Résumé
The success of primordial nucleosynthesis has been limited by the long-standing lithium problem. We use a self-consistent perturbative analysis of the effects of the relevant theoretical parameters on primordial nucleosynthesis, including variations of nature's fundamental constants, to explore the problem and its possible solutions in the context of the latest observations and theoretical modeling. We quantify the amount of depletion needed to solve the lithium problem, and show that transport processes of chemical elements in stars are able to account for it. Specifically, the combination of atomic diffusion, rotation, and penetrative convection allows us to reproduce the lithium surface abundances of Population II stars, starting from the primordial lithium abundance. We also show that even with this depletion factor, a preference for a value of the fine-structure constant at this epoch remains that is larger than the value currently obtained in the laboratory by a few parts per million of relative variation at a statistical significance level of two to three standard deviations. This preference is driven by the recently reported discrepancy between the best-fit values for the baryon-to-photon ratio (or equivalently, the Deuterium abundance) inferred from cosmic microwave background and primordial nucleosynthesis analyses, and is largely insensitive to the Helium-4 abundance. We thus conclude that the lithium problem most likely has an astrophysical solution, while the Deuterium discrepancy provides a possible indication of new physics.