Big Bang Nucleosynthesis Constraints on Universal Extra Dimensions and Varying Fundamental Constants

The successful prediction of light element abundances from Big Bang Nucleosynthesis has been a pillar of the standard model of Cosmology. Because many of the relevant reaction rates are sensitive to the values of fundamental constants, such as the fine structure constant and the strong coupling constant, BBN is a useful tool to probe and to put constraints on possible cosmological variations of these constants, which arise naturally from many versions of extra-dimensional theories. In this paper, we study the dependences of fundamental constants on the radion field of the universal extra dimension model, and calculate the effects of such varying constants on BBN. We show that the discrepancy between BBN and the Wilkinson Microwave Anisotropy Probe data on the baryon-to-photon ratio may be reduced if the volume of the extra dimensions was slightly larger - by $\mathcal{O} (10^{-3})$ - at the BBN era compared to its present value, which would result in smaller gauge couplings at BBN by the same factor.