Primordial nucleosynthesis with varying fundamental constants: Improved constraints and a possible solution to the Lithium problem

Primordial nucleosynthesis is an observational cornerstone of the Hot Big Bang model and a sensitive probe of physics beyond the standard model. Its success has been limited by the so-called Lithium problem, for which many solutions have been proposed. We report on a self-consistent perturbative analysis of the effects of variations in nature's fundamental constants, which are unavoidable in most extensions of the standard model, on primordial nucleosynthesis, focusing on a broad class of Grand Unified Theory models. A statistical comparison between theoretical predictions and observational measurements of ${}^4$He, D, ${}^3$He and, ${}^7$Li consistently yields a preferred value of the fine-structure constant $\alpha$ at the nucleosynthesis epoch that is larger than the current laboratory one. The level of statistical significance and the preferred extent of variation depend on model assumptions but the former can be more than four standard deviations, while the latter is always compatible with constraints at lower redshifts. If Lithium is not included in the analysis, the preference for a variation of $\alpha$ is not statistically significant. The abundance of ${}^3$He is relatively insensitive to such variations. Our analysis highlights a viable and physically motivated solution to the Lithium problem, which warrants further study.