  We consider a brane generated by a scalar field domain wall configuration in
4+1 dimensions, interpolating, in most cases, between two vacua of the field.
We study the cosmology of such a system in the cases where the effective
four-dimensional brane metric is de Sitter or anti de Sitter, including a
discussion of the bulk coordinate singularities present in the de-Sitter case.
We demonstrate that a scalar field kink configuration can support a brane with
dS$_4$ cosmology, despite the presence of coordinate singularities in the
metric. We examine the trapping of fermion fields on the domain wall for
nontrivial brane cosmology.
