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Standard Big Bang Nucleosynthesis (SBBN) is a major success because the theory is well understood, close connections have developed between theory and observation, and observations are becoming more reliable.

The early attempts to include physics in the mathematical model of the expanding universe lead to an understanding of the creation of the elements and the development of standard big bang theory, including the predictions of the CMB.

The general success of SBBN is based on the robustness of the theory, and the resulting predictions of the abundances of the light nuclei. The abundances of 4He , 7Li and D can be explained with a single value for the free parameter eta , and the implied Omegab agrees with other estimates.

This agreement is used to limit physics beyond that in SBBN, including alternative theories of gravity, inhomogeneous baryon density, extra particles which were relativistic during BBN, and decays of particles after BBN. After decades owere f detailed study, no compelling major departures from SBBN have been found, and few departures are allowed.

Using SBBN predictions and measured abundances, we obtain the best estimates for the cosmological parameters eta and Omegab .

The abundances of D, 4He and 7Li have all been measured in gas where there has been little stellar processing. In all three cases, the observed abundance are near to the primordial value remaining after SBBN. The D/H measured toward QSOs has the advantage of simplicity: D is not made after BBN, there are no known ways to destroy D in the QSO absorbers, and D/H can be extracted directly from the ultraviolet spectra, without corrections. There are now three cases of low D/H which seem secure. There remains the possibility that D/H is high in other absorbers seen towards other QSOs, but such high D must be very rare because no secure cases have been found, yet they should be an order of magnitude easier to find than the examples which show low D.

We use low D/H as the best estimator of eta and the baryon density. SBBN then gives predictions of the abundance of the other light nuclei. These predictions suggest that Yp is high, as suggested by Izotov, Thuan and collaborators. Low D also implies that 7Li has been depleted by about a factor of two in the halo stars on the Spite plateau, which is more than some expect.

The high Omegab from SBBN plus low D/H is enough to account for about 1/8th of the gravitating matter. Hence the remaining dark matter is not baryonic, a result which was established decades ago using SBBN and D/H in the ISM.

The near coincidence in the mass densities of baryons and non-baryonic dark matter is perhaps explained if the dark matter is a supersymmetric neutralino [194].

At redshifts z appeq 3 the baryons are present and observed in IGM with an abundance similar to Omegab . Hence there was no dark, or missing baryonic matter at that time. Today the same is true in clusters of galaxies. Outside clusters the baryons are mostly unseen, and they may be hard to observe if they have been heated to 105 - 107 K by structure formation.

The number of free parameters in BBN has been decreasing over the years: Fermi & Terkovich gave nuclear reaction rates, the half-life of the neutron was measured, and then the number of families of neutrinos was measured. In standard BBN we are now left with one parameter, the baryon density, which is today measured with D/H using SBBN. When, in the next few years, this parameter is also measured, SBBN will have no free parameters. When free parameters can be adjusted to obtain consistency with the data, it is hard to tell if a hypothesis is correct. The agreement between SBBN theory and measurement has grown stronger over the decades, as more parameters were constrained by independent measurements, and abundance measurements improved. This is the most convincing evidence that BBN happened and has been understood.

This work was funded in part by grant G-NASA/NAG5-3237 and by NSF grants AST-9420443 and AST-9900842. We are grateful to Steve Vogt, the PI for the Keck HIRES instrument which enabled our work on D/H. Scott Burles and Kim Nollet kindly provided the figures for this paper. It is a pleasure to thank Scott Burles, Constantine Deliyannis, Carlos Frenk, George Fuller, Yuri Izotov, David Kirkman, Hannu Kurki-Suonio, Sergei Levshakov, Keith Olive, Jerry Ostriker, Evan Skillman, Gary Steigman and Trinh Xuan Thuan for suggestions and many helpful and enjoyable discussions. We thank the organizers of this meeting, Lars Bergstrom, Per Carlson & Claes Fransson for their gracious hospitality.

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