Primordial nucleosynthesis with varying fundamental constants: Degeneracies with cosmological parameters

Abstract: The success of primordial nucleosynthesis as a cornerstone of the hot Big Bang model has been limited by the long-standing lithium problem. Recent work presented a self-consistent perturbative analysis of the effects of variations in nature's fundamental constants on primordial nucleosynthesis for a broad class of grand unified theory models, showing that such models provide a possible solution to the lithium problem, provided the value of the fine-structure constant $\alpha$ at the nucleosynthesis epoch is larger than the current laboratory one by a few parts per million of relative variation. Here we extend the earlier analysis, focusing on how this preferred value of $\alpha$ is affected if relevant cosmological parameters are also allowed to vary--specifically focusing on the baryon-to-photon ratio, the number of neutrinos, and the neutron lifetime. We rephrase the lithium problem in terms of the values of these parameters that would be needed to solve it within this class of grand unified theories, thus obtaining values that would disagree with the results of other experiments by several standard deviations. Using these experimental results as priors in the analysis, we find that a larger value of $\alpha$ is still preferred, confirming our previous results. By excluding lithium from the analysis, we also obtain upper limits on possible variations of $\alpha$ at the primordial nucleosynthesis epoch. At the two-sigma level, these are $|\Delta\alpha/\alpha|<50$ ppm without nuclear physics, cosmology, or atomic clocks priors, or alternatively $|\Delta\alpha/\alpha|<5$ ppm if these priors are used. While the simplest solution to the lithium problem is likely to be found within observational astrophysics, our work shows that varying fundamental constants remain a viable alternative.