  The effect of variations of the fundamental nuclear parameters on big-bang
nucleosynthesis are modeled and discussed in detail taking into account the
interrelations between the fundamental parameters arising in unified theories.
Considering only \he4, strong constraints on the variation of the neutron
lifetime, neutron-proton mass difference are set. These constraints are then
translated into constraints on the time variation of the Yukawa couplings and
the fine structure constant. Furthermore, we show that a variation of the
deuterium binding energy is able to reconcile the \li7 abundance deduced from
the WMAP analysis with its spectroscopically determined value while maintaining
concordance with D and \he4. The analysis is strongly based on the potential
model of Flambaum and Shuryak that relates the binding energy of the deuteron
with the nucleon and $\sigma$ and $\omega$ mesons masses, however, we show that
an alternative approach that consists of a pion mass dependence necessarily
leads to equivalent conclusions.
