  We present constraints on the number of relativistic species from a joint
analysis of cosmic microwave background (CMB) fluctuations and light element
abundances (helium and deuterium) compared to big bang nucleosynthesis (BBN)
predictions. Our BBN calculations include updates of nuclear rates in light of
recent experimental and theoretical information, with the most significant
change occuring for the d(p,gamma)^3He cross section. We calculate a likelihood
function for BBN theory and observations that accounts for both observational
errors and nuclear rate uncertainties and can be easily embedded in
cosmological parameter fitting. We then demonstrate that CMB and BBN are in
good agreement, suggesting that the number of relativistic species did not
change between the time of BBN and the time of recombination. The level of
agreement between BBN and CMB, as well as the agreement with the standard model
of particle physics, depends somewhat on systematic differences among
determinations of the primordial helium abundance. We demonstrate that
interesting constraints can be derived combining only CMB and D/H observations
with BBN theory, suggesting that an improved D/H constraint would be an
extremely valuable probe of cosmology.
