Big-bang nucleosynthesis plays a crucial role in shaping some of the new cosmological paradigms which have emerged in the past few years. In this paper we summarize the particular limits which primordial nucleosynthesis places on the nature and origin of the cosmic quintessence vacuum energy, along with its associated quintessential inflation mechanism. We also describe some constraints on the possible effects of higher-dimensional brane-world physics. The importance of eliminating the remaining uncertainties in nuclear reactions and the inferred primordial abundances is highlighted.
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