Discrepancy problem in lithium? Why is there a discrepancy between the amount of lithium-7 predicted to be produced in Big Bang nucleosynthesis and the amount observed in very old stars?
 A: The discrepancy between the predicted big bang nucleosynthetic abundance of Lithium 7 and the measured value can be summarised as follows.
If we take what we know about the the baryonic mass density of the universe and the Hubble constant, we get a self-consistent picture between the cosmic microwave background, observations of galaxy recession etc. and the estimated primordial abundances of Helium and Deuterium.
The problem arises that these same cosmological parameters predict a primordial lithium abundance of $(4.7\pm 0.7)\times10^{-10}$, when expressed as a ratio to the hydrogen abundance (e.g. Cyburt et al. 2016).
On the other hand, measurements of the Li abundance present in the photospheres of the oldest stars ("halo stars") in our Galaxy suggest that the primordial abundance was actually about $(1.6\pm 0.3)\times10^{-10}$.
The factor of 3 difference between these numbers is about 4-5 times the uncertainty. This is the so-called "Lithium problem".
The potential solutions are reviewed by Fields (2012). They fall into the following categories.


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*Astrophysical solutions - that we don't understand our measurements of the Li abundances because of an imperfect understanding of the atmospheres of low metallicity stars; or that we don't understand interior mixing mechanisms that mean at the photosphere, we see material that has been mixed upwards from the interior where the Li has been depleted in nuclear reactions.

*Nuclear physics - maybe the details of the reaction rates and cross-sections in the big bang model are awry? There are still some sizeable uncertainties here which remain to be nailed down, but are seen as rather unlikely solutions.

*Additions to the standard big bang model. This includes things like inhomogeneous nucleosynthesis in the early universe - i.e. that it was clumpy even at this early stage. Other possibilities include that the equilibrium reactions in big bang nucleosynthesis were upset by the decay of massive dark matter particles.

*Perhaps the fundamental constants have changed with time resulting in somewhat different binding energy differences between different nuclei? Scherrer & Scherrer (2017) for example discuss a scenario where the mass difference between 2 He nuclei and a $^8$Be nucleus changes with time in such a way that lots of  $^8$Be is produced during big bang nucleosynthesis, but decays back into He later on. This does not alter the primordial He abundance inferred from present-day observations, but the removal of He at early epochs results in a lower production of $^7$Li.
Thus there are lots of ideas to solve this problem and other ideas which suggest it is not so much a problem, but that we can't do the measurements properly.
EDIT: Update 18/11/19 from the "Lithium in the Universe" conference in Frascati, Rome.
Having sat through a few review talks today, I can summarise progress as:
Explanation 2 (Nuclear Physics) is dead. All avenues appar to be explored and the likely remaining uncertainties are at the level of 10%.
A further class of explanations has arisen, that rely on the properties of magnetic fields - always the last refuge of the astrophysical theoretician!


*Inhomogeneous magnetic fields, contributing significant energy density in the early universe may have led to temperature fluctuations at the epoch of nucleosynthesis. Such fluctuations could reduce the predicted Li abundances a bit, but they also change the predicted deuterium abundance and this wouldn't fit with the now quite precise measurements of the primordial D abundance and the Planck value of $\Omega_b h^2$.

*It has been hypothesised that magnetic fields can play a role in filtering how much primordial Li makes into the structures that form galaxies. i.e. There is a sort of chemical differentiation caused when there is a gradient of the magnetic field strength at right angles to the magnetic field. This accelerates ions down the gradient and possibly away from forming structures. Since Li is easily ionised in the early universe (compared with H and He), this might lead to the gas that formed the first stars being Li-poor.
