As seen in the panels of Fig. 3 above, the observed primordial lithium abundance differs sharply from the BBN+CMB prediction . This discrepancy constitutes the “Lithium Problem”, which was foreshadowed before CMB determinations of η, and has persisted over the dozen years since the first WMAP data release. For a detailed recent review of the lithium problem, see . Here we briefly summarize the current status.
The most conventional means to resolve the primordial lithium problem invokes large lithium depletion in halo stars . As noted above (Section 3.3), recent observations of the Spite plateau “meltdown” at very low metallicity, [Fe/H] < −3, seem to demand that some stars have depleted their lithium [95, 94]. Could the other plateau halo stars have also destroyed their lithium? Such a scenario cannot be ruled out, but raises other questions that remain unanswered: why is the Li/H dispersion so small at metallicities above the “meltdown”? And why is there a “lithium desert” with no stars having lithium abundances between the plateau and the primordial abundance?
It is worthwhile to find other sites for Li/H measurements, as clearly halo star lithium depletion is theoretically complex and observationally challenging. Unfortunately, the CMB itself does not yet provide an observable signature of primordial lithium . However, a promising new direction is the observation of interstellar lithium in low-metallicity or high-z galaxies . Interstellar measurements in the Small Magellanic Cloud (metallicity ∼ 1/4 solar) find Li / HISM,SMC = (4.8 ± 1.8) × 10−10 . This value is consistent with the CMB+BBN primordial abundance, but the SMC is far from primordial, with a metallicity of about 1/4 solar. Indeed, the SMC interstellar lithium abundance agrees with that of Milky Way stars at the same [Fe/H], which are disk (Population I) stars in which Li/H is rising from the Spite plateau due to Galactic production. Thus we see consistency between lithium abundances at the same metallicity, but measured in very different systems with very different systematics. This strongly suggests that stellar lithium depletion has not been underestimated, at least down to this metallicity. Moreover, this observation serves as a proof-of-concept demonstration that measurements of interstellar lithium in galaxies with lower metallicities would could strongly test stellar depletion and potentially rule out this solution to the lithium problem.
Another means of resolving the lithium problem within the context of the standard cosmology and Standard Model microphysics is to alter the BBN theory predictions due to revisions in nuclear reaction rates [17, 41, 42]. But as we have seen, all of the reactions that are ordinarily the most important for BBN have been well measured at the energies of interest. Typically, cross sections are known to ∼ 10% or better, and these errors are already folded into Fig. 3. A remaining possibility is that a reaction thought to be unimportant could contain a resonance heretofore unknown, which could boost its cross section enormously, analogously to the celebrated Hoyle 12C resonance that dominates the 3α → 12C rate .
In BBN, the densities and timescales prior to nuclear freezeout are such that only two-body reactions are important, and it is possible to systematically study all two-body reactions that enhance the destruction of 7Be. A small number candidates emerge, for which one can make definite predictions of the needed resonant state energy and width: 7Be(d, γ)9B, 7Be(3He, γ)10C, and 7Be(t,γ)10B [43, 44, 45]. However, measurements in 7Be(d, d)7Be , 9Be(3He, t)9B , and an R-matrix analysis of 9B  all rule out a 9B resonance. Similarly, 10C data rule out the needed resonance in 10C . The upshot is that a “nuclear option” to the lithium problem is essentially excluded.
It is thus a real possibility that the lithium problem may point to new physics at play during or after nucleosynthesis. A number of possible solutions have been proposed and are discussed in the reviews cited above. Here we simply note that a challenge to all such models is that they must reduce 7Li substantially, yet not perturb the other light elements unacceptably. Generally, there is a tradeoff between 7Be destruction and D production (usually as a by-product of 4He disruption) [121, 76]. Essentially all successful models drive D/H to the maximum abundance allowed by observations. However, the new very precise D/H measurements (Section 3.2) dramatically reduce the allowed perturbations and will challenge most of the existing new-physics solutions to the lithium problem. It remains to be seen whether it is possible to introduce new physically-motivated perturbations that satisfy the D/H constraint while still solving or at least substantially reducing the lithium problem.