The Lithium Problem: BBN's One Unresolved Discrepancy

Big Bang nucleosynthesis is one of the most precise quantitative predictions of cosmology. The light-element abundances forged in the first three minutes after the Big Bang are calculated from a small set of well-measured inputs — the baryon-to-photon ratio from the CMB, the standard nuclear reaction rates, and the expansion rate at the relevant temperatures — and the resulting predictions for helium-4 and deuterium have stood up to forty years of increasingly precise observational tests. The agreement is remarkable: the helium-4 mass fraction $Y_p=0.245$ matches the observed value to within $\sim 1\%$, and the deuterium-to-hydrogen ratio $D/H=2.5\times 10^{-5}$ matches to within $\sim 5\%$.

The single significant exception is lithium-7. The BBN-predicted primordial ${}^7$Li abundance is approximately $(4\text{–}5)\times 10^{-10}$ relative to hydrogen. The observed abundance, inferred from spectroscopy of the atmospheres of the oldest, most metal-poor stars in our galaxy, is approximately $(1.6\text{–}1.8)\times 10^{-10}$. The factor-of-three discrepancy, dubbed the lithium problem, has been one of the most persistent unresolved anomalies in observational cosmology since it was first identified in the late 1980s.

This post is about the lithium problem in detail: what BBN predicts, what stars actually show, and the three leading categories of explanation that the field has been pursuing for decades.

What BBN says

Lithium-7 in BBN is produced through several reaction chains, depending on the baryon density. At the actual baryon density measured by Planck, the dominant production route is the beryllium pathway:

${}^3\mathrm{He}+{}^4\mathrm{He}\to {}^7\mathrm{Be}+\gamma$

with the beryllium-7 produced cosmologically later decaying through electron capture to lithium-7 once neutral atoms form during recombination:

${}^7\mathrm{Be}+e^{-}\to {}^7\mathrm{Li}+{\nu }_e$

(half-life 53 days). The competing direct lithium production:

${}^3\mathrm{H}+{}^4\mathrm{He}\to {}^7\mathrm{Li}+\gamma$

is sub-dominant because the tritium abundance is small.

The relevant nuclear reaction rates are measured in dedicated laboratory experiments at the keV-to-MeV energies that correspond to BBN temperatures. Recent precision measurements at LUNA (Laboratory for Underground Nuclear Astrophysics) at LNGS have refined the key cross-sections to a few-percent precision. Folding these inputs into a BBN code such as PArthENoPE or AlterBBN gives a prediction

${}^7\mathrm{Li}/\mathrm{H}{|}_{\mathrm{BBN}}=(4.5\pm 0.5)\times 10^{-10}$

at the Planck-measured baryon density. The quoted uncertainty is dominated by the nuclear reaction rates.

What the stars say

Primordial lithium is observed indirectly through the atmospheres of the oldest stars in the Milky Way. The relevant stars are metal-poor halo stars with metallicities (iron abundance relative to solar) less than about $[Fe/H]=-2$ — the lowest metallicities found in our Galaxy, corresponding to stars formed within the first billion years of cosmic history before substantial heavy-element production.

In the 1980s, Monique Spite and François Spite discovered that these old stars all show essentially the same lithium-7 abundance, independent of metallicity — the so-called Spite plateau at approximately

$A(\mathrm{Li})={\log }_{10}(\mathrm{Li}/\mathrm{H})+12=2.2$

corresponding to ${}^7$Li/H $\approx 1.6\times 10^{-10}$. The flatness of the plateau across many orders of magnitude in metallicity was originally taken to mean that these stars preserve the primordial lithium abundance unchanged — that the observed value is the BBN value.

That interpretation produced an immediate problem when more precise BBN calculations (and later, precise Planck baryon-density measurements) gave the higher value $4.5\times 10^{-10}$. The factor-of-three discrepancy is the lithium problem.

The discrepancy is highly statistically significant. The BBN prediction has $\sim 10\%$ uncertainty, the stellar observations have $\sim 10\%$ uncertainty, and the central values differ by a factor of three. Random observational error cannot account for the gap. Either BBN is wrong, the stars do not preserve the primordial abundance, or some systematic in interpreting the stellar data is missed.

Stellar destruction: the leading explanation

The most widely-favoured explanation is that lithium is destroyed in the surface convection zones of metal-poor stars over their long lifetimes.

Lithium-7 is destroyed by proton capture at temperatures above about $2.5\times 10^6$ K through the reaction

${}^7\mathrm{Li}+p\to {}^4\mathrm{He}+{}^4\mathrm{He}$

In a low-mass main-sequence star, the surface convection zone descends to a depth where the temperature is just below this destruction temperature. Any lithium that is mixed below the convection zone reaches hotter material and is destroyed. If the mixing extends a bit deeper than the simplest 1D models predict, lithium destruction proceeds over the multi-billion-year main-sequence lifetime of the star.

Several specific mechanisms can produce this enhanced mixing:

Atomic diffusion: gravitational settling of heavy ions in the radiative zone below the convection zone, which slowly depletes the convection zone of lithium over Gyr timescales. The standard 1D stellar-evolution calculation including atomic diffusion predicts depletion factors of roughly 2-3, accounting for most or all of the BBN-Spite gap.

Rotational mixing: angular-momentum-driven circulation that brings lithium from the convection zone to deeper, hotter layers where it is destroyed. The rotation rates required to produce the observed depletion are consistent with the spin-down history of metal-poor stars.

Convective overshoot: turbulent extension of the convection zone slightly past its formal boundary, exposing lithium to higher-temperature material. The amount of overshoot required is small but non-zero.

Most modern stellar-evolution models include these processes and predict primordial lithium of $A(\mathrm{Li})\approx 2.7$ — approximately the BBN value — at the time of formation, with depletion to the observed $A(\mathrm{Li})\approx 2.2$ over the star’s lifetime.

The most powerful test of this picture has been observations of globular cluster turn-off stars, which sample stars of slightly different masses at the same age. The lithium abundance shows a clear mass-dependent trend that fits the depletion prediction. Newer observations of metal-poor stars across a wide age and mass range have continued to support the stellar-depletion picture.

Nuclear-physics revisions

A second category of explanation considers whether the nuclear reaction rates used in BBN calculations are systematically biased.

The key reactions for lithium are the beryllium production rate ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ (which sets how much ${}^7$Be is produced and therefore how much ${}^7$Li is left after electron capture), and the lithium destruction rate ${}^7\mathrm{Li}(p,\alpha {)}^4\mathrm{He}$.

Measurements at very low energies — relevant to BBN temperatures around 0.1 MeV — are technically difficult because the Coulomb barrier suppresses the reaction rate exponentially. Most laboratory measurements are done at higher energies and extrapolated to BBN energies using theoretical models of the cross-section’s energy dependence. Errors in this extrapolation can shift the BBN prediction.

Several precision measurements over the past two decades, including dedicated low-energy campaigns at LUNA, have substantially reduced these uncertainties. The current BBN-prediction error is dominated by the ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ rate at the 5-10% level. Even with conservative uncertainty estimates, the BBN prediction sits at $A(\mathrm{Li})\approx 2.7\pm 0.05$, still substantially above the Spite plateau at 2.2.

The nuclear-physics explanation is therefore unable to account for the full discrepancy on its own, although improved reaction rates may marginally tighten the central values.

New-physics scenarios

The third category of explanation invokes beyond-Standard-Model physics that specifically affects lithium during BBN.

Late-decaying massive particles introduced to the early universe at temperatures around the BBN epoch can produce non-equilibrium effects. If a heavy relic particle decays into hadrons or electromagnetic radiation around the time when ${}^7$Be is being produced, the resulting reactions can deplete ${}^7$Be (and consequently ${}^7$Li) without affecting deuterium or helium-4 substantially. This scenario predicts specific signatures in other light-element abundances that have not been observed, constraining but not eliminating the parameter space.

Modified neutrino-sector physics that affects only the relevant epoch — for example, a small departure from the standard $N_{\mathrm{eff}}=3$ during just the ${}^7$Be-formation window — could in principle produce the observed shift. However, such tuned scenarios are theoretically unmotivated and require fine-tuning.

Variation of fundamental constants during the BBN epoch — particularly the strong coupling constant or the deuteron binding energy — could produce specific shifts in nuclear reaction rates, but the same shifts would generically affect deuterium and helium-4 abundances as well, producing tensions elsewhere.

None of these new-physics explanations has been definitively confirmed or excluded by the available data. The general consensus is that new physics is less attractive than the stellar-destruction explanation, but it remains a possible alternative.

The lithium-6 sub-problem

A separate observational claim from the 2000s involved lithium-6, an isotope that BBN produces at negligible levels (about $10^{-14}$ relative to hydrogen) but that some authors reported at observable levels (about $10^{-12}$) in some metal-poor stars. If correct, this would have been an even more striking anomaly than the lithium-7 problem.

Subsequent reanalyses, however, have shown that the apparent lithium-6 signal in stellar spectra is largely an artefact of asymmetric line shapes in the convective atmospheres of these stars. Modern 3D non-LTE stellar atmosphere modelling produces line shapes that exactly mimic what was once interpreted as lithium-6 absorption. The lithium-6 detections are now generally considered to be observational artefacts, and the lithium-6 sub-problem has been substantially resolved.

The lithium-7 problem itself remains unresolved.

Where this leaves the field

The current consensus is that stellar destruction is the most likely explanation, accounting for most or all of the BBN-Spite discrepancy through atomic diffusion plus rotational mixing in metal-poor stars over their lifetimes. The most detailed modern stellar-evolution calculations are quantitatively consistent with this picture and predict depletion factors that close the BBN-observation gap to within the combined uncertainties.

But the explanation is not yet fully confirmed. Direct observation of the primordial lithium abundance — independent of any stellar-evolution model — is essentially impossible: lithium has no equivalent of the deuterium Lyman-alpha absorption-line technique that provides a clean cosmological probe. The Spite plateau in metal-poor stars is the only available observational handle, and inferring the primordial value from it requires explicit stellar-evolution modelling.

Several upcoming observational programmes will help. WEAVE and 4MOST survey spectrographs will produce large samples of metal-poor stars at higher precision than current surveys. High-resolution spectroscopy of metal-poor stars in dwarf-galaxy satellites of the Milky Way will provide tests of whether the Spite plateau depends on host-galaxy properties as the stellar-destruction scenario would predict. Improved 3D non-LTE atmosphere models will refine the inferred lithium abundances from the observed spectra.

If these efforts continue to be consistent with stellar depletion as the explanation, the lithium problem will eventually fade as a clearly-explained but observationally subtle phenomenon. If they continue to show tensions, the new-physics alternatives will receive renewed attention.

Why it matters for neutrino cosmology

The lithium problem sits in a broader context where BBN provides one of the cleanest probes of early-universe physics. The agreement of helium-4 and deuterium with their predictions has constrained the effective number of neutrino species to $N_{\mathrm{eff}}^{\mathrm{BBN}}=2.86\pm 0.15$, fully consistent with three flavors. The lithium discrepancy must therefore not require a substantial modification of the neutrino sector — any new physics that resolves lithium must leave helium-4 and deuterium essentially intact.

This is part of why the stellar-destruction explanation is so widely favoured: it preserves the entire BBN framework while accounting for the one stubborn discrepancy through processes happening after the universe finished synthesising the light elements. The alternative explanations require BBN-epoch new physics that affects only one isotope, which is harder to construct without fine-tuning.

Summary

The lithium problem is a factor-of-three discrepancy between the BBN-predicted primordial ${}^7$Li/H ratio of approximately $4.5\times 10^{-10}$ and the observed abundance in the atmospheres of the oldest, most metal-poor stars at approximately $1.6\times 10^{-10}$ — the Spite plateau. The discrepancy has been one of the most persistent unresolved anomalies in observational cosmology since the late 1980s. The leading explanation is stellar destruction: lithium is depleted in the surface convection zones of metal-poor stars over their multi-billion-year lifetimes through atomic diffusion, rotational mixing, and convective overshoot, bringing the primordial value down to the observed Spite plateau. Modern 1D-and-3D stellar-evolution models that include these processes are quantitatively consistent with the observed depletion. Alternative explanations involving revised nuclear reaction rates or new physics during the BBN epoch remain on the table but are less favoured. The reported lithium-6 anomaly has been substantially resolved as a 3D non-LTE atmosphere artefact. The lithium-7 problem remains the one significant unresolved BBN discrepancy and represents a quiet but persistent reminder that even one of cosmology’s best-tested frameworks contains a corner where the standard picture does not yet quite agree with observations.