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The effect of variations of the fundamental nuclear parameters on big-bangnucleosynthesis are modeled and discussed in detail taking into account theinterrelations between the fundamental parameters arising in unified theories.Considering only \he4, strong constraints on the variation of the neutronlifetime, neutron-proton mass difference are set. These constraints are thentranslated into constraints on the time variation of the Yukawa couplings andthe fine structure constant. Furthermore, we show that a variation of thedeuterium binding energy is able to reconcile the \li7 abundance deduced fromthe WMAP analysis with its spectroscopically determined value while maintainingconcordance with D and \he4. The analysis is strongly based on the potentialmodel of Flambaum and Shuryak that relates the binding energy of the deuteronwith the nucleon and $\sigma$ and $\omega$ mesons masses, however, we show thatan alternative approach that consists of a pion mass dependence necessarilyleads to equivalent conclusions.Comment: 12 pages, 6 figures. Revised sensitivity of B_D with the fundamental  parameters. Added section on the sensitivity of B_D with the pion mass.  Conclusions unchange

Coupled variations of fundamental couplings and primordial nucleosynthesis