  We analyze the observational constraints on brane-world cosmology whereby the
universe is described as a three-brane embedded in a five-dimensional anti-de
Sitter space.
  In this brane-universe cosmology, the Friedmann equation is modified by the
appearance of extra terms which derive from existence of the extra dimensions.
  In the present work we concentrate on the ``dark radiation'' term which
diminishes with cosmic scale factor as $a^{-4}$.
  We show that, although the observational constraints from primordial
abundances allow only a small contribution when this term is positive, a much
wider range of negative values is allowed. Furthermore, such a negative
contribution can reconcile the tension between the observed primordial $\he4$
and D abundances.
  We also discuss the possible constraints on this term from the power spectrum
of CMB anisotropies in the limit of negligible cosmological perturbation on the
brane world. We show that BBN limits the possible contribution from dark
radiation just before the nucleosynthesis epoch to lie between -65% and $+5%$
of the background photon energy density. Combining this with the CMB constraint
reduces this range to between -24% and $+3.5%$ at the $2\sigma$ confidence
level.
