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The main abundance parameter is the baryon-to-photon ratio $\eta =n_B/n_{\gamma }$, often expressed as ${\eta }_{10}=10^{10}\eta$. For the measured mean cosmic microwave background temperature, ${\eta }_{10}\simeq 274{\Omega }_b{h}^2$. Standard Big Bang nucleosynthesis also depends on the expansion rate, the effective number of neutrino species, the neutron lifetime and the nuclear reaction rates.

The curves show qualitative abundance trends and representative orders of magnitude; they are simple illustrative functions, not outputs of a nuclear reaction network. Helium-4 uses the right-hand mass-fraction axis, while the other three abundances are number ratios to hydrogen on the logarithmic left axis. The lithium valley and its rising high-density branch are important and must not be replaced by a monotone curve.

At higher $\eta$, two-body reactions proceed more rapidly relative to cosmic expansion and burn deuterium more efficiently, so D/H falls strongly, approximately as ${\eta }^{-1.6}$ near the favored density. Helium-3 decreases more gently. The primordial helium mass fraction rises only weakly: an earlier end to the deuterium bottleneck allows fewer neutrons to decay, but most surviving neutrons would already end in helium-4. Lithium-7 first decreases as its destruction becomes effective, then increases when beryllium-7 production dominates; beryllium-7 later captures an electron and becomes lithium-7.

A faster expansion changes both freeze-out and the time available for reactions. In units $\hslash =c=k_B=1$, weak neutron–proton conversion has rate ${\Gamma }_w\propto G_F^2{T}^5$, whereas $H\propto \sqrt{g_{\ast }}{T}^2/M_{\mathrm{Pl}}$; consequently $T_f\propto g_{\ast }^{1/6}$. Since the equilibrium neutron-to-proton ratio is $e^{-(m_n-m_p)/T_f}$, additional radiation raises it; the shorter subsequent decay interval also raises $Y_p$. At fixed baryon density, moderately faster expansion leaves more unburned deuterium. A longer neutron lifetime similarly increases neutron survival. These trends assume ordinary efficient burning and no independent modifications of the nuclear or weak rates.

Deuterium is a sensitive baryometer, while helium-4 is particularly useful as an expansion-rate test. Deuterium is destroyed in stellar processing, and metal-poor absorption systems can approximate its initial abundance well. Helium's weak dependence on $\eta$ limits its precision as a baryometer, and its spectroscopic corrections matter. Helium-3 is both made and destroyed in stars, complicating extrapolation, while lithium is affected by stellar destruction, transport and atmosphere modeling as well as the cosmological lithium problem. Accurate comparisons therefore require nuclear-rate and astrophysical uncertainties, not merely narrow instrumental error bars. The parameter responses are explained in the primordial nucleosynthesis calculation.

The primordial light-element abundance determination uses minimally processed material and estimates its residual processing rather than directly observing the universe at a few minutes old.

For deuterium, high-redshift, low-metallicity quasar absorption systems resolve isotope-shifted D I lines from the H I Lyman series. The deuterium feature is displaced by about $82{\mathrm{km}\mathrm{s}}^{-1}$ from hydrogen; fitting several transitions and the velocity components distinguishes genuine deuterium from an unrelated hydrogen blend. The ratio of the inferred columns estimates D/H after the ionization and component structure are checked. Low metallicity minimizes stellar destruction, giving a representative primordial ratio of roughly $(2.5\text{–}3)\times 10^{-5}$.

For helium-4, helium and hydrogen recombination-emission lines in metal-poor H II regions of nearby dwarf galaxies give a mass fraction. Several lines constrain temperature, electron number density and corrections for collisional excitation, ionization structure, radiative transfer and underlying stellar absorption. Extrapolation of helium enrichment against metallicity towards zero metallicity estimates $Y_p$, approximately $0.24$–$0.25$, corresponding to helium/hydrogen by number near $0.08$.

For helium-3, the approximately $8.665$ GHz hyperfine line of ${}^3{\mathrm{He}}^{+}$ in Galactic H II regions probes the abundance, with ionization and nebular structure corrections. Stellar production and destruction make its primordial value hard to extract; a characteristic abundance near $10^{-5}$ relative to hydrogen is compatible with standard nucleosynthesis but is not a comparably clean primordial measurement.

For lithium-7, the approximately $6708$ Å Li I absorption doublet in warm, old, metal-poor halo stars gives a photospheric abundance after stellar-atmosphere and effective-temperature corrections. The Spite plateau suggests an initial number ratio of order $(1\text{–}2)\times 10^{-10}$ if depletion is small; transport below the photosphere, nuclear destruction and atmosphere systematics can lower the measured value relative to the birth abundance. Standard Big Bang nucleosynthesis at the deuterium- and microwave-background-favored baryon density instead predicts several $10^{-10}$, roughly $(4\text{–}5)\times 10^{-10}$ in exam-era calculations. This discrepancy is the cosmological lithium problem, not a measurement of an independently adjustable primordial lithium parameter.

The approximate values deliberately represent exam-era orders of magnitude rather than a claim of current precision; the contemporary abundance assessment discusses the inference and tensions.

True as a major quantitative test of the hot Big Bang, with a significant lithium qualification. Big Bang nucleosynthesis predicts several abundances from one main baryon-density parameter using measured nuclear and weak rates, rather than fitting a separate primordial composition for every species. Comparisons involve distinct observing environments and an independent cosmic microwave background determination at a much later epoch. Their overall agreement is powerful; it is not a claim that every light-element measurement is mutually consistent without stellar or observational corrections. The cosmological lithium problem must be included in that assessment.

In standard Big Bang nucleosynthesis, with the radiation content and reaction rates fixed, the main adjustable abundance parameter is the baryon-to-photon ratio $\eta$. The baryon-density consistency between nucleosynthesis and the microwave background usesIncreasing cosmological baryon density makes deuterium burn more efficiently, so D/H falls steeply. The primordial helium mass fraction grows only slowly, because its dominant control is the surviving neutron fraction. Near the observationally favored density, lithium-7 production, much of it initially as beryllium-7, rises with density. At lower densities the full lithium curve has a valley; the sketch focuses on the branch relevant to the baryon-density comparison.

For the historical meaning of “current” in this 2008 paper, representative 2007–2008 fits near ${\eta }_{10}\simeq 6$ areThese local fits, with nuclear-rate uncertainties, and representative D/H and lithium ranges are documented in Steigman's 2007 nucleosynthesis analysis. They are not a replacement for a nuclear network outside their calibrated range.

The cosmic microwave background acoustic peak pattern measures baryon loading at recombination, independently of the abundance measurements. For example, the five-year WMAP cosmological analysis gives ${\Omega }_{b,0}{h}^2=0.02273\pm 0.00062$ from WMAP alone, corresponding to ${\eta }_{10}\simeq 6.23\pm 0.17$. For $h\simeq 0.7$, this is ${\Omega }_{b,0}\simeq 0.046$. Galaxy-cluster baryon fractions combined with independent total-matter density provide another, more astrophysically model-dependent cross-check.

At ${\eta }_{10}\simeq 6.2$, the fitted predictions are D/H $\simeq 2.5\times 10^{-5}$, $Y_p\simeq 0.249$, and ${}^{7}Li/H\simeq 4.6\times 10^{-10}$. A representative observed D/H range around $(2.7\pm 0.3)\times 10^{-5}$ overlaps the prediction; its inferred density ${\eta }_{10}\simeq 6.0\pm 0.4$ is compatible with the cosmic microwave background. The helium result $Y_p=0.2477\pm 0.0029$ from the 2007 helium analysis also agrees. Other helium analyses had lower central values, illustrating why ionization and temperature systematics matter.

In contrast, a representative plateau estimate $12+{\log }_{10}({}^{7}Li/H)\simeq 2.1\pm 0.1$ corresponds to roughly $(1.0$–$1.6)\times 10^{-10}$, a factor of several below the prediction at the same density. This is the cosmological lithium problem. The three abundance ranges therefore should not all be described as exact simultaneous agreement: deuterium and helium broadly support the independently measured baryon density, while lithium has a substantial discrepancy. The plotted ranges explicitly refer to the 2007–2008 comparison, not present-day parameter estimates.

The agreement of the main light-element abundances with a hot early nuclear-burning phase, and the independent baryon-density consistency between nucleosynthesis and the microwave background, gives strong support to the hot Big Bang framework. These measurements connect the first minutes to recombination, despite their very different temperatures, densities and observables. In particular, the large primordial helium mass fraction and residual deuterium are natural outputs of Big Bang nucleosynthesis, rather than arbitrary products of subsequent star formation.

The cosmological lithium problem prevents claiming that the simplest abundance calculation explains every observation without qualification. One must distinguish nuclear-rate uncertainties, stellar depletion, atmosphere and abundance systematics, and possible new particle physics. Thus the broad hot Big Bang framework is strongly supported, while lithium tests the completeness of its simplest nucleosynthesis and stellar-abundance interpretation. An unresolved lithium discrepancy alone does not erase the independent successes of deuterium, helium and the cosmic microwave background.