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Given the standard models of cosmology and particle physics, SBBN predicts the primordial abundances of D, 3He, 4He, and 7Li, which may be compared with the observational data. Of the light nuclides, deuterium is the baryometer of choice, while 4He is an excellent chronometer. The universal density of baryons inferred from SBBN and the adopted primordial D abundance is in excellent (exact!) agreement with that derived from non-BBN, mainly CBR data (Spergel et al. 2003): eta10(SBBN) = 6.10+0.67-0.52; eta10(CBR) = 6.14 ± 0.25. For this baryon density, the predicted primordial abundance of 3He is also in excellent agreement with the (very uncertain) value inferred from observations of an outer-Galaxy HII region (Bania et al. 2002). In contrast, the SBBN-predicted mass fraction of 4He for the concordant baryon density is YP = 0.248 ± 0.001, while that inferred from observations of recombination lines in metal-poor, extragalactic HII regions is lower (Olive et al. 2000): YPobs = 0.238 ± 0.005. Since the uncertainties in the observationally inferred primordial value are likely dominated by systematics, this ~ 2sigma difference may not be cause for (much) concern. Finally, there appears to be a more serious issue concerning the predicted and observed lithium abundances. While the predicted abundance is [Li]P approx 2.6 ± 0.1, current observations of metal-poor halo stars suggest a considerably smaller value approx 2.2 ± 0.1.

It has been seen that the tension between D and 4He (or between the baryon density and 4He) can be relieved by either of two variations of the standard model (slower than standard early expansion rate; nonzero chemical potential for the electron neutrino). However, in neither of these cases does the BBN-predicted 7Li abundance move any closer to that inferred from the observations.

In the current, data-rich era of cosmological research, BBN continues to play an important role. The spectacular agreement in the baryon density inferred from processes occurring at widely separated epochs confirms the general features of the standard models of cosmology and particle physics. The tensions with 4He and 7Li provide challenges, and opportunities, to cosmology, to astrophysics, and to particle physics. To outline these challenges and opportunities, let us consider each of the light nuclides in turn.

For deuterium the agreement between SBBN and non-BBN determinations is perfect. This may be surprising given the unexpectedly large dispersion among the handful of extant D abundance determinations at high redshifts and low metallicities. Here, the challenge is to observers and theorists. Clearly more data are called for. Perhaps new data will reduce the dispersion. In that case it can be anticipated that the SBBN-predicted baryon density will approach the accuracy of that currently available from non-BBN data. On the other hand, newer data may support the dispersion, suggesting unexpectedly large variations in the D abundance at evolutionary times earlier than expected (Jedamzik & Fuller 1997). Perhaps there is more to be learned about early chemical evolution.

From studies of 3He in Galactic HII regions (Balser et al. 1997; Bania et al. 2002) it appears that in the course of Galactic chemical evolution there has been a very delicate balance between post-BBN production and destruction. If either had dominated, a gradient of the 3He abundance with galactocentric distance should have been seen in the data (see Romano et al. 2003, and references therein). So far, none is. Clearly, more data and a better understanding of the lower mass stars, which should dominate the production and destruction of 3He, would be of value.

The very precise value of the baryon density inferred either from D and SBBN or from non-BBN data, coupled with the very weak dependence of the SBBN abundance of 4He on the baryon density, leads to a very precise prediction of its primordial mass fraction. Although there exists a very large data set of 4He abundance determinations, the observational situation is confused at present. It seems clear that while new data would be valuable, quality is much more important than quantity. Data that can help resolve various corrections for temperature, for temperature and density fluctuations, for ionization corrections, would be of greater value than merely collecting more data that are incapable of addressing these issues. Because of the very large data set(s), the statistical uncertainty in the derived primordial mass fraction is very small, sigmaYP approx 0.002 - 0.003, while uncertain systematic corrections are much larger gtapprox 0.005. At this point it is systematics, not statistics that dominate the uncertainty in the primordial helium abundance. In this context it is worth considering non-emission line observations that might provide an independent abundance determination. Just such an alternative, the so-called R-parameter method using globular cluster stars was proposed long ago by Iben (1968) and by Iben & Faulkner (1968). It too has many systematic uncertainties associated with its application, but they are different from those for the emission-line studies. Very recently, Cassisi, Salaris, & Irwin (2003), using new stellar models and nuclear reactions rates, along with better data, find YP = 0.243 ± 0.006. This is in much better agreement with the expected value (within ltapprox 1sigma) and should stimulate further investigations.

The apparent conflict between the predicted and observed abundances of 7Li, if not simply traceable to the statistical and systematic uncertainties, suggests a gap in our understanding of the structure and evolution of the very old, metal-poor, halo stars. It would appear from the comparison between the predicted and observed abundances that lithium may have been depleted or diluted from the surfaces of these stars by ~ 0.2 - 0.4 dex. Although a variety of mechanisms for depletion/dilution exist, the challenge is to account for such a large reduction without at the same time producing a large dispersion around the Spite plateau.

The wealth of observational data accumulated over the last decade or more have propelled the study of cosmology from youth to maturity. BBN has played, and continues to play, a central role in this process. There have been many successes, but much remains to be done. Whether the resolution of the current challenges are observational or theoretical, the future is bright.

Acknowledgements I am grateful to all the colleagues with whom I have worked, in the past as well as at present, for all I have learned from them; I thank them all. Many of the quantitative results (and figures) presented here are from recent collaborations with V. Barger, J. P. Kneller, J. Linsky, D. Marfatia, K. A. Olive, R. J. Scherrer, S. M. Viegas, and T. P. Walker. I thank V. V. Smith for permission to use Figure 9. My research is supported at OSU by the DOE through grant DE-FG02-91ER40690.

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