  We discuss isotropic and homogeneous D-brane-world cosmology with non-Abelian
Born-Infeld (NBI) matter on the brane. In the usual Friedmann-Robertson-Walker
(FRW) model the scale non-invariant NBI matter gives rise to an equation of
state which asymptotes to the string gas equation $p=-\epsilon/3$ and ensures a
start-up of the cosmological expansion with zero acceleration. We show that the
same state equation in the brane-world setup leads to the Tolman type evolution
as if the conformal symmetry was effectively restored. This is not precisely so
in the NBI model with symmetrized trace, but the leading term in the expansion
law is still the same. A cosmological sphaleron solution on the D-brane is
presented.
