  We investigate the effect of a variation of fundamental constants on
primordial element production in Big Bang nucleosynthesis (BBN). We focus on
the effect of a possible change in the nucleon-nucleon interaction on nuclear
reaction rates involving the A=5 (5Li and 5He) and A=8 (8Be) unstable nuclei.
The reaction rates for 3He(d,p)4He and 3H(d,n)4He are dominated by the
properties of broad analog resonances in 5Li and 5He compound nuclei
respectively. While the triple-alpha process 4He(aa,g)12C is normally not
effective in BBN, its rate is very sensitive to the position of the "Hoyle
state" and could in principle be drastically affected if 8Be were stable during
BBN. We found that the effect of the variation of constants on the 3He(d,p)4He,
3H(d,n)4He nd 4He(aa,g)12C reaction rates is not sufficient to induce a
significant effect on BBN, even with a stable 8Be. The main influences come
from the weak rates and the A=2, n(p,g)d, bottleneck reaction.
