The Case of the Missing Lithium
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Time evolution of the light element abundances during BBN. Time (upper axis) increases to the right, and so the temperature is shown to decrease to the right. From Yeh et al. (2023).
The cosmological lithium problem is one of the biggest unsolved puzzles in astrophysics. Right after the Big Bang, the universe was filled with hot, dense protons, neutrons and other particles. As it cooled, some of the protons and neutrons fused into light nuclei, leaving a universe of mostly hydrogen and helium, with a trace of lithium (Fields, 2011).
Billions of years later, we look at old, metal-poor stars, which should still carry that lithium. But there’s way less lithium-7 (⁷Li) than expected! According to our well-trusted Big Bang Nucleosynthesis (BBN) calculations, we should be seeing about three times more lithium than what we actually observe (Cyburt & Davids, 2008). So where did it go?
The first few minutes
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Simplified BBN nuclear network, showing the 12 reactions important for determining light-element abundances. From Fields (2023).
In the first few minutes after the Big Bang, the universe was a hot, dense plasma in which nuclear reactions made the light elements. Protons and neutrons fused into deuterium, helium-4 (⁴He), a little lithium-7 and even less beryllium (Fields, 2011). The standard BBN model predicts these abundances precisely, and the observed amounts of deuterium and helium-4 match its predictions (Serpico et al., 2004).
But then there’s lithium-7. Instead of matching the theoretical predictions, the amount we actually see in ancient stars is dramatically lower (Spite & Spite, 1982).
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BBN theory predictions for light nuclide abundances versus the cosmic baryon-to-photon ratio . Curve widths: 1 theoretical uncertainties. Cyan vertical band: Planck CMB determination of (Aghanim & others, 2020). Yellow boxes: light-element observations and corresponding ranges. Hatched vertical band: D/H+ concordant range for . (From BBN review in Particle Data Group et al. (2020)). From Fields (2023).
Tracking the missing Lithium
Lithium is measured in some of the oldest stars in the galaxy, metal-poor stars that formed early and should still have roughly the chemical makeup of the early universe. The strength of the lithium absorption line at 670.8 nm in their spectra tells us how much lithium-7 they contain (Meléndez & Ramírez, 2004).
What they find is the so-called Spite plateau, a nearly constant level of lithium abundance across different low-metallicity stars (Spite & Spite, 1982). But that plateau is far below what BBN predicts! So either the lithium was destroyed or hidden somewhere, or our understanding of nuclear physics or cosmology needs an update.
Proposed explanations range from lithium being destroyed inside stars or by cosmic rays to new physics beyond the Standard Model (Pospelov & Pradler, 2010).
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Lithium abundances in selected metal-poor Galactic halo stars. For each star, elemental Li = Li + Li is plotted at the star’s metallicity [Fe/H] = log10[(Fe/H)/(Fe/H)]. The flatness of Li vs Fe is the “Spite plateau” and indicates that the bulk of the lithium is unrelated to Galactic nucleosynthesis processes and thus is primordial. The horizontal band gives the BBN+WMAP prediction; the gap between this and the plateau illustrates the Li problem. Points below the plateau show Li abundances; the apparent plateau constitutes the Li problem. From Fields (2011).
Suspect #1: A game of Hide and Seek
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Comparison of BBN light-element abundance predictions and observations. Likelihood curves (normalized to peak at unity) for BBN+CMB predictions are shown in magenta. Primordial abundances inferred from astronomical observations are shown in yellow. The CMB determination of He is shown in cyan. From Fields et al. (2020).
Suppose standard cosmology and particle physics are right, and so are our nuclear physics calculations of mass-7 production. Then why the heck are we seeing way less lithium-7 than expected? Theoretically, there should be about three to four times more lithium than what we observe (Fields, 2011).
Lithium abundance is usually determined by studying absorption lines in the photospheres of very old, low-metallicity stars. The Spite plateau, a flat trend in lithium abundance across these stars, suggests that lithium is primordial and hasn’t been significantly affected by later galactic processes (Spite & Spite, 1982). But what if we’ve made a mistake somewhere in our assumptions?
One possible error comes from the fact that we measure lithium’s 670.8 nm absorption line, which is sensitive to neutral lithium (Li⁰). However, most lithium in these ancient stars is actually ionized (Li⁺). That means we need to introduce an ionization correction factor, which is super sensitive to the stellar temperature (Richard et al., 2005). If we systematically underestimated how hot these stars are, then lithium levels could actually be higher than we thought. Some studies suggest that tweaking the temperature scale upwards by around 500–600 K might help, but so far, that fix hasn’t fully solved the problem (Meléndez & Ramírez, 2004).
Then there’s the big question: is the lithium we see today the same lithium that was originally there? Over billions of years, these stars might have depleted some of their lithium due to high-temperature effects. Processes like convection, turbulence, and diffusion can mess with lithium abundance, but modeling these effects precisely is tricky (Pinsonneault, 1997). Some studies argue that if lithium was being destroyed inside stars, we should see variations in lithium levels across different stars, which we don’t, at least not much. However, newer models suggest that even after depleting lithium by a factor of three, we could still see a narrow Spite plateau due to turbulent diffusion and convective overshoot (Fu et al., 2015).
So stellar effects might explain part of the gap, but they don’t seem to account for all of the missing lithium. That leaves nuclear physics, or new physics beyond the Standard Model.
Suspect #2: Did we mess up the math?
What if the measurements are right, and the problem lies in how we calculate Big Bang Nucleosynthesis (BBN) (Fields, 2011)?
BBN is based on solid physics: General Relativity governs the cosmic expansion, and nuclear reactions follow the Standard Model. But nuclear networks are super complex, and mistakes in reaction rates could throw off our lithium predictions (Cyburt & Davids, 2008).
One idea is that we might have underestimated or overlooked certain nuclear reactions that influence lithium-7 production. The most important reaction for making mass-7 nuclides is ³He(α, γ)⁷Be. While its cross-section has been measured with high precision, absolute values are notoriously difficult to pin down (Coc et al., 2004). But this reaction is also responsible for solar neutrino production, and solar neutrino measurements match predictions almost perfectly. That means tweaking this reaction to solve the lithium problem would mess up our understanding of the Sun, so that’s probably not the answer.
Other nuclear processes, like weak interaction rates, have been extensively tested and don’t seem to be the issue either (Serpico et al., 2004). Studies also looked into alternative thermonuclear rates, plasma effects, and electron screening, but none of these offered a viable solution (Boyd et al., 2010; Itoh et al., 1997; Voronchev et al., 2010). Even reactions involving beryllium-7, like ⁷Be(d, α)αp, turned out to be way less significant than hoped (Boyd et al., 2010).
That leaves resonances, energy states in nuclear reactions that could have been overlooked. Some proposed resonances, like ⁷Be + d → ⁹B* (16.71 MeV) and ⁷Be + t → ¹⁰B*, could theoretically help balance the lithium discrepancy, if their reaction widths are large enough (Cyburt & Pospelov, 2012). But recent studies suggest that while they might help, they don’t fully solve the problem. In fact, Iliadis & Coc (2020) concluded that nuclear physics alone is unlikely to fix this mystery.
Suspect #3: Time to break the rules?
If standard astrophysics and nuclear physics can’t solve the lithium problem, what’s left is new physics beyond the Standard Model (Pospelov & Pradler, 2010).
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Abundance contours vs decay lifetime. The colored areas indicate parameter regions in which the predicted light-element abundances disagree with observations, and the remaining, white regions are allowed. From R. Cyburt et al. (2010).
One idea is that dark matter could be playing a role. Dark matter is still a huge mystery, but we know it must exist. Some theoretical models propose that dark matter particles, perhaps Weakly Interacting Massive Particles (WIMPs), could decay into high-energy particles that mess with primordial element abundances (R. Cyburt et al., 2010). If these decays happened during or just after BBN, they could have influenced lithium levels. In fact, certain decay lifetimes (~10²–10³ seconds) seem to line up with observed lithium-7 levels. But while this helps with lithium, it messes up the deuterium predictions.
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Contours of in the (mass, abundance) plane. From R. Cyburt et al. (2010).
Another idea comes from supersymmetry (SUSY). If a spin-3/2 gravitino was once a heavier particle that decayed into dark matter, it could create an optimal trade-off between lithium destruction and deuterium production (Jedamzik, 2006). Supersymmetry hasn’t been confirmed by experiments like those at the Large Hadron Collider (LHC) though, so this stays speculative.
There’s also the possibility that fundamental constants aren’t actually constant. Observations of atomic transitions in distant quasars hint that the fine-structure constant (α_EM) might have changed over cosmic time (Coc et al., 2007). If true, this could impact nuclear physics in BBN and potentially explain lithium discrepancies. However, the evidence for varying constants is still debated, and alternative studies show no change.
Lastly, some have suggested nonstandard cosmologies, like variations in the baryon-to-photon ratio across different regions of the universe. Maybe lithium-7 measurements reflect a local underdensity rather than a true overall abundance. It’s a cool idea, but current constraints make it tricky to justify.