Constraining the variation of the coupling constants with big bang nucleosynthesis

We consider the possibility of the coupling constants of the $\mathrm{SU}\mathrm{}\left(3\right)\mathrm{}\times \mathrm{SU}\mathrm{}\left(2\right)\mathrm{}\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ gauge interactions at the time of big bang nucleosynthesis having taken different values from those we measure at present, and investigate the allowed difference requiring the shift in the coupling constants not to violate the successful calculation of the primordial abundances of the light elements. We vary the gauge couplings and Yukawa couplings (fermion masses) within the context of a model in which their relative variations are governed by a single scalar field, the dilaton, as found in string theory. The results include a limit on the fine structure constant $-6.0\times {10}^{-4}<\Delta {\alpha }_{\mathrm{e}.\mathrm{m}.\mathrm{}}/{\alpha }_{\mathrm{e}.\mathrm{m}.\mathrm{}}<1.5\mathrm{}\times {10}^{-4},$ which is two orders of magnitude stricter than the limit obtained by considering the variation of ${\alpha }_{\mathrm{e}.\mathrm{m}.\mathrm{}}$ alone.