get the primordial helium mass fraction (the share of the early universe's ordinary matter that became helium-4).  The article calls it the most precise helium measurement made so far, and says the team changed method as well as data.

1. 5a.

   Section Abstract:  “By weighted average of our 15 low-metallicity targets, we determine Y_p = 0.2458 ± 0.0013. This result achieves an unprecedented precision of 0.5%, and it is in good agreement with the BBN result, Y_p = 0.2467 ± 0.0002, based on the Planck determination of the baryon density.”  The sample is 54 metal-poor H II regions observed with the Large Binocular Telescope, cut to 41 and then to the 15 high signal-to-noise, low-metallicity (O/H < 4 × 10⁻⁵) targets used for the average. ↩ ↩ ↩

2. 5b.

   Section §1:  Listing the systematics:  “These have been identified as reddening by the intervening ISM, the stellar absorption profiles underlying the emission lines, the collisional excitation of H lines (which requires measuring the neutral hydrogen fraction), and the radiative transfer gains and losses in the He triplet lines due to the presence of the 2³S metastable level.”  “The absence of direct measurements of the physical quantities which enter into the model may lead to significant systematic uncertainties in the derived helium abundance.”  Section §2.1:  §2.1 lists the eight helium line ratios used, including λ10830 measured against the infrared Paschen-γ line. ↩

Fields, Brian D. et al.  “Big-Bang Nucleosynthesis after Planck.”  JCAP (03):010.  2020.  A 2020 status report on Big Bang nucleosynthesis, the theory of how the light elements formed in the first few minutes, by four researchers at the universities of Illinois and Minnesota.  They updated their earlier analysis with the final Planck data, and found that the lithium problem remains (an erratum is printed in JCAP 11 (2020): E02).  The article uses it for how helium-4 and deuterium respond to the baryon density, which is the amount of ordinary matter, and for the planned test of the neutrino count.

1. 6a.

   Figure 4:  “We see excellent agreement for D/H, good agreement for ⁴He, and strong discrepancy in ⁷Li constitutes the persistent lithium problem.”  Section VII (Discussion):  “As much as the concordance between BBN theory, light element abundance observations, and measurements of the CMB is impressive, the elephant in the room is the ⁷Li abundance.” ↩

2. 6b.

   Table II:  The abundance sensitivities to the baryon-to-photon ratio, run at η₁₀ = 6.129: Y_p ∝ η^0.039, D/H ∝ η^−1.597, ³He/H ∝ η^−0.583, ⁷Li/H ∝ η^+2.094.  The same table gives the sensitivity to the neutron lifetime (Y_p ∝ τ_n^0.729) and to Newton's constant (Y_p ∝ G_N^0.357), which is why helium is a probe of the expansion rate rather than of the density. ↩ ↩ ↩ ↩ ↩

3. 6c.

   Section VI (The Future Impact of CMB-Stage 4 Measurements):  The passage concerns the next generation of microwave-background experiments.  “the CMB-S4 target sensitivity is σ_S4(N_eff|BBN) = 0.030!  If this can be achieved, then it would be possible to resolve the difference N_eff − N_ν = 0.045 due to neutrino heating.  This would offer a new probe of neutrino interactions during the BBN epoch.” ↩

4. 6d.

   Section VII (Discussion):  “There is a clear mismatch between the BBN predicted abundance and the abundance seen in metal-poor stars.  We have largely ignored this discrepancy as its not clear whether its resolutions lies in nuclear physics, beyond the Standard Model particle physics, the observational determination, or the stellar history of ⁷Li.”  The grammatical slips are in the original. ↩

Yanagisawa, Hiroto et al.  “EMPRESS. XV. A New Determination of the Primordial Helium Abundance Suggesting a Moderately Low Y_P Value.”  Astrophysical Journal 1004:55.  2026.  A 2026 observing paper by a team based mainly in Japan that took near-infrared spectra of 29 galaxies with the Subaru telescope, 14 of them extremely metal-poor galaxies (galaxies with very few elements heavier than hydrogen and helium), and added 58 galaxies from earlier studies.  It gives the primordial helium abundance, the share by mass of helium-4 that the Big Bang made, as 0.2402 plus or minus 0.0040, about 1 sigma (the usual unit of uncertainty) below most earlier estimates.  The authors say more observations and further checks of systematic uncertainties are needed before the tension with the Standard Model can be tested more rigorously.  The article uses it as one of the two best modern measurements, and the two disagree.  Mirror:  arXiv

1. 7a.

   Section Abstract:  “we perform Subaru near-infrared spectroscopy of 29 galaxies, including 14 EMPGs.  By incorporating existing optical spectra, we derive He/H for each galaxy using photoionization modeling of helium and hydrogen emission lines, including the He i 10830Å line to break the density-temperature degeneracy.  After carefully selecting galaxies with robust He/H determinations, and adding 58 galaxies from previous studies, we obtain Y_P = 0.2402 (+0.0040/−0.0040).  This Y_P value is ∼1σ lower than most of the previous estimates … Our result indicates N_eff = 2.54 (+0.20/−0.25), showing a mild (∼2σ) tension with the Standard Model and Planck results.” ↩ ↩ ↩ ↩

Molaro, P. et al.  “Extragalactic ⁸⁵Rb/⁸⁷Rb and ⁶Li/⁷Li ratios in the Small Magellanic Cloud.”  Astronomy & Astrophysics 690:A38.  2024.  A 2024 re-analysis of interstellar lithium in the Small Magellanic Cloud, measured in gas toward the star Sk 143.  It revises the 2012 paper of which Howk is the first author, and Molaro is a co-author of the Particle Data Group's nucleosynthesis review.  It finds an absolute lithium abundance of A(⁷Li) ≈ 2.2, which the authors say differs from the expectation from Big Bang nucleosynthesis.  The article uses it as the one lithium measurement free of stellar destruction, and as evidence against the explanation that old stars destroyed their own lithium.  Mirror:  arXiv

1. 8a.

   Section Abstract:  “the low metallicity of the cloud leads to an absolute Li abundance of A(⁷Li) ≈ 2.2, which differs from the expectation from big bang nucleosynthesis.  Because the gas-phase abundance is not affected by stellar depletion, the burning of Li inside the halo stars is probably not the solution for the cosmological ⁷Li problem.” ↩ ↩ ↩

2. 8b.

   Section 4:  “assuming [Zn/Fe] = 0 and allowing a mild overabundance in [K/Fe] = 0.1 from [Zn/H]₁₄₃ = −1.28 ± 0.06, we obtain a value of [K/H]₁₄₃ ≈ −1.18 for the potassium abundance in the cloud,”.  This gives, in their Eq. 4:  “A(⁷Li)_SK143 = 2.16 (±0.12).”  On the change from 2012:  “Howk et al. (2012) took the K abundance from stellar determinations, which is higher by about 0.7 dex, taken from the stars, and therefore, computed a much higher value of A(⁷Li).” ↩

3. 8c.

   Section Conclusion:  “while the theory of turbulent diffusion … may be invoked to explain this discrepancy in stars, it cannot have any effect on the ⁷Li as measured in low-metallicity interstellar gas, and our measurement in metal-poor gas toward Sk 143 in the SMC challenges the stellar depletion solution.” ↩

Cooke, Ryan J.  “Big Bang Nucleosynthesis.”  Encyclopedia of Astrophysics.  Elsevier.  2024.  A chapter in an encyclopedia, with a glossary and learning objectives, that explains how the light elements were made in the first minutes after the Big Bang and summarizes the state of the measurements.  It is written by the person who made the one-percent primordial deuterium measurement, so the reader should weigh its verdicts on that measurement with that in mind.  The article uses it to explain the deuteron bottleneck and when each light element was fixed.

1. 9a.

   Section §3.2 Helium-4 — The search for physics beyond the Standard Model:  “this was one of the first triumphs of BBN calculations, which were able to postdict the mass fraction of ⁴He, giving extra credibility to the idea of a hot Big Bang.”  The word is the author's own. ↩ ↩

2. 9b.

   Section §3.4 Lithium-7 — The Cosmic Lithium Problem:  On the origin of the lithium problem, the first WMAP results.  “provided a tight bound on the baryon density, and this revealed that the Spite plateau disagreed significantly with the Standard Model value, based on the CMB-derived baryon density.”  The author adds that remeasurement made it worse:  “the improved models have made the disagreement with the Standard Model slightly more pronounced … the refined measurements of the reaction rates also made the disagreement even more pronounced.” ↩

3. 9c.

   Section §1.3 Genesis of the first elements:  On the deuteron bottleneck:  “because baryons are so underabundant — by a factor of ∼10⁹ — compared to the photons, deuterons are destroyed by the high energy tail of the blackbody distribution until the photon temperature drops to well below the deuteron binding energy. This is known as the 'deuteron bottleneck' (and sometimes incorrectly as the 'deuterium bottleneck'). The creation and destruction rates of Equation 7 are equal when the Universe is at a temperature of k_BT ≃ 0.06 MeV, and at this point deuteron production begins in earnest.” ↩ ↩

4. 9d.

   Section §2 Calculating the creation of the first nuclides:  On freeze-out times:  “The first nuclides to freeze-out (i.e. change by ≲ 0.1% relative to the final state of the Universe) are ¹H and ⁴He … This freeze-out occurred ∼ 6 minutes after the Big Bang. Of the nuclides shown in Figure 2, ⁷Be freezes-out next, at around ∼ 4 hours after the Big Bang, while ²H, ³H, ³He, and ⁷Li all freeze-out at roughly the same time, around ∼ 8 − 10 hours after the Big Bang.”  On the beryllium-7 decay:  “⁷Be begins decaying to ⁷Li via electron-capture … starting at a redshift z ∼ 35,000 (i.e. ∼ 600 years after the Big Bang…), and this process continues until z ∼ 27,500.” ↩ ↩

5. 9e.

   Section §2 (end):  “Thus, ⁷Li/H is the most sensitive primordial abundance to the baryon density, closely followed by D/H. However, the nuclear reactions that are most relevant to deuteron nucleosynthesis are known to better precision than that of ⁷Li. The D/H ratio is therefore more suitable to determine the baryon density at high precision than any other primordial nuclide.” ↩

6. 9f.

   Section §2 (end):  “It is also noteworthy that the primordial helium abundance is relatively insensitive to the baryon density, making it an important probe of deviations from the Standard Model expansion rate.” ↩

7. 9g.

   Section §3.4 Lithium-7 — The Cosmic Lithium Problem:  The author says that stars are.  “good at burning ⁷Li. Convective motions (particularly in cool stars) mix the ⁷Li near the surface of the star into the deeper layers where ⁷Li is burned. Meanwhile ⁷Li-deficient material is brought to the surface. To mitigate the effects of this process, observations typically focus on the warmest metal-poor stars, which have thin convective zones, and the measured ⁷Li abundance does not correlate with temperature. This key realization came from Spite and Spite (1982), who reported the first measurement of the ⁷Li abundance in metal-poor stars.”  The reference is Spite, F., and Spite, M., "Abundance of lithium in unevolved stars and old disk stars: interpretation and consequences," A&A 115 (1982): 357-366. ↩ ↩ ↩

8. 9h.

   Section §3.4 Lithium-7 — The Cosmic Lithium Problem:  On the Small Magellanic Cloud measurement:  “most of the lithium in this neutral gas cloud is singly ionized; transitions of Li ii occur at energies > 1 Ryd, and are not observable … The only transitions available come from neutral ⁷Li, and require a substantial ionization correction (about a factor of ∼100× the measured value) … it is worth bearing in mind that there is still some uncertainty in this correction.”  On the plateau:  “the Spite Plateau appears to break down at metallicities less than 1/300 of solar.” ↩ ↩

Janot, Patrick, and Stanisław Jadach.  “Improved Bhabha cross section at LEP and the number of light neutrino species.”  Physics Letters B 803:135319.  2020.  A 2020 reanalysis of data from the LEP electron-positron collider at CERN, by a CERN physicist and a physicist at the Institute of Nuclear Physics in Kraków.  They recalculated the rate of Bhabha scattering, a process used to measure the collider's luminosity (how many collisions it produces), which lowers that rate by about 0.048 percent, and recomputed the number of light neutrino species as 2.9963 ± 0.0074.  The article uses it as the accelerator measurement of the neutrino count, set against the light-element result.

1. 10a.

   Section Abstract:  “When accounted for, these changes modify the number of light neutrino species (and its accuracy), as determined from the LEP measurement of the hadronic cross section at the Z peak, to N_ν = 2.9963 ± 0.0074.  The 20-years-old 2σ tension with the Standard Model is gone.”  The superseded LEP electroweak working group value, quoted in the same paper, was N_ν = 2.9840 ± 0.0082. ↩ ↩ ↩ ↩

Mossa, V. et al.  “The baryon density of the Universe from an improved rate of deuterium burning.”  Nature 587:210–213.  Nov 12, 2020.  A laboratory measurement by the LUNA Collaboration, which the paper says cuts cosmic-ray muons by a million-fold.  It measured the reaction that burns deuterium to better than 3 percent and used the result to estimate the baryon density from Big Bang nucleosynthesis, obtaining 0.02233 ± 0.00036.  The article uses that value as the deuterium-only baryon density, and as the measurement that resolved the 2018 disagreement with the microwave background.

1. 11a.

   Section Discussion:  “It should be noted that Ω_bh² from the CMB reflects the baryon density of the Universe at the re-combination epoch, some 380,000 years after the Big Bang.  However, according to the ΛCDM model, the baryon density can only vary as a result of the expansion of the Universe and thus its present-day value inferred from either CMB and BBN should be the same.  Therefore, the evaluation of Ω_bh² based on BBN alone is critical as it can either support the ΛCDM model or point to new physics between the BBN and CMB epochs.” ↩

2. 11b.

   Section Results:  “We obtain Ω_bh²(BBN) = 0.02233 ± 0.00036.  As shown in Figure 2, this value is a factor of 2 more precise than that obtained using a previous S factor and now in much better agreement with the Ω_bh² based on CMB data. … The fact that the present-day values of Ω_bh²(BBN) and Ω_bh²(CMB) are fully consistent with each other (Table 1) offers evidence of the validity of the ΛCDM model adopted here.”  Their measurement precision:  “we have measured the D(p,γ)³He reaction cross section to an unprecedented precision of better than 3% by exploiting the million-fold reduction in cosmic-ray muons at LUNA.” ↩ ↩ ↩

3. 11c.

   Section Results:  Running the calculation the other way:  “if we use the baryon density provided by the PLANCK Collaboration, we derive a theoretical prediction on deuterium abundance (D/H)_BBN = (2.52 ± 0.03 ± 0.06) × 10⁻⁵, in excellent agreement with astronomical observations (D/H)_obs = (2.527 ± 0.030) × 10⁻⁵.” ↩

Pitrou, Cyril et al.  “A new tension in the cosmological model from primordial deuterium?”  Monthly Notices of the Royal Astronomical Society 502:2474–2481.  2021.  A 2021 paper by the same four authors as the 2018 paper.  It uses newer measurements of a key nuclear reaction and of the neutron lifetime to recompute the baryon density implied by primordial deuterium alone, and compares it with the value from the cosmic microwave background, reporting a tension of about 1.8 standard deviations.  The article uses it because the same tension appears there, and the authors did not soften it.  Mirror:  arXiv

1. 12a.

   “we obtain for BBN only Ω_bh² = 0.02195 ± 0.00022. … This is a 1.6σ tension with CMB and 1.84σ tension with CMB+BAO.”  Run the other way:  “we then find the theoretical expectation (D/H) = (2.439 ± 0.037) × 10⁻⁵.” ↩

2. 12b.

   “This is indeed a mild warning but it sheds some light on the sector of the big-bang theory, indicating that it should be watched carefully, both on the nuclear and astrophysical data sides.”  “If confirmed, the status of BBN, with the lithium-problem and a mildly-constraining helium-4, would have to be reconsidered.”  They name the cause:  “because of the importance of the d+d reaction rates, in particular, the D(d,n)³He one, further investigations are needed to reconcile Trojan Horse results (Tumino et al. 2014) with direct measurements.” ↩

Schöneberg, Nils.  “The 2024 BBN baryon abundance update.”  JCAP 06:006.  2024.  A 2024 update by one author at the Institut de Ciències del Cosmos of the University of Barcelona.  It compares several BBN codes and a wide range of deuterium-burning rates, and reports the baryon density that the light elements imply.  It finds that the choice of nuclear rates moves that result more than anything else, and the article uses its conservative estimate as one of its BBN values.  Mirror:  arXiv

1. 13a.

   Section Abstract:  “We find that the largest differences between the final baryon abundances are typically driven by the assumed Deuterium burning rates, characterized in this work by the underlying code.  The rates from theoretical ab-initio calculations favor smaller baryon abundances, while experimentally-determined rates prefer higher abundances.  Through robust marginalization over a wide range of nuclear rates, the recently released PRyMordial code allows for a conservative estimate of the baryon abundance at Ω_bh² = 0.02218 ± 0.00055 (using PDG-recommended light element abundances) in ΛCDM. … These additional relics themselves are constrained to ΔN_eff = −0.14 ± 0.21 by light element abundances alone.” ↩

Planck Collaboration.  “Planck 2018 results. VI. Cosmological parameters.”  Astronomy & Astrophysics 641:A6.  2020.  The final analysis of the full Planck satellite mission's maps of the cosmic microwave background, the leftover light from the early universe.  It fits the standard six-parameter model to the temperature, polarization and lensing data, and reports the baryon density from that fit.  The article uses it as the CMB value in its comparison of the baryon density with the nuclear-physics value, and for its helium results.  Mirror:  arXiv

1. 14a.

   Table 2:  TT,TE,EE+lowE+lensing: Ω_bh² = 0.02237 ± 0.00015; Ω_ch² = 0.1200 ± 0.0012; H₀ = 67.36 ± 0.54; Ω_m = 0.3153 ± 0.0073. ↩ ↩

2. 14b.

   Section 7.6:  “We do not discuss other light elements, such as tritium and lithium, since the observed abundance measurements and their interpretation in terms of the standard models of BBN are more controversial.”  The same section reports:  “Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations.” ↩ ↩

3. 14c.

   Section 7.6.1:  “Izotov et al. (2014) find a higher value, Y_P^BBN = 0.2551 ± 0.0022 (68 % CL) in moderate (2.2σ to 2.9σ) tension with the previous two.  Aver et al. (2015) discuss the differences between their results and Izotov et al. (2014), which are caused by modelling differences involving neutral hydrogen collisional emission, corrections for dust absorption, and helium emissivities, amongst other effects.  This raises the issue, which has long-plagued helium abundance measurements, of whether the systematic errors are accurately incorporated in the quoted uncertainties.”  After comparing the codes:  “in 3.6-3.8σ tension with the Izotov et al. (2014) results.  Evidently, there is an urgent need to resolve the differences between the helium abundance measurements and this tension should be borne in mind when we use the Aver et al. (2015) measurements below.”  The CMB-only helium value, from the same section, is Y_P = 0.239 ± 0.013. ↩ ↩ ↩ ↩ ↩ ↩

Poulin, Vivian et al.  “What could an emerging Big Bang Nucleosynthesis discrepancy be hinting at?”  arXiv preprint.  Jul 22, 2026.  A July 2026 preprint by four physicists, one of them Cyril Pitrou, a co-author of the 2018 and 2021 papers above.  The authors test whether a short-lived extra energy component during nucleosynthesis could explain the deuterium tension, which is about 2 standard deviations between the measured deuterium and the microwave-background baryon density.  The article uses it because the authors say the deuterium agreement depends on nuclear rates, and because they take the discrepancy seriously enough to propose a new field.

1. 15a.

   Section Abstract:  “The latest measurement of the primordial deuterium abundance is in ∼2σ tension with several state-of-the-art predictions of standard big bang nucleosynthesis (BBN), when using the baryon density inferred from the ΛCDM model fit to cosmic microwave background (CMB) data. … We test whether this discrepancy could be pointing to a non-standard expansion history during BBN. … Together with inflation, dark energy, and EDE, our results hint at the presence of another light scalar-field in cosmology.”  Their own footnote reduces the tension when the newer deuterium compilation is used:  “this lower D/H value would shift the inferred baryon density upward to ω_b ≃ 0.0220, reducing the tension to about 1.6σ.” ↩ ↩

2. 15b.

   Section Introduction:  “The 'ω_b tension' is not identical in all modern BBN calculations: the standard D/H prediction of PArthENoPE, or that of Ref. [3], is in closer agreement with Eq. (1).  The difference mainly comes from the deuterium-burning nuclear rates.  While D(p, γ)³He has been precisely measured, the D(D, n)³He and D(D, p)³H rates remain less certain, and different justified conversions of the data into nuclear rates lead to different predictions in PRIMAT and PArthENoPE.”  On why helium is the stable anchor:  “The helium-4 abundance is well measured, and its theoretical prediction is comparatively robust across modern BBN codes because it is controlled mainly by the neutron-to-proton ratio at weak freeze-out rather than by the late nuclear rates.” ↩

Calabrese, Erminia et al.  The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models.  2025.  A collaboration paper from the ACT (Atacama Cosmology Telescope) team, built on the sixth data release of its microwave-background measurements and combined with other surveys.  It tests the standard model of cosmology against extensions to it, and it reports an effective number of neutrino species, N_eff, a count of light particles that behave like neutrinos, that is consistent with the standard model.  The article uses its neutrino counts, from light elements alone and from the microwave background alone, and its helium value from the microwave background's damping tail.

1. 16a.

   Section §6.2:  “By assuming the PDG averages for helium and deuterium abundances and employing PRyMordial as the BBN calculator, we can also derive a pure BBN constraint on N_eff, finding N_eff = 2.93 ± 0.21 (68%, D-He) after marginalizing over η_b.  This estimate shows that the number of neutrinos at BBN and at the CMB recombination epoch are in very good agreement.”  The CMB-side value is from the abstract:  Section Abstract:  “N_eff = 2.86 ± 0.13.” ↩ ↩ ↩

2. 16b.

   Section Abstract:  “Our data are consistent with standard big bang nucleosynthesis (we find Y_p = 0.2312 ± 0.0092).”  This is from the CMB damping tail, with no astronomical helium input. ↩ ↩

3. 16c.

   Section §6.2:  “We do not discuss here abundances of other light elements, such as tritium, ³He, and ⁷Li; these elements are more uncertain in both their determination and their interpretation.”  Their footnote 28 also records the unresolved helium dispute, saying the PDG average.  “does not incorporate the recent measurements from the EMPRESS survey … which indicate a helium abundance, Y_p = 0.2370 ± 0.0034, ≈ 2.4σ lower than the PDG value.” ↩ ↩

Cooke, Ryan J. et al.  “One Percent Determination of the Primordial Deuterium Abundance.”  Astrophysical Journal 855:102.  2018.  A measurement paper in which the authors re-analysed one near-pristine gas cloud, seen in absorption against the quasar Q1243+307 with the Keck telescope's HIRES spectrograph, and combined it with six earlier systems.  Together the seven systems give a primordial deuterium-to-hydrogen ratio of (2.527 ± 0.030) × 10⁻⁵, a one percent measurement.  The article uses it to show why deuterium is measured in gas clouds with about the threshold amount of neutral hydrogen, and as the 2018 value that later compilations are compared with.  Mirror:  arXiv

1. 17a.

   Section §1:  “absorption line systems that have H i column densities near the threshold of a damped Lyα system (DLA; N(H i) ≃ 10^20.3 cm⁻²) are the most suitable environments to precisely measure the primordial deuterium abundance … In this H i column density regime, the H i Lyα transition exhibits Lorentzian damped wings that uniquely determine the total H i column density, while up to ∼10 high order unsaturated D i lines are available to determine the total D i column density.” ↩

2. 17b.

   Section Abstract:  On the new system toward Q1243+307, the abstract says it.  “has an oxygen abundance [O/H] = −2.769 ± 0.028 (≃ 1/600 of the solar abundance)”.  and that the deuterium abundance is measured.  “on the basis of eight D i absorption lines.” ↩

3. 17c.

   Section Abstract:  “we deduce that the primordial deuterium abundance is log₁₀(D/H)_P = −4.5974 ± 0.0052 or, expressed as a linear quantity, 10⁵(D/H)_P = 2.527 ± 0.030; this value corresponds to a one percent determination of the primordial deuterium abundance.”  Seven systems, all analysed by the same group in the same way. ↩

4. 17d.

   Section §4.3 (Intrinsic Scatter):  Their maximum-likelihood fit:  “σ ≤ 0.027 (95% confidence)”.  The paper adds this note:  “the intrinsic dispersion, σ, has a maximum likelihood value of zero; we therefore quote a 2σ upper limit.” ↩

5. 17e.

   Section §5 (Cosmological Consequences):  “100 Ω_B,0h²(BBN) = 2.166 ± 0.015 ± 0.011”.  set against.  “100 Ω_B,0h²(CMB) = 2.226 ± 0.023”.  and their verdict:  “This difference corresponds to a 2σ discrepancy. As discussed by Cooke et al. (2016), there is still some tension between the computed and the empirically measured d(p, γ)³He cross-section that is used as input into the BBN calculations.”  Swapping in the empirical rate gives.  “100 Ω_B,0h²(BBN) = 2.235 ± 0.016 ± 0.033 … This value is in better agreement with the CMB measurement. In the near future, we expect to hear the results of a d(p, γ)³He measurement campaign from the Laboratory for Underground Nuclear Astrophysics (LUNA…)” ↩ ↩ ↩

Pitrou, Cyril et al.  “Precision big bang nucleosynthesis with improved helium-4 predictions.”  Physics Reports 754:1–66.  2018.  A 2018 paper by four French physicists that recalculates the helium-4 prediction of the hot Big Bang, adding corrections for weak interactions and for the plasma of the early universe.  They report a helium-4 mass fraction of 0.24709 ± 0.00017 and provide a Mathematica code for the full calculation.  The article uses it for the lithium problem, which the authors say is unsolved, and for their account of the deuterium data.  Mirror:  arXiv

1. 18a.

   Section Abstract:  “Now that the number of neutrino families and the baryonic densities have been fixed by laboratory measurements or CMB observations, the model has no free parameter and its predictions are rigid.”  Section Conclusion:  Their conclusion on lithium:  “Our predicted lithium abundance remains a factor of ≈3 above the Spite plateau.  The solution of this problem probably involves several mechanisms including stellar depletion and possibly some physics beyond the standard model.” ↩

2. 18b.

   Section II.C:  On the deuterium data:  “Until recently, the distribution of D/H observations showed a significant scatter (see e.g. Pettini and Cooke (2012)).  It allowed Olive et al. (2012) to adopt a weighted mean of D/H = (3.02 ± 0.23) × 10⁻⁵ without excluding an upper limit of D/H = 4 × 10⁻⁵.  This is not possible anymore thanks to the recent new observations or reanalyses of existing data … that now display a plateau as a function of redshift (and metallicity) with a very small scatter.” ↩ ↩

Peebles, P. J. E.  “Primordial Helium Abundance and the Primordial Fireball. II.”  Astrophysical Journal 146:542–552.  1966.  A 1966 calculation of the helium, helium-3 and deuterium that the hot early universe would have made, assuming the new microwave background was its leftover heat at 3 K.  Peebles ran it for two values of the present matter density and for a range of possible changes in the rate of expansion of the early universe.  The article uses it to show that the predicted helium amount moved as the density changed, so the early prediction was a real calculation and not a later fix made to answer critics.

1. 19a.

   “For these models the final helium abundance by mass was found to be 28 per cent if the present mass density is ρ₀ = 1.8 × 10⁻²⁹ gm/cm³, and 26 per cent if ρ₀ = 7 × 10⁻³¹ gm/cm³.”  That is a factor of twenty-six in density for a two-percentage-point change in helium.  The paper's conclusion also states that the observation did not yet exist:  “Apparently a primordial abundance this high cannot yet be ruled out because we do not have a reliable measure of the helium abundance in very old Population II stars.” ↩ ↩

Aver, Erik et al.  “Improving helium abundance determinations with Leo P as a case study.”  JCAP (03):027.  2021.  A measurement paper that refines how astronomers read helium from glowing gas clouds (H II regions) in very metal-poor galaxies, testing the refinements on Leo P, a galaxy with about 3 percent of the sun's metallicity that was observed with the LBT (Large Binocular Telescope).  It cuts the uncertainty in Leo P's helium abundance by about 70 percent and combines the result with other observations to give a primordial helium mass fraction (the share of the early universe's ordinary matter that became helium-4) of 0.2453 ± 0.0034.  The article lists this value in its table of helium measurements as the entry that added Leo P.

1. 20a.

   Section Abstract:  “This result is combined with data from other observations to estimate the primordial helium mass fraction, Y_p = 0.2453 ± 0.0034.” ↩

Matsumoto, Akinori et al.  “EMPRESS. VIII. A New Determination of Primordial He Abundance with Extremely Metal-Poor Galaxies.”  Astrophysical Journal 941:167.  2022.  A 2022 observational study by the EMPRESS team of helium in extremely metal-poor galaxies, using new near-infrared spectra from the Subaru telescope for 10 such galaxies, of which only five gave reliable helium values.  Combined with earlier data for 3 extremely metal-poor and 51 moderately metal-poor galaxies, it gives a primordial helium mass fraction of 0.2370, about one sigma below earlier measurements, and suggests a lepton asymmetry (an excess of some lepton particles over their antiparticles) as one possible resolution of the tensions with the Standard Model.  The article uses it as one of its recent helium values, in its table of helium measurements.

1. 21a.

   Section Abstract:  “we obtain Y_P = 0.2370 (+0.0034/−0.0033) by linear regression in the (He/H) − (O/H) plane.”  They report.  “≳1 − 2σ tensions with the Standard Model and Planck”.  and propose a lepton asymmetry as one resolution. ↩

Lind, K. et al.  “The lithium isotopic ratio in very metal-poor stars.”  Astronomy & Astrophysics 554:A96.  2013.  A 2013 reanalysis by five researchers of the lithium isotope ratio in four very metal-poor halo stars, two of which had earlier reports of lithium-6.  They used realistic three-dimensional model atmospheres and a non-local treatment of how atoms absorb light (NLTE, non-local thermodynamic equilibrium), and found no significant lithium-6 signal in any of the four.  The article uses it as the study that removed the claimed lithium-6 signals.

1. 22a.

   Section Abstract (Results):  “By accounting for NLTE line formation in realistic 3D hydrodynamical model atmospheres, we can model the Li resonance line and other neutral lines with a consistency that is superior to LTE, with no need for additional line asymmetry caused by the presence of ⁶Li.  Contrary to the results from 1D and 3D LTE modelling, no star in our sample has a significant (2σ) detection of the lighter isotope in NLTE.”  The sample is four halo stars, two of which carried published detections. ↩ ↩

2. 22b.

   Section Abstract (Conclusions):  “The observational support for a significant and non-standard ⁶Li production source in the early universe is substantially weakened by our findings.” ↩

Wang, E. X. et al.  “Non-detection of ⁶Li in Spite plateau stars with ESPRESSO.”  MNRAS 509:1521–1535.  2021.  An observing paper that searched for the rare lithium isotope lithium-6 in Spite plateau stars with the ESPRESSO spectrograph and did not detect it.  The article uses it as the observation that closed the lithium-6 question in 2021.  Mirror:  arXiv

1. 23a.

   Section Abstract:  “We do not detect ⁶Li in any of the three stars, and find consistent results between our different methods.  We estimate 2σ upper limits to ⁶Li/⁷Li of 0.7 %, 0.6 %, and 1.7 % respectively for HD 84937, HD 140283, and LP 815-43.  Our results indicate that there is no second cosmological lithium problem, as there is no evidence of ⁶Li in Spite Plateau stars.” ↩ ↩

Korn, Andreas.  “The ups and downs of inferred cosmological lithium.”  EPJ Web of Conferences 297:01007.  2024.  A 2024 conference summary by Andreas Korn of Uppsala University of the stellar side of the cosmological lithium problem, the mismatch between the lithium that stars show and the predicted primordial value.  Korn argues that atomic diffusion, the internal transport of elements inside stars, may be fully responsible for lowering surface lithium to the observed levels, and that inferred lithium-6 abundances in stars have all but disappeared.  The article quotes Korn on lithium-6 to show that the claimed signal has been dropped.

1. 24a.

   Section 3 (Lithium-6: first off the chart, now off the table):  “In summary, the stellar verdict for lithium-6 in connection with BBN is the following:  There is no lithium-6 plateau among warm halo stars.  Consequently, it seems groundless from an observational point of view to discuss lithium-6 in the context of BBN.”  Korn also lists why the 2006 claim was fragile: the effect is subtle, the models did not account for convective line asymmetries, and stellar evolution predicts pre-main-sequence destruction of lithium-6. ↩ ↩

Fields, Brian D., and Keith A. Olive.  “Implications of the non-observation of ⁶Li in halo stars for the primordial ⁷Li problem.”  JCAP (10):078.  2022.  A 2022 theoretical analysis by two astrophysicists of recent searches for lithium-6 in old halo stars, the outer stars of the galaxy, which found only upper limits.  The authors show that those limits fall far below the cosmic-ray predictions, implying that lithium-6 has been destroyed in these stars by factors up to 50.  The article uses it for their argument that an equal amount of lithium-7 destruction would be more than enough to resolve the lithium problem.

1. 25a.

   Section Abstract:  “The tight new ⁶Li upper limits generally fall far below the predictions of cosmic-ray nucleosynthesis, implying that substantial ⁶Li depletion has occurred — by factors up to 50.  We show that in stars with ⁶Li limits and thus lower bounds on ⁶Li depletion, an equal amount of ⁷Li depletion is more than sufficient to resolve the primordial ⁷Li Problem.  In fact, this picture is consistent with stellar models in which ⁷Li is less depleted than ⁶Li, and strengthen the case that the Lithium Problem has an astrophysical solution.” ↩

Howk, J. Christopher et al.  “Observation of interstellar lithium in the low-metallicity Small Magellanic Cloud.”  Nature 489:121–123.  2012.  A 2012 observation by four researchers of lithium in the gas of the Small Magellanic Cloud, a nearby galaxy with a quarter of the Sun's metallicity (its share of elements heavier than helium), made with the 8.2-metre Very Large Telescope.  The lithium in that gas is nearly equal to the Big Bang prediction, while the predicted value is four times the amount measured in the atmospheres of Milky Way halo stars.  The value was superseded by Molaro et al. 2024, on which Howk is a co-author, and the article uses the 2012 paper as the first detection of interstellar lithium beyond the Milky Way.

1. 26a.

   Section Abstract:  “The present-day ⁷Li abundance in the Small Magellanic Cloud is nearly equal to the BBN predictions, severely constraining the amount of possible subsequent enrichment of the gas by stellar and cosmic ray nucleosynthesis.  Our measurements can be reconciled with standard BBN with an extremely fine-tuned depletion of stellar Li with metallicity.”  Their recommended value, stated in the body of the paper:  “Our recommended absolute abundance is A(⁷Li)_SMC = 2.68 ± 0.16, or (⁷Li/H)_SMC = (4.8 ± 1.8) × 10⁻¹⁰.” ↩

Yeh, Tsung-Han et al.  “Probing physics beyond the standard model: limits from BBN and the CMB independently and combined.”  JCAP 10:046.  2022.  A theory paper that tests new physics by combining the light-element limits from big-bang nucleosynthesis (the making of the lightest nuclei in the first seconds to minutes of the universe) with the limits from the cosmic microwave background.  Its joint analysis gives an effective neutrino count of 2.898 plus or minus 0.141, and it says the two limits can be compared to search for changes in the baryon-to-photon ratio between the two epochs.  The article uses it for the test of whether that ratio changed between them.  Mirror:  arXiv

1. 27a.

   Figure 8, panel (b): treating η_BBN and η_CMB as independent quantities and measuring their difference gives Δη₁₀ = 0.095 ± 0.169.  The caption says:  “We see that the best-fit point lies within 1σ of the Standard Cosmology η^CMB = η^BBN shown by the dotted line. … We see the peak lies near the Standard Cosmology Δη = 0 value, and that there are rather tight limits on deviations away from this value.” ↩

Hoyle, F., and R. J. Tayler.  “The Mystery of the Cosmic Helium Abundance.”  Nature 203:1108–1110.  1964.  A 1964 paper in Nature by Hoyle and Tayler that predicted a primordial helium mass fraction of 0.36 ± 0.04.  That value is wrong by almost three of its own error bars against the modern 0.2458 ± 0.0013:  (0.36 − 0.2458) / 0.04 = 2.9.  The article uses it as a prediction offered as a test before the measurement existed, and the measurement did not match it. ↩

1. 28a.

   From Manuel Peimbert, "The Primordial Helium Abundance" (arXiv:0811.2980), reporting Hoyle and Tayler:  “Hoyle & Tayler (13) based on computations of BBN with two families of neutrinos found that Y_P = 0.36 ± 0.04.  They mentioned that this value of Y_P probably is a lower limit of the true value because the number of neutrino families might be larger than two.  They stated that if it is established empirically that the value of Y is considerably smaller than 0.36 in any astronomical object in which there has not been separation of hydrogen and helium by gravitational settling, it can be concluded that the universe did not originate during a big bang.”  This is Peimbert's summary, not Hoyle and Tayler's own words.  The independent confirmation is Wagoner, Fowler & Hoyle 1967, printed p. 4, where Hoyle describes the earlier paper. ↩

Wagoner, Robert V. et al.  “On the Synthesis of Elements at Very High Temperatures.”  Astrophysical Journal 148:3–49.  1967.  A theory paper that works out how light elements could have been made in a hot, expanding universe, and compares the results with abundances measured in the solar system.  The authors find that deuterium (a heavy form of hydrogen), helium-3, helium-4 and lithium-7 are the only nuclei such a universe makes in significant amounts, and that the agreement with solar-system values is reasonable if the present temperature is 3 K.  The authors worked at Caltech and Cambridge, and the article uses it for the 1967 predictions of helium-4 and lithium-7.

1. 29a.

   Section §X, Conclusion 1, page 42:  “The mass fraction of He⁴ produced lies between 0.2 and 0.3 for the universal fireball (assuming T₀ = 3° K), but can be higher in a massive object.  It is therefore of great importance to determine helium concentrations in different astronomical bodies.  A confirmation of X(He⁴) ≈ 0.4 for B stars and for some planetary nebulae could point toward massive objects as the site of origin for the helium.  On the other hand, if it could be shown that X(He⁴) is always close to 0.27, this would be evidence favorable to a universal fireball.” ↩

2. 29b.

   Page 24:  Their best-fit comparison table: computed He⁴ 0.25 against a solar-system 0.27; computed Li⁷ 3 × 10⁻¹⁰ against an observed 10⁻⁸, an under-prediction by a factor of about 33, the opposite sign to the modern lithium problem. ↩ ↩

Hebert, Jake.  “Astronomy Magazine: Big Bang in Crisis?”  Creation Science Update.  Institute for Creation Research.  May 21, 2020.  A 2020 commentary by Jake Hebert, Ph.D., of the Institute for Creation Research, on a May 2020 Astronomy magazine article that asks whether the Big Bang is in crisis.  The commentary argues that the Big Bang's success in matching the hydrogen and helium abundances is less impressive than it first seems.  The article quotes it as the creationist description of the Big Bang's adjustable parameter.

1. 30a.

   “The Big Bang model has an adjustable parameter, like a tuning knob on a radio, that theoreticians can adjust to ensure that the Big Bang produces the amounts of hydrogen and helium necessary to match observations.”  The footnote the commentary attaches to that sentence names the knob:  “This adjustable parameter is called the baryon-to-photon ratio.” ↩

Faulkner, Danny R.  The Expanse of Heaven: Where Creation and Astronomy Intersect.  Master Books.  2017.  A popular book on astronomy and the Bible by a young-earth astronomer.  Chapter 10 surveys modern cosmology and argues that the big bang's claimed successes, the microwave background and the light-element abundances, were constraints fitted into the model rather than predictions made by it.  It is the best-credentialed young-earth statement of the retrofit charge answered here.

1. 31a.

   Chapter 10, section Changes in the Big Bang Model:  “A common claim is that the big bang model correctly predicts the abundances of these isotopes, and since the measured abundances of those isotopes agree with the prediction, this is further proof of the big bang model. However, the abundances of the light elements were known prior to the prediction of the model. In reality, the measured abundances of these isotopes constrained the physical conditions within the first three minutes of the big bang. Hence, these isotopic abundances were not a prediction of the model but rather were constraints placed on the model.” ↩

Alpher, R. A. et al.  “Physical Conditions in the Initial Stages of the Expanding Universe.”  Physical Review 92:1347–1361.  1953.  A 1953 theoretical calculation of the first minutes of the expanding universe, by three authors.  It asks what would happen if all the neutrons available at the start of element-making went into helium nuclei, and it gives a hydrogen-to-helium ratio of about 7:1 to 10:1 for the range of proton-neutron ratios it computes.  The article uses it as the early predicted helium value, and to show that the observations of the day spanned a much wider range than the calculation did.

1. 32a.

   “It is interesting to note that if all the neutrons available at the start of element synthesis were used in making helium nuclei only, then the ratio of hydrogen to helium abundances corresponding to the range of proton-neutron ratios computed above would be from ~7:1 to ~10:1. … These values are consistent with the range of values obtained from astronomical data, viz., ~5:1 to ~30:1 as found in planetary nebulae, stellar atmospheres, and theoretical stellar models.”  Converted to helium mass fraction, the 7:1 to 10:1 ratio is 0.36 down to 0.29, and their observational range of 5:1 to 30:1 is 0.44 down to 0.12.  Section Abstract:  Their abstract also claims:  “The numerical results are unique in that they involve no disposable parameters which would affect the time dependence of pressure, temperature, and density.” ↩ ↩ ↩

Henry, Jonathan.  “The elements of the universe point to creation: introduction to a critique of nucleosynthesis theory.”  Journal of Creation 20(2):53–60.  Aug 2006.  A 2006 essay by the creationist Jonathan Henry arguing that nucleosynthesis theory, the account of how the elements formed, has not predicted the cosmic hydrogen-helium ratio or the microwave background temperature, and that those predictions were retrodictions, meaning predictions made after the fact.  It was reposted on creation.com on 28 March 2008, and it is often misattributed to the physicist John Hartnett; the byline is Henry's.  The article quotes its deuterium sentence and checks the two references Henry gives for it.

1. 33a.

   “The interstellar medium and the intergalactic medium have D/H abundance ratios that do not fit into conventional NST.”  "NST" is Henry's abbreviation for nucleosynthesis theory, defined earlier in the article.  The sentence sits in a devotional passage about the uniformity of the elements; the next sentence is "Indeed, God has named each star (Psalm 147:4); a fact suggesting that perhaps each one is truly unique in some way." ↩

2. 33b.

   The two references attached to that sentence are Henry's notes 23 and 24: "Henry, J., Heliosiesmology: implications for the standard solar model, CRSQ 40(1):34-40, 2003; p. 36" — a self-citation about the sun, in the Creation Research Society Quarterly — and "Shull, J., Intergalactic pollution, Nature 394:17-18, 1998; p. 17," a two-page News & Views commentary.  Neither is a deuterium measurement.  (The misspelling "Heliosiesmology" is in creation.com's reference list.) ↩

3. 33c.

   “A significant consequence of sizing the baryon-to-photon ratio by recourse to big bang theory is that the density of the universe works out to be about two orders of magnitude less than that required for closure, i.e. long-term 'stability'.  This putative density deficiency has led to the claim that dark matter must exist to provide the closure which visible matter does not.”  Henry continues:  “Thus the belief in dark matter is at least partly due to retro-fitting big bang theory to the observed H/He cosmic abundance ratio.”  The supporting reference is Burbidge, Hoyle and Narlikar's 1999 Physics Today advocacy piece for the steady-state model. ↩

Mitchell, William C.  “The Big Bang Theory Under Fire.”  Physics Essays 10(2).  Jun 1997.  A critical essay that lists what its author sees as problems with the Big Bang theory, including the singularity, the horizon problem, the abundance of the light elements and red-shift anomalies.  The author was a retired engineer writing as a big-bang dissident.  The essay's reference list identifies the author as the writer of The Cult of the Big Bang (Cosmic Sense Books, 1995), the author's own imprint.  The article uses it for the claim that helium predictions were adjusted to fit the data, and for the older universe that the author offers in place of the Big Bang.

1. 34a.

   Section 9, Source of Light Elements?:  “The study of historical data shows that over the years predictions of the ratio of helium to hydrogen in a Big Bang universe have been repeatedly adjusted to agree with the latest available estimates of that ratio as observed in the real universe.  (Human science is very fallible!)  The estimated ratio is dependent on a ratio of baryons to photons (the baryon number) that has also been arbitrarily adjusted to agree with the currently established helium to hydrogen ratio.  These appear to have not been predictions, but merely adjustments of theory ('retrodictions') to accommodate current data.” ↩

2. 34b.

   Section 9:  The next paragraph of the same section names the author's alternative:  “If, for example, another cosmology should suggest that helium has accumulated as a result of other processes (37,38) (such as stellar nucleosynthesis over tens of billions of years)…” ↩

Searle, L., and W. L. W. Sargent.  “Inferences from the Composition of Two Dwarf Blue Galaxies.”  Astrophysical Journal 173:25–33.  1972.  A 1972 analysis of the light from two small, compact galaxies, I Zw 18 and II Zw 40, measuring the oxygen, neon and helium in their glowing gas.  The authors found oxygen and neon low, compared with the gas near the Sun, and helium normal, which they took as evidence that the helium is primordial.  The article uses it to show that in 1972 the authors still called earlier attempts to measure primordial helium a failure.

1. 35a.

   Section V.c, Regarding the Primordial Helium Abundance:  “In our view the attempt to do this by analyzing the photospheres of halo stars has failed because of the discovery that the compositions of these photospheres are quite exotic and hard to accept as being primordial.  Analyses of the composition of halo planetary nebulae are also difficult to interpret because of the possibility that the ejected envelope is contaminated by the products of nuclear burning within these highly evolved stars.”  Section Abstract:  Their own result, from the abstract:  “Oxygen and neon have lower abundances (relative to hydrogen) than does the interstellar gas near the Sun, while helium has a normal abundance. … the normal helium abundance is taken as evidence that this abundance is primordial.”  Their He/H = 0.1 by number is Y ≈ 0.286 by mass. ↩

Peimbert, M., and S. Torres-Peimbert.  “Chemical Composition of H II Regions in the Large Magellanic Cloud and Its Cosmological Implications.”  Astrophysical Journal 193:327–333.  1974.  A 1974 measurement of the helium and hydrogen in H II regions, which are glowing clouds of ionized gas, in the Large Magellanic Cloud.  The authors used a spectrophotometer on four such regions and combined the results with those from other galaxies to estimate the original helium amount.  The article uses it because the authors took Wagoner's theoretical curves as fixed and read the density of the universe off them, so the theory came first.

1. 36a.

   Section Abstract:  “From the chemical composition of H II regions in our Galaxy and other galaxies it is found that the primeval value of A(He)/A(H) is 0.069 ± 0.008 (Y = 0.216 ± 0.02) and that the chemical evolution of galaxies is characterized by ΔY ~ 3.3 ΔZ.”  The direction of inference:  “From the big-bang computations by Wagoner for no neutrino degeneracy we obtain for the present density of the Universe, −31.41 < log ρ₀ < −30.6.”  Section Introduction:  Their introduction records how loose the pre-existing measurements were:  “The results derived from studies of H II regions in our Galaxy and other galaxies have led to a general value of N(He)/N(H) = 0.10 ± 0.02”.  a range spanning Y = 0.24 to 0.32. ↩

Thomas, Brian.  “Big Bang Fizzles under Lithium Test.”  Creation Science Update, Institute for Creation Research.  Sep 22, 2014.  A 2014 article by Brian Thomas, who holds a Ph.D. and writes for the Institute for Creation Research, about an experiment at the LUNA underground accelerator in Italy.  The experiment fired helium nuclei at deuterium nuclei to make lithium-6 under conditions meant to copy the early Big Bang, and Thomas reports that the result matched the predicted ratio.  The article uses it because it states the lithium-6 and lithium-7 claims that the article corrects, and because it credits its headline to a real experiment.

1. 37a.

   “no historical evidence corroborates this primordial nucleosynthesis, an idea beset by a theoretical barrier called the 'lithium problem.'” ↩

2. 37b.

   “Put simply, the universe has way too much lithium-6 than the Big Bang could produce.” ↩

3. 37c.

   “the areas of outer space that secularists associate with that early time show at best only half the predicted amounts of lithium-7.” ↩

4. 37d.

   “Unfortunately for Big Bang theorists, their experiment succeeded.  The details, published in Physical Review Letters, demonstrated that if lithium actually formed by some primordial nucleosynthesis, it should indeed have formed in the predicted ratio.” ↩

Anders, M. et al.  “First Direct Measurement of the ²H(α,γ)⁶Li Cross Section at Big Bang Energies and the Primordial Lithium Problem.”  Physical Review Letters 113:042501.  2014.  A laboratory experiment by the LUNA (Laboratory for Underground Nuclear Astrophysics) collaboration, run deep underground at Gran Sasso in Italy.  It made the first measurement of the cross section, the measure of how likely a nuclear reaction is, for deuterium and helium-4 to join into lithium-6 at early-universe energies, and it found a primordial lithium-6 to lithium-7 ratio of (1.5 ± 0.3) × 10⁻⁵ from its data and standard Big Bang theory.  The article cites it because even this paper hedges on the lithium-6 claims in its own introduction.

1. 38a.

   Section Introduction, pages 042501–1:  “Recently, many of the claimed ⁶Li detections have been debated [9] but for a few metal-poor stars a significant excess of ⁶Li has been confirmed.”  Section Abstract:  Their measured result, from the abstract:  “The primordial ⁶Li/⁷Li isotopic abundance ratio has been determined to be (1.5 ± 0.3) × 10⁻⁵, from our experimental data and standard BBN theory.”  Section Introduction:  The same introduction states the ⁷Li deficit as:  “a factor 2-4.” ↩

Humphreys, D. Russell.  “Origin of the elements — Bible vs the big bang.”  Creation Ministries International.  Aug 28, 2012.  A reader-feedback article in which the creationist physicist Russell Humphreys answers a reader's question about where the heavy elements came from.  Humphreys argues that Scripture answers the question, and that God made at least some heavy elements directly, so the naturalistic answer is not needed.  The site's byline misspells the surname as Humphries.  The article quotes it as a creationist answer to the heavy-element question.

1. 39a.

   “I don't feel compelled to explain the existence of heavy elements by some semi-naturalistic nucleosynthesis process.  God may have done that for some of the heavy elements, but He definitely didn't make all of them that way.”  Earlier in the same reply, Humphreys notes the terminology:  “to astronomers and astrophysicists, a 'heavy' element is any element heavier than beryllium or lithium, because the alleged Big Bang is not supposed to have been able to produce anything heavier than that.” ↩

Peebles, P. J. E.  “How Physical Cosmology Grew.”  Nobel Lecture.  2019.  The 2019 Nobel lecture in which the Princeton cosmologist tells how the field grew, beginning with the author's own work on the large-scale universe from 1964, under Robert Dicke.  The article uses it because a Nobel laureate on the standard side states the strongest form of the objection to extrapolating physics from the lab and the solar system to the scale of the whole universe.

1. 40a.

   “The BAO theory assumes standard physics, including the general theory of relativity.  That is an extrapolation from the tests in the solar system and smaller, on scales ≳ 10¹³ cm, to the scales of cosmology, ~10²⁸ cm.  Would you be inclined to trust an extrapolation of fifteen orders of magnitude?” ↩

Peebles, P. J. E.  “Discovery of the hot Big Bang: What happened in 1948.”  European Physical Journal H 39:205–223.  2014.  A close reading by a Princeton cosmologist of the eleven publications from 1948 that first discussed the sea of thermal radiation.  The author shows that the best-known paper of that year, by Alpher, Bethe and Gamow, assumed a cold Big Bang and never mentions thermal radiation.  The article uses it to show that this famous paper did not predict helium, which is a common myth.  Mirror:  arXiv

1. 41a.

   Page 3:  Page 3 of the arXiv preprint version.  “Alpher, Bethe, and Gamow (1948) assume a cold Big Bang cosmology, and it makes no mention of thermal radiation.  Also, the picture in this paper is physically inconsistent.  The inconsistency was resolved later that year by the proposal that elements formed in the early universe in a sea of thermal radiation.” ↩

Ross, Hugh.  The Creator and the Cosmos: How the Greatest Scientific Discoveries of the Century Reveal God.  NavPress.  3rd edition.  2001.  A popular book by an astronomer who accepts the big bang and an old universe and argues that its beginning points to a Creator.  Chapter 5 counts the helium, deuterium and lithium abundances, and the baryon density they imply, among the evidences for that beginning.  It shows how Christians who accept the timescale use the evidence this article weighs, and it was written before the 2003 WMAP results that exposed the lithium problem.

1. 42a.

   Chapter 5, section Deuterium and Lithium Abundances:  “In their words, the deuterium and lithium abundances fit the big bang predictions “extremely well.””  Section Density of Protons and Neutrons:  “These independent confirmations of the cosmic baryon density deduced from primordial helium, deuterium, and lithium abundances give yet more evidence for a big bang creation event.” ↩ ↩