Big bang nucleosynthesis and CMB constraints on dark energy

Current observational data favor cosmological models which differ from the standard model due to the presence of some form of dark energy and, perhaps, by additional contributions to the more familiar dark matter. Primordial nucleosynthesis provides a window on the very early evolution of the universe and constraints from big bang nucleosynthesis (BBN) can bound the parameters of models for dark matter or energy at redshifts of the order of ten billion. The spectrum of temperature fluctuations imprinted on the cosmic microwave background (CMB) radiation opens a completely different window on the universe at epochs from redshifts of the order of ten thousand to nearly the present. The CMB anisotropy spectrum provides constraints on new physics which are independent of and complementary to those from BBN. Here we consider three classes of models for the dark matter or energy: extra particles which were relativistic during the early evolution of the universe (``X'') ; quintessence models involving a minimally coupled scalar field (``Q'') ; models with a non-minimally coupled scalar field which modify the strength of gravity during the early evolution of the universe (``G''). We constrain the parameters of these models using data from BBN and the CMB and identify the allowed regions in their parameter spaces consistent with the more demanding joint BBN and CMB constraints. For ``X'' and ``Q'' such consistency is relatively easy to find; it is more difficult for the ``G'' models with an inverse power law potential for the scalar field.