Big Bang Nucleosynthesis Constraints and Light Element Abundance Estimates

To elucidate the significance of the effect of systematic uncertainties in light element abundance estimates on cosmological bounds derivable from Big Bang Nucleosynthesis (BBN) we present tables giving bounds on $\Omega_{baryon}$ and $N_{\nu}$ as one changes the limits on primordial \he and $^7$Li. This allows us to derive new relations between these estimates and constraints on $\Omega_{baryon}$ and $N_{\nu}$. For example, only if the helium mass fraction, $Y_p \ge .245$ does $^7$Li (or D) presently play a role in placing an upper limit on the baryon density, and only if $Y_p \ge .250$ does $^4$He cease to play a role in bounding $\etaten$. All the elements combine together tend to give a stringent upper bound of $0.16$ on $\Omega_{baryon}$. We also find that $Y_p$ must exceed .239 for consistency between theory and observation if D+$^3$He/H is less than $ 10^{-4}$. Updated nuclear reaction rates, an updated neutron half life, Monte Carlo techniques, and correlations between the predicted abundances are incorporated in our analysis. We also discuss the handling of systematic uncertainties in the context of statistical analyses of BBN predictions.