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Using the semi-analytic method proposed by \citet{Esma91} we calculate theabundances of the light elements produced during primordial nucleosynthesisassuming that the gauge coupling constants of the fundamental interactions mayvary. We analyze the dependence of the nucleon masses, nuclear binding energiesand cross sections involved in the calculation of the abundances with thefundamental constants assuming the chiral limit of QCD. The abundances of lightelements as a function of the fundamental constants are obtained. Finally,using the observational data of $\De$, $\Het$, $\He$ and $\Li$ we estimateconstraints on the variation of the fundamental constants between theprimordial nucleosynthesis and the present. All observational abundances andthe WMAP estimate of the baryon density, can be fitted to the theoreticalpredictions with varying coupling constants. The possible systematic errors inthe observational data, precludes from stronger conclusions.

Primordial Nucleosynthesis with Varying Fundamental Constants: A Semianalytical Approach