  We obtain a class of solutions for the AdS$_5$ two-brane models by imposing
the observed value of cosmological constant and Newton coupling constant on the
visible brane. When all terms up to the first order of matter density are
included, the cosmological evolution on the observable brane depends on the
equation of state of the matter and consequently when the pressure exists, the
cosmology of these models deviates from FLRW cosmology. We show that it is
possible to choose the matter equation of state on the hidden brane to
neutralize its contribution on the cosmological evolution of the visible brane.
We compare the prediction of these models for primordial {\it $^4$He} yield
with observations. In standard BBN with $n_{\nu}^{light} = 3$ this brane model
is ruled out. If in addition to 3 SM neutrinos there is one light sterile
neutrino, this model reconciles the observed {\it $^4$He} yield with a high
${\Omega}_b \sim 0.033 h^{-2}$ suggested by BOOMERANG and MAXIMA experiments.
