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1. INTRODUCTION

The early Universe was hot and dense behaving as a cosmic nuclear reactor during the first twenty minutes of its evolution. It was, however, a ``defective'' nuclear reactor, expanding and cooling very rapidly. As a result, only a handful of the lightest nuclides were synthesized before the density and temperature dropped too low for the nuclear reaction rates to compete with the universal expansion rate. After hydrogen (1H ident protons) the next most abundant element to emerge from the Big Bang is helium (4He ident alpha particles). Isotopes of these nuclides (deuterium and helium-3) are the next most abundant primordially. Then there is a large gap to the much lower abundance of lithium-7. The relative abundances of all other primordially-produced nuclei are very low, much smaller than their locally observed (or, presently observable!) abundances. After a brief description of the early evolution of the Universe emphasizing those aspects most relevant to primordial, or ``Big Bang'' nucleosynthesis (BBN), the predicted abundances of the light nuclides will be presented as a function of the one ``free'' parameter (in the simplest, ``standard'' model: SBBN), the nucleon (or ``baryon'') abundance. Then, each element will be considered in turn in a confrontation between the predictions of SBBN and the observational data. At present (Summer 1999) there is remarkable agreement between the SBBN predictions of the abundances of four nuclides (D, 3He, 4H3, and 7Li) and their primordial abundances inferred from the observations. However, there are some hints that this concordance of the hot big bang model may be imperfect, so we will also explore some variations on the theme of the standard model with regard to their modifications of the predicted primordial abundances of the light elements.

In the simplest, standard, hot big bang model the currently observed large-scale isotropy and homogeneity of the Universe is assumed to apply during earlier epochs in its evolution. Given the currently observed universal expansion and the matter and radiation (CBR: ``cosmic background radiation'', the 2.7K ``black body radiation'') content, it is a straightforward application of classical physics to extrapolate back to earlier epochs in the history of the Universe. At a time of order 0.1 s after the expansion began the Universe was filled with a hot, dense plasma of particles. The most abundant were photons, electron-positron pairs, particle-antiparticle pairs of all known ``flavors'' of neutrinos (nue, nuยต, and nutau), and trace amounts of neutrons and protons (``nucleons'' or ``baryons''). At such early times the thermal energy of these particles was very high, of order a few MeV. With the exception of the nucleons, it is known or assumed that all the other particles present were extremely relativistic at this time. Given their high energies (and velocities close to, or exactly equal to the speed of light) and high densities, the electroweak interactions among these particles were sufficiently rapid to have established thermal equilibrium. As a result, the numbers and distributions (of momentum and energy) of all these particles is accurately predicted by well-known physics.

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