The Lithium Problem

Big Bang Nucleosynthesis is one of the great triumphs of the hot Big Bang model: with a single free parameter — the baryon-to-photon ratio $\eta$ , equivalently the physical baryon density $\Omega_b h^2$ — it predicts the primordial abundances of $^2$ H, $^3$ He, $^4$ He, and $^7$ Li across nine orders of magnitude. When the cosmic microwave background independently fixes $\Omega_b h^2 = 0.0224$ , the predicted deuterium and helium abundances match the data beautifully, closing what once was a fitted parameter into a measured one. Lithium-7 is the sole holdout: the standard prediction overshoots the abundance seen in old stars by roughly a factor of three. That stubborn gap is the lithium problem, and it has outlived four decades of attempts to close it. The observational anchor is the Spite plateau. In 1982 François and Monique Spite found that warm, metal-poor halo dwarf stars share a nearly constant surface lithium abundance, almost independent of both metallicity and temperature. Because lithium is fragile — it burns at only $2.5\times10^6\,\mathrm{K}$ , far below a star's core — the flatness was read as a fingerprint of the pristine primordial value, preserved on the stellar surface. The theory side is subtler than it looks: at the CMB baryon density most mass-7 is not synthesised as $^7$ Li at all but as $^7$ Be, which only much later captures an electron and becomes lithium. So the "lithium" prediction is really beryllium physics. This article traces the CMB-fixed baryon density through the mass-7 reaction network, quantifies the discrepancy in both linear and logarithmic measure, shows why retuning $\eta$ cannot rescue it without breaking deuterium, and surveys the three live escape routes — stellar depletion, revised nuclear rates, and new physics — each of which must survive the joint light-element constraint.

Key takeaways

Standard BBN, with $\Omega_b h^2 = 0.0224$ fixed by the CMB, predicts a primordial abundance $\mathrm{^7Li/H} = (4.5\pm0.4)\times10^{-10}$ .
Warm metal-poor halo stars show a flat "Spite plateau" at $\mathrm{Li/H}\approx1.6\times10^{-10}$ — a factor $\sim2.8$ , about $0.46$ dex, below the prediction.
The tension is $\sim4\text{–}5\sigma$ and, unlike deuterium and helium, is not resolved by the CMB-determined $\eta$ — that is precisely what makes it a problem.
At the CMB density most mass-7 freezes out as $^7$ Be via $^3\mathrm{He}(\alpha,\gamma)^7\mathrm{Be}$ , later becoming $^7$ Li by electron capture; the yield rises as $\mathrm{^7Li/H}\propto\eta^{2}$ .
Lowering $\eta$ to fix lithium overproduces deuterium ( $\mathrm{D/H}\propto\eta^{-1.6}$ ), so a pure baryon-density shift fails — the abundances must be fit jointly.
Three solution classes remain live: stellar surface depletion, revised nuclear cross-sections, and new physics during or after BBN, none yet decisive.
Key idea: at the CMB-fixed baryon density, standard BBN robustly predicts $\mathrm{^7Li/H}\approx4.5\times10^{-10}$ (dominated by $^7$ Be production and later electron capture), yet the Spite plateau gives $\approx1.6\times10^{-10}$ — a factor- $\sim3$ , $\sim4\text{–}5\sigma$ discrepancy that stands out because deuterium and helium agree.

The core insight

At the CMB-fixed baryon density, standard BBN robustly predicts $\mathrm{^7Li/H}\approx 4.5\times10^{-10}$ (dominated by $^7$ Be production and later electron capture), yet the Spite plateau in metal-poor stars gives $\approx 1.6\times10^{-10}$ — a factor- $\sim3$ , $\sim4\text{–}5\sigma$ discrepancy that stands out because deuterium and helium agree.

Where this lives today

The lithium problem is an active frontier precisely because each escape route can be tested. On the nuclear side, the LUNA underground accelerator at Gran Sasso has measured the production reaction $^3\mathrm{He}(\alpha,\gamma)^7\mathrm{Be}$ to percent-level precision, finding no gap-closing error, and the last major loophole — a hypothetical resonance in a $^7$ Be destruction channel — was directly attacked by the n_TOF collaboration at CERN, which measured neutron reactions on a radioactive $^7$ Be target and found the cross-sections too small to help; the nuclear door is now widely regarded as shut. On the stellar side, three-dimensional non-LTE model atmospheres and diffusion-plus-turbulence models are refining how much surface lithium halo dwarfs can quietly destroy, while the observed meltdown of the plateau below $[\mathrm{Fe/H}]\approx-3$ is read as evidence that some depletion is real. A striking counterpoint comes from the Small Magellanic Cloud, where lithium measured in the interstellar gas — never inside a star, so never subject to stellar depletion — sits close to the BBN value, complicating any purely stellar resolution. Meanwhile every extension of the standard model, from extra relativistic species to decaying dark-sector particles, is now routinely tested against the joint light-element vector, with lithium the sharpest single stress test.

The physical picture

Picture BBN as a brief cooking window a few minutes long. Deuterium is the ignition switch — nothing heavier forms until deuterium survives photodissociation (the deuterium bottleneck), and deuterium is a leftover fuel whose amount falls steeply as $\eta$ rises. Because deuterium is now measured cleanly in high-redshift gas clouds and matches the CMB $\eta$ superbly, the framework's clock and thermometer are validated. That validation is exactly what forbids waving lithium away as a broken model: the same machinery that gets D and $^4$ He right is the machinery that overpredicts $^7$ Li. The first figure makes this concrete — it plots the predicted mass-7 abundance against $\eta$ and shows where the CMB drops us.

Figure

The mass-7 valley: predicted primordial ⁷Li/H versus the baryon-to-photon ratio η₁₀. The direct ⁷Li branch falls while the ⁷Be branch rises, so the curve is V-shaped, and the CMB value η₁₀ = 6.1 lands on the rising ⁷Be branch at 4.5×10⁻¹⁰ — a factor 2.8 above the observed Spite plateau at 1.6×10⁻¹⁰

Two features of that curve do the work. First, the abundance-versus- $\eta$ relation is V-shaped: at low $\eta$ mass-7 is made directly as $^7$ Li through $^3\mathrm{H}(\alpha,\gamma)^7\mathrm{Li}$ and falls with $\eta$ ; at high $\eta$ it is made as $^7$ Be through $^3\mathrm{He}(\alpha,\gamma)^7\mathrm{Be}$ and rises with $\eta$ . The CMB baryon density sits firmly on the rising $^7$ Be branch, so the prediction is governed by beryllium production and the subsequent electron capture $^7\mathrm{Be}\to{}^7\mathrm{Li}$ . Second, that rising branch is steep, $\mathrm{^7Li/H}\propto\eta^{2}$ , which makes lithium a sensitive baryometer but also means any downward fix by lowering $\eta$ is fighting a steep slope — and drags deuterium the wrong way. The observational side has its own subtlety, shown in the second figure: the plateau's flatness is a double-edged sword. Independence of metallicity was the original argument that the plateau is primordial. But that same flatness would also arise if every one of these stars depletes surface lithium by a similar, temperature-tuned amount, erasing the primordial spread while hiding a uniform factor-of-three reduction. Distinguishing "pristine and flat" from "uniformly depleted and flat" is the crux of the stellar-depletion hypothesis, and the meltdown of the plateau at the very lowest metallicities is the clue that the surface value may not be pristine after all.

Figure

The Spite plateau: surface lithium A(Li) = 12 + log₁₀(Li/H) in warm metal-poor halo dwarfs stays flat near 2.2 across two decades of metallicity, while standard BBN predicts 2.66 (dashed amber) — an offset of 0.46 dex. Below metallicity Fe/H ≈ −3 the plateau shows a downturn and scatter, the meltdown that complicates a pristine reading

Finally, any "new physics" fix must thread a needle: it has to suppress $^7$ Be plus $^7$ Li by a factor of three without spoiling the excellent deuterium and helium fits. Deuterium in particular is a razor-sharp constraint — many proposed particle-decay scenarios that destroy lithium also over- or under-produce deuterium — so the lithium problem is really a joint-abundance optimisation over the whole light-element vector, not a one-number tweak.

The core equations

Lithium abundances are quoted on a logarithmic scale anchored to hydrogen. The number an observer reports and the number a BBN code predicts are both written this way, so translating between the scale and the raw ratio is the first move in every lithium calculation.

A(\mathrm{Li}) \equiv 12 + \log_{10}\!\left(\frac{N_{\mathrm{Li}}}{N_{\mathrm{H}}}\right) \qquad (1)

where: $A(\mathrm{Li})$ — logarithmic lithium abundance on the standard astronomical scale where hydrogen is set to $A(\mathrm{H})\equiv12$ ; $N_{\mathrm{Li}}/N_{\mathrm{H}}$ — number ratio of lithium to hydrogen nuclei. Reading: a plateau value $A(\mathrm{Li})=2.2$ is a ratio $10^{2.2-12}=10^{-9.8}$ , and each $0.30$ dex is a factor of two. The observed anchor is the Spite plateau — the mean lithium abundance of warm, metal-poor halo dwarfs, remarkably constant across metallicity and temperature.

A(\mathrm{Li})_{\rm plateau} \approx 2.2 \;\Longleftrightarrow\; \frac{\mathrm{Li}}{\mathrm{H}} \approx 1.6\times10^{-10} \qquad (2)

where: $A(\mathrm{Li})_{\rm plateau}$ — plateau abundance in halo dwarfs with $T_\mathrm{eff}\gtrsim5900\,\mathrm{K}$ and $-3\lesssim[\mathrm{Fe/H}]\lesssim-1.5$ . Reading: this is the value read as primordial before depletion was suspected. The theory anchor is the BBN prediction at the CMB baryon density — a robust output of a well-tested reaction network, not a fit.

\left(\frac{\mathrm{^7Li}}{\mathrm{H}}\right)_{\rm BBN} = (4.5 \pm 0.4)\times10^{-10} \quad\text{at}\quad \Omega_b h^2 = 0.0224 \qquad (3)

where: $\Omega_b h^2$ — physical baryon density fixed by the Planck CMB, equivalent to $\eta_{10}\equiv10^{10}\eta = 6.1$ . Reading: converting with (1), this is $A(\mathrm{Li})=2.66$ , sitting $0.46$ dex above the plateau. At this density mass-7 is produced overwhelmingly as beryllium, through radiative $\alpha$ -capture on $^3$ He, not as lithium directly.

{}^3\mathrm{He} + {}^4\mathrm{He} \longrightarrow {}^7\mathrm{Be} + \gamma \qquad (4)

where: $^7\mathrm{Be}$ — beryllium-7, the dominant mass-7 carrier on the high- $\eta$ branch; $\gamma$ — emitted photon carrying the reaction $Q$ -value. Reading: the rate of this one reaction, $^3\mathrm{He}(\alpha,\gamma)^7\mathrm{Be}$ , sets the entire lithium prediction. The beryllium becomes lithium only much later, once the universe is cool and neutral enough for a bound electron to be captured.

{}^7\mathrm{Be} + e^- \longrightarrow {}^7\mathrm{Li} + \nu_e, \qquad t_{1/2}\approx 53\,\mathrm{d} \qquad (5)

where: $e^-$ — captured bound electron, efficient once recombination supplies bound states; $\nu_e$ — emitted electron neutrino; $t_{1/2}$ — terrestrial electron-capture half-life of $^7$ Be, about 53 days. Reading: the lithium we observe is inherited beryllium, so its abundance traces the $^7$ Be yield. On the beryllium branch the yield climbs steeply with the baryon density, which is why lithium is a sensitive baryometer and why a downward fix by lowering $\eta$ is hard.

\frac{\mathrm{^7Li}}{\mathrm{H}}\bigg|_{\rm BBN} \propto \eta^{\,n}, \qquad n \approx +2 \ \ (\text{Be branch, high } \eta) \qquad (6)

where: $\eta$ — baryon-to-photon ratio, $\eta_{10}\equiv10^{10}\eta$ ; $n$ — local logarithmic slope, positive and steep on the beryllium branch. Reading: doubling the prediction needs only a $\sqrt2\approx1.4$ change in $\eta$ , but such shifts wreck deuterium. The discrepancy itself is best stated two ways — as a linear ratio and as a logarithmic offset — because the two measures speak to the two families of solution.

\frac{(\mathrm{^7Li/H})_{\rm BBN}}{(\mathrm{^7Li/H})_{\rm obs}} \approx \frac{4.5\times10^{-10}}{1.6\times10^{-10}} \approx 2.8, \qquad \Delta A(\mathrm{Li}) = 2.66 - 2.20 \approx 0.46\ \mathrm{dex} \qquad (7)

where: $\approx2.8$ — factor by which theory exceeds observation; $\Delta A(\mathrm{Li})$ — logarithmic offset, the amount stellar depletion would have to hide. Reading: with quoted errors this is a $\sim4\text{–}5\sigma$ tension.

Derivation AWhy the lithium prediction is really beryllium physics

The goal is to establish the single most important and least obvious fact about this problem: at the CMB baryon density the primordial "lithium" abundance is not set by lithium synthesis at all but by the yield of $^7$ Be, which survives BBN and only becomes $^7$ Li long afterward through electron capture. We build this from the relative fragility of the two mass-7 nuclei to proton bombardment, the timing of freeze-out, and the delayed capture, so that every later statement about the $\eta$ -dependence of lithium is understood as a statement about beryllium.

Step 1. During BBN, at temperatures $T\gtrsim3\times10^8\,\mathrm{K}$ , mass-7 nuclei are assembled by $\alpha$ -capture: $^3\mathrm{H}(\alpha,\gamma)^7\mathrm{Li}$ makes lithium directly, while $^3\mathrm{He}(\alpha,\gamma)^7\mathrm{Be}$ makes beryllium. At high baryon density $^3$ He survives better than $^3$ H (tritium beta-decays and is burned), so the beryllium channel wins. Why: the branch that dominates is fixed by which mass-3 nucleus is more abundant when $\alpha$ -capture freezes out, and at CMB $\eta$ that is $^3$ He.

Step 2. The two mass-7 nuclei have very different survival odds. Directly-made $^7$ Li is destroyed almost instantly by $^7\mathrm{Li}(p,\alpha)^4\mathrm{He}$ , a fast charged-particle reaction, so at high $\eta$ any direct lithium is burned away. Beryllium is comparatively shielded: $^7\mathrm{Be}(p,\gamma)^8\mathrm{B}$ is slow, and $^7\mathrm{Be}(n,p)^7\mathrm{Li}$ is throttled by the collapsing neutron abundance after neutron freeze-out. Why: robustness against destruction, not production rate alone, decides what actually freezes out, and beryllium is the robust carrier.

Step 3. As the universe expands and cools below $T\sim3\times10^8\,\mathrm{K}$ , every relevant reaction rate drops below the Hubble expansion rate and the mass-7 abundance freezes out, dominated by $^7$ Be at a level of a few $\times10^{-10}$ relative to hydrogen. Why: freeze-out is the generic BBN mechanism — abundances lock in when reactions can no longer keep pace with expansion — and here it locks in beryllium.

Step 4. Hundreds of thousands of years later, once recombination provides bound electrons, $^7\mathrm{Be}+e^-\to{}^7\mathrm{Li}+\nu_e$ converts essentially all the surviving beryllium to lithium. The observable primordial $^7$ Li therefore equals the frozen-out $^7$ Be plus the small surviving direct $^7$ Li. Why: this delayed conversion is why a nucleus that was mostly beryllium during BBN is seen as lithium today, and why the prediction inherits the $\eta$ -dependence of the $^7$ Be production rate.

Go deeper · Derivation B · 2 minFrom the baryon density to the predicted lithium abundance

Derivation BFrom the baryon density to the predicted lithium abundance

The goal is to trace the parametric logic that turns the CMB-measured baryon density into the number $4.5\times10^{-10}$ , without solving the full reaction network, so the reader sees exactly which inputs the prediction rests on and why it is considered robust rather than a tunable fit. We fix $\eta$ from the CMB, identify the dominant channel, follow the beryllium branch's $\eta^2$ scaling, and quote the network result that anchors the whole discrepancy.

Step 1. Fix the baryon density from the CMB acoustic peaks: $\Omega_b h^2 = 0.0224$ , equivalent to $\eta_{10}\equiv10^{10}\eta = 6.1$ using $\eta_{10}\approx274\,\Omega_b h^2$ . This is an external input to BBN, measured from an epoch $380{,}000$ years later, not a parameter fitted to the light elements. Why: because $\eta$ is pinned independently, BBN has zero free parameters left, so a mismatch in any one element cannot be absorbed by retuning.

Step 2. Identify the dominant channel at $\eta_{10}\approx6$ : mass-7 forms mainly as $^7$ Be via $^3\mathrm{He}(\alpha,\gamma)^7\mathrm{Be}$ , because the higher density favours $^3$ He survival and beryllium robustness (Derivation 1). The prediction is therefore controlled by one production cross-section. Why: concentrating the sensitivity in a single well-studied nuclear rate is what makes the prediction sharp — and what makes that rate a prime suspect.

Step 3. Apply the branch scaling. On the beryllium branch $\mathrm{d}\ln(\mathrm{^7Li/H})/\mathrm{d}\ln\eta\approx+2$ , so $\mathrm{^7Li/H}\propto\eta^2$ : more baryons means more $^3$ He and $^4$ He fusing to $^7$ Be. Between the low- $\eta$ minimum and $\eta_{10}=6.1$ the abundance climbs by roughly an order of magnitude. Why: the steep positive slope both explains why lithium is a good baryometer and warns that reconciling it downward is fighting a stiff dependence.

Step 4. Add the delayed electron capture: after recombination the frozen-out $^7$ Be becomes $^7$ Li, so the observable equals the beryllium yield plus a small direct-lithium remnant. Why: this is the step that lets a beryllium calculation be quoted as a lithium abundance.

Step 5. Quote the network result. Full BBN codes such as those of Cyburt, Fields and Olive give $\mathrm{^7Li/H} = (4.5\pm0.4)\times10^{-10}$ at $\eta_{10}=6.1$ , equivalently $A(\mathrm{Li})=2.66$ . This is the theory value that enters the discrepancy. Why: the parametric argument fixes the scaling and the escape routes, but the precise anchor number comes from integrating the full coupled network.

Go deeper · Derivation C · 1 minQuantifying the discrepancy and ruling out a baryon-density fix

Derivation CQuantifying the discrepancy and ruling out a baryon-density fix

The goal is to convert theory and observation into a single ratio and dex offset, assess its statistical weight, and then demonstrate that the most obvious escape — simply lowering $\eta$ until lithium falls into line — is blocked by deuterium, so that the tension cannot be dissolved within standard BBN by retuning the one free parameter. We form the ratio, translate it to dex, and propagate the required $\eta$ shift into the deuterium prediction.

Step 1. Take the observed plateau, $A(\mathrm{Li})=2.20$ , i.e. $\mathrm{Li/H}=10^{-9.80}=1.6\times10^{-10}$ , and the BBN value, $4.5\times10^{-10}$ . Form the ratio $4.5/1.6\approx2.8$ ; equivalently $\Delta A = 2.66-2.20 = 0.46$ dex. Why: stating the gap both as a linear factor and as a logarithmic offset connects it to the two solution families — a factor to nuclear or new-physics suppression, a dex offset to stellar depletion.

Step 2. Weigh the significance. Combining the observational scatter of the plateau with the roughly $10\%$ theory uncertainty, the offset is about $4\text{–}5$ standard deviations — large enough that it cannot be a statistical fluctuation, small enough that it is not an order-of-magnitude failure. Why: the intermediate size is exactly what makes the problem stubborn — too significant to ignore, too modest to signal a broken framework.

Step 3. Test the $\eta$ fix. On the beryllium branch $\mathrm{^7Li/H}\propto\eta^2$ , so matching the plateau needs $\eta$ lower by $\sqrt{4.5/1.6}\approx1.7$ , i.e. $\eta_{10}$ from $6.1$ down to $\approx3.6$ . Why: quantifying the required shift is the only way to check whether it is compatible with the other elements.

Step 4. Propagate that shift into deuterium, which scales as $\mathrm{D/H}\propto\eta^{-1.6}$ . Lowering $\eta$ by $1.7$ raises D/H by $1.7^{1.6}\approx2.3$ , from the observed $(2.5\pm0.03)\times10^{-5}$ to $\approx5.7\times10^{-5}$ — a catastrophic, many-hundred- $\sigma$ break of the tightest light-element constraint. Why: this is the decisive result — the one parameter that could fix lithium is nailed down by deuterium, so the resolution must lie outside standard BBN's parameter space.

Limiting cases

The predicted $^7$ Li depends on where the CMB baryon density places us on the abundance-versus- $\eta$ curve and on which production channel dominates there.

Case	Result	Meaning
Low baryon density (direct $^7$ Li branch)	$\eta_{10}\lesssim3$	Mass-7 is made mainly as $^7$ Li directly via $^3\mathrm{H}(\alpha,\gamma)^7\mathrm{Li}$ ; the yield falls with increasing $\eta$ .
CMB baryon density (Be branch — the actual case)	$\eta_{10}\approx6.1,\ \Omega_b h^2=0.0224$	Mass-7 is made mainly as $^7$ Be; predicted $\mathrm{^7Li/H}\approx4.5\times10^{-10}$ , rising with $\eta$ . This is where the problem lives.
High baryon density limit	$\eta_{10}\gtrsim10$	$^7$ Be production dominates strongly; predicted $^7$ Li climbs further above observations, worsening the gap.
Depleted-star limit	$A(\mathrm{Li})_{\rm obs}\approx2.2\ll A(\mathrm{Li})_{\rm BBN}\approx2.66$	If plateau stars have destroyed $\sim0.5$ dex of surface lithium by mixing or diffusion, theory and observation reconcile with no new physics.

Common trapThe primordial mass-7 is mostly made as lithium

It is not. At the relevant baryon density mass-7 is made overwhelmingly as $^7$ Be through $^3\mathrm{He}(\alpha,\gamma)^7\mathrm{Be}$ , which only becomes $^7$ Li much later by electron capture once bound electrons exist. So the $\eta$ -dependence people attribute to "lithium" is really beryllium nuclear physics. The two mass-7 channels run in opposite directions with $\eta$ — direct $^7$ Li falling, indirect $^7$ Be rising — which is exactly why the $\mathrm{^7Li}(\eta)$ curve is V-shaped, and why the CMB value landing on the rising $^7$ Be branch is what turns a coincidence into a problem. Treating the prediction as if it were lithium synthesis obscures which nuclear rate to blame and which escape routes are open.

Worked examples

1 · The size of the discrepancy, both ways (fully worked)

Given the Spite plateau $A(\mathrm{Li})_{\rm obs}=2.20$ and the standard BBN yield $\mathrm{^7Li/H}=4.5\times10^{-10}$ , find the linear discrepancy factor and the logarithmic offset, and state the significance.

Step 1. Convert the plateau to a ratio with equation (1): $\mathrm{Li/H}=10^{A-12}=10^{2.20-12}=10^{-9.80}=1.58\times10^{-10}$ . This is the "observed" $\mathrm{^7Li/H}$ .

Step 2. Convert the BBN yield to the log scale: $A(\mathrm{Li})_{\rm BBN}=12+\log_{10}(4.5\times10^{-10})=12-9.347=2.653\approx\mathbf{2.66}$ .

Step 3. Linear factor: $(\mathrm{^7Li/H})_{\rm BBN}/(\mathrm{^7Li/H})_{\rm obs}=4.5/1.58=\mathbf{2.85}$ . Logarithmic offset: $\Delta A=2.653-2.20=\mathbf{0.45\ dex}$ , consistent since $\log_{10}(2.85)=0.455$ .

Step 4. Significance: folding the plateau scatter and the $\sim10\%$ theory error, the offset is about $\mathbf{4\text{–}5\sigma}$ — a firm tension, not a fluctuation, and not resolved by the CMB-fixed $\eta$ that makes D and $^4$ He agree. The prediction exceeds observation by a factor $\approx2.8$ , i.e. $\approx0.46$ dex.

2 · Why lowering the baryon density cannot rescue lithium (fully worked)

Suppose you try to fix lithium by lowering $\eta$ alone, using $\mathrm{^7Li/H}\propto\eta^2$ . Find the required $\eta$ and the deuterium abundance it would predict, given $\mathrm{D/H}\propto\eta^{-1.6}$ and observed $\mathrm{D/H}=(2.5\pm0.03)\times10^{-5}$ .

Step 1. To pull $\mathrm{^7Li/H}$ down by the factor $2.8$ with an $\eta^2$ law, reduce $\eta$ by $\sqrt{2.8}=\mathbf{1.68}$ . Starting from $\eta_{10}=6.1$ this gives $\eta_{10}\to6.1/1.68=\mathbf{3.6}$ .

Step 2. Propagate to deuterium: lowering $\eta$ by $1.68$ multiplies $\mathrm{D/H}$ by $1.68^{1.6}$ . Compute $1.68^{1.6}=e^{1.6\ln1.68}=e^{1.6\times0.519}=e^{0.830}=\mathbf{2.29}$ .

Step 3. New deuterium: $\mathrm{D/H}\to2.5\times10^{-5}\times2.29=\mathbf{5.7\times10^{-5}}$ , against an observed $(2.5\pm0.03)\times10^{-5}$ . The discrepancy is $(5.7-2.5)/0.03\approx100$ standard deviations.

Step 4. Conclusion: the $\eta$ that fixes lithium destroys the deuterium concordance many times over. A pure baryon-density shift is ruled out; the abundances must be fit jointly, which is why the resolution must lie in stellar physics, nuclear rates, or new physics.

3 · The depletion budget a plateau star would need

If the plateau is not primordial but depleted, how much surface lithium must each star have destroyed to hide a $0.46$ dex offset, and is that plausible?

Step 1. A $0.46$ dex offset means the surviving fraction is $10^{-0.46}=0.35$ , so each star must have destroyed $1-0.35=\mathbf{0.65}$ , roughly two-thirds of its initial surface lithium.

Step 2. Atomic-diffusion models with turbulent mixing can deplete $\sim0.4\text{–}0.5$ dex, comfortably in this range in magnitude. The difficulty is not the amount but the flatness: the depletion must be almost identical across a wide span of temperature and metallicity to preserve the plateau's remarkable tightness. Depleting $\sim0.5$ dex is achievable; doing it uniformly enough to keep the plateau flat is the open challenge.

Physics of the portrait

The lithium problem has no single equation to its name and no lone discoverer — it emerged where a stellar-spectroscopy observation collided with a cosmological prediction. But its observational heart is one measurement, made by a husband-and-wife team at Meudon who noticed that the oldest stars in the halo all carry the same trace of lithium.

Origins · 1 minFrançois Spite and how this was discovered

François Spite

b. 1932 · stellar spectroscopy and the primordial lithium plateau

François Spite and his wife Monique Spite, working at the Observatoire de Paris-Meudon, published in 1982 the observation that turned lithium into a cosmological probe. Measuring the weak $670.8\,\mathrm{nm}$ resonance line in warm, metal-poor halo dwarfs, they found the surface lithium abundance nearly the same star to star — flat against both effective temperature (above about $5900\,\mathrm{K}$ ) and metallicity across more than a decade in iron content. They argued that such uniformity in stars formed from nearly pristine gas could only mean they were seeing the primordial lithium of the Big Bang, essentially untouched by stellar evolution, since a nucleus so fragile it burns at $2.5\times10^6\,\mathrm{K}$ would otherwise show a spread or be destroyed if surface material had been cycled through the interior. This "Spite plateau" gave cosmology a direct handle on a fourth primordial abundance, alongside deuterium, $^3$ He and $^4$ He. The irony is that the same flatness the Spites read as pristine is now the crux of the debate: if every plateau star has quietly depleted a similar amount, the plateau could sit a factor of three below the true primordial value. Their measurement remains the observational anchor of the entire problem.

History

1948

— Alpher, Bethe and Gamow propose primordial nucleosynthesis of the light elements

1982

— François and Monique Spite discover the flat lithium plateau in metal-poor halo dwarfs

2003

— WMAP fixes the baryon density, pinning the BBN lithium prediction and sharpening the gap

2011

— Fields codifies the primordial lithium problem in an annual review

2016

— Cyburt, Fields, Olive and Yeh confirm lithium's factor-three isolation amid BBN concordance

Going further

Texts. Ryden, Introduction to Cosmology, 2nd ed., Ch. 10 (Nucleosynthesis and the Early Universe) · Dodelson, Modern Cosmology, Ch. 3 (The Early Universe / BBN) · Carroll & Ostlie, An Introduction to Modern Astrophysics, 2nd ed., Ch. 30 (Cosmology) · Mo, van den Bosch & White, Galaxy Formation and Evolution, Ch. 3 (thermal history and nucleosynthesis) · Spite & Spite (1982), "Abundance of lithium in unevolved halo stars," Nature 297, 483 · Fields (2011), "The Primordial Lithium Problem," Ann. Rev. Nucl. Part. Sci. 61, 47 · Cyburt, Fields, Olive & Yeh (2016), "Big Bang Nucleosynthesis: Present Status," Rev. Mod. Phys. 88, 015004. The key numerical values used throughout this article are: Spite plateau $A(\mathrm{Li})\approx2.2$ , $\mathrm{Li/H}\approx1.6\times10^{-10}$ ; BBN prediction $\mathrm{^7Li/H}=(4.5\pm0.4)\times10^{-10}$ at $\Omega_b h^2=0.0224$ ( $\eta_{10}=6.1$ , using $\eta_{10}\approx274\,\Omega_b h^2$ ); discrepancy factor $\approx2.8$ , i.e. $\approx0.46$ dex, $\sim4\text{–}5\sigma$ ; $^7$ Be electron-capture half-life $\approx53$ d; observed $\mathrm{D/H}=(2.5\pm0.03)\times10^{-5}$ ; D/H scaling $\propto\eta^{-1.6}$ , Li scaling $\propto\eta^{2}$ . The worked checks are: ratio $4.5/1.58=2.85$ , dex offset $2.653-2.20=0.45$ , required $\eta$ reduction factor $\sqrt{2.8}=1.68$ , and the resulting $\mathrm{D/H}\to5.7\times10^{-5}$ .

Prerequisites. Big Bang Nucleosynthesis · Primordial Helium Abundance and the Deuterium Bottleneck · Baryon Asymmetry and Baryogenesis · Thermal History of the Universe. Leads to. Recombination and the Saha Equation · Last Scattering Surface and Photon Decoupling.

Ask the tutor: Ask me to walk through why lowering the baryon density fixes lithium but wrecks deuterium, or to lay out which of the three solution classes is closest to being ruled out.

Why is the lithium problem taken seriously when BBN otherwise works so well?

Precisely because BBN otherwise works so well. The same baryon density $\Omega_b h^2=0.0224$ — measured independently from the CMB, not fitted — yields excellent agreement for deuterium and helium-4 across many orders of magnitude in abundance. With that one parameter pinned, BBN has no freedom left to absorb a mismatch. So when the identical machinery overpredicts $^7$ Li by a factor of three, the failure cannot be blamed on a broken model or a wrong $\eta$ ; it must point to something specific to mass-7. A discrepancy in an otherwise-failing theory would be unremarkable, but a lone discrepancy inside a spectacularly successful one is a genuine anomaly worth chasing.

If it is mostly beryllium, why do we call it the lithium problem?

Because lithium is what we observe. During BBN the mass-7 nuclei freeze out overwhelmingly as $^7$ Be, which is more robust against destruction than $^7$ Li at the CMB baryon density. But $^7$ Be is unstable to electron capture, and hundreds of thousands of years later, once recombination supplies bound electrons, essentially all of it converts to $^7$ Li by $^7\mathrm{Be}+e^-\to{}^7\mathrm{Li}+\nu_e$ . The lithium an astronomer measures in an old star is therefore inherited beryllium. Naming the anomaly after the observed element is natural, but it hides where the physics actually lives: the prediction's sensitivity to the baryon density is the sensitivity of the $^3\mathrm{He}(\alpha,\gamma)^7\mathrm{Be}$ production rate, a beryllium reaction.

Could the Spite plateau simply be depleted rather than primordial?

This is the leading astrophysical hope. If gravitational settling and turbulent mixing carry surface lithium down to layers hot enough to burn it, each halo dwarf could destroy a fraction of its lithium. The magnitude needed — about two-thirds, or $0.5$ dex — is within reach of diffusion-plus-turbulence models. The obstacle is the plateau's flatness: depletion generally depends on stellar mass, temperature and metallicity, yet the plateau is remarkably uniform, so the destruction would have to be finely tuned to be nearly the same in every star. The observed downturn and increased scatter of the plateau below $[\mathrm{Fe/H}]\approx-3$ , the so-called meltdown, is read by many as direct evidence that at least some depletion is real, softening the case that the surface value is perfectly pristine.

Has the nuclear-physics route been ruled out?

Nearly. Because the prediction is set by $^7$ Be, attention focused on the production reaction $^3\mathrm{He}(\alpha,\gamma)^7\mathrm{Be}$ and the destruction reactions $^7\mathrm{Be}(n,p)^7\mathrm{Li}$ and $^7\mathrm{Be}(d,p)2\alpha$ . Underground measurements at LUNA pinned the production rate to percent level with no gap-closing error. The last serious loophole was a hypothetical unmeasured resonance that would let neutrons destroy $^7$ Be faster; the n_TOF experiment at CERN measured neutron reactions on a radioactive $^7$ Be target directly and found the cross-sections far too small to help. The consensus is now that no plausible nuclear revision closes the factor-of-three gap while leaving deuterium and helium intact, so the nuclear door is widely regarded as shut.

What kind of new physics could lower the lithium abundance?

Several ideas exist, all constrained by the other light elements. A massive particle decaying or annihilating after $t\sim100\,\mathrm{s}$ can inject non-thermal photons or hadrons that photodissociate $^7$ Be or convert it to easily-burned $^7$ Li, lowering the final abundance. A negatively charged massive particle can bind to $^7$ Be and catalyse its destruction (catalysed BBN). Variations in fundamental constants during BBN would shift the nuclear rates. Every such scenario, however, also perturbs deuterium, which is measured to about one percent, so the viable parameter space is narrow: a mechanism that removes the needed factor of three from lithium while keeping D/H at $2.5\times10^{-5}$ is hard to arrange, which is why no new-physics fix has been accepted.

Does the lithium problem threaten the hot Big Bang model?

No — if anything it sharpens confidence in it. The concordance of deuterium, helium-4 and the CMB baryon density validates the expansion history, the effective number of relativistic species, and the standard thermal timeline to high precision. Lithium's isolation means the anomaly is confined to mass-7 physics — nuclear or stellar — rather than being a global failure of cosmology. A broken framework would fail across the board; instead one element out of four is off by a factor of three while the rest are exact. That pattern points to specific, testable causes and makes lithium a stress test for any extension of the standard model, not a crack in the foundation of the hot Big Bang.