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The success of primordial nucleosynthesis has been limited by thelong-standing Lithium problem. We use a self-consistent perturbative analysisof the effects of relevant theoretical parameters on primordialnucleosynthesis, including variations of nature's fundamental constants, toexplore the problem and its possible solutions, in the context of the latestobservations and theoretical modeling. We quantify the amount of depletionneeded to solve the Lithium problem, and show that transport processes ofchemical elements in stars are able to account for it. Specifically, thecombination of atomic diffusion, rotation and penetrative convection allows usto reproduce the lithium surface abundances of Population II stars, startingfrom the primordial Lithium abundance. We also show that even with thisdepletion factor there is a preference for a value of the fine-structureconstant at this epoch that is larger than the current laboratory one by a fewparts per million of relative variation, at the two to three standarddeviations level of statistical significance. This preference is driven by therecently noticed discrepancy between the best-fit values for thebaryon-to-photon ratio (or equivalently the Deuterium abundance) inferred fromcosmic microwave background and primordial nucleosynthesis analyses, and islargely insensitive to the Helium-4 abundance. We thus conclude that theLithium problem most likely has an astrophysical solution, while the Deuteriumdiscrepancy provides a possible hint of new physics.

Primordial nucleosynthesis with varying fundamental constants: Solutions to the Lithium problem and the Deuterium discrepancy