  We discuss observational constrains coming from supernovae Ia
\cite{Perlmutter99} imposed on the behaviour of the Randall-Sundrum models. In
the case of dust matter on the brane, the difference between the best-fit
general relativistic model with a $\Lambda$-term \cite{Perlmutter99} and the
best-fit brane models becomes detectable for redshifts $z > 0.6$. It is
interesting that brane models predict brighter galaxies for such redshifts
which is in agreement with the measurement of the $z = 1.7$ supernova
\cite{Riess01} and with the New Data from the High Z Supernovae Search Team
\cite{schmit02}. We also demonstrate that the fit to supernovae data can also
be obtained, if we admit the "super-negative" dark energy $p = - (4/3) \varrho$
on the brane, where the dark energy in a way mimics the influence of the
cosmological constant. It also appears that the dark energy enlarges the age of
the universe which is demanded in cosmology. Finally, we propose to check for
dark radiation and brane tension by the application of the angular diameter of
galaxies minimum value test.
