Model independent predictions of Big Bang nucleosynthesis from $^{4}$He and $^{7}$Li consistency and implications

We examine in detail how BBN theory is constrained, and what predictions it can make, when using only the most model-independent observational constraints. We avoid the uncertainties and model-dependencies that necessarily arise when solar neighborhood D and \he3 abundances are used to infer primordial D and \he3 via chemical and stellar evolution models. Instead, we use \he4 and \li7, thoroughly examining the effects of possible systematic errors in each. Via a likelihood analysis, we find near perfect agreement between BBN theory and the most model-independent data. Given this agreement, we then {\it assume} the correctness of BBN to set limits on the single parameter of standard BBN, the baryon-to-photon ratio, and to predict the primordial D and \he3 abundances. We also repeat our analysis including recent measurements of D/H from quasar absorption systems and find that the near perfect agreement between theory and observation of the three isotopes, D, \he4 and \li7 is maintained. These results have strong implications for the chemical and stellar evolution of the light elements, in particular for \he3. In addition, our results (especially if the D/H measurements are confirmed) have implications for the stellar depletion of \li7. Finally, we set limits on the number \nnu\ of neutrino flavors, using an analysis which carefully and systematically includes all available experimental constraints. The value \nnu = 3.0 fits best with BBN and a 95\% CL upper limit of \nnu \la 4 is established.