Big Bang Nucleosynthesis with Stable $^8$Be and the Primordial Lithium
  Problem
  A change in the fundamental constants of nature or plasma effects in the
early universe could stabilize $^8$Be against decay into two $^4$He nuclei. Coc
et al. examined this effect on big bang nucleosynthesis as a function of $B_8$,
the mass difference between two $^4$He nuclei and a single $^8$Be nucleus, and
found no effects for $B_8 \le 100$ keV. Here we examine stable $^8$Be with
larger $B_8$ and also allow for a variation in the rate for $^4$He + $^4$He
$\longrightarrow$ $^8$Be to determine the threshold for interesting effects. We
find no change to standard big bang nucleosynthesis for $B_8 < 1$ MeV. For $B_8
\gtrsim 1$ MeV and a sufficiently large reaction rate, a significant fraction
of $^4$He is burned into $^8$Be, which fissions back into $^4$He when $B_8$
assumes its present-day value, leaving the primordial $^4$He abundance
unchanged. However, this sequestration of $^4$He results in a decrease in the
primordial $^7$Li abundance. Primordial abundances of $^7$Li consistent with
observationally-inferred values can be obtained for reaction rates similar to
those calculated for the present-day (unbound $^8$Be) case. Even for the
largest binding energies and largest reaction rates examined here, only a small
fraction of $^8$Be is burned into heavier elements, consistent with earlier
studies. There is no change in the predicted deuterium abundance for any model
we examined.
