We show how to define a consistent braneworld cosmology in a model in which
the brane is constructed as a field-theoretic domain wall of finite thickness.
The Friedmann, Robertson-Walker metric is recovered in the region of the brane,
but, remarkably, with scale factor that depends on particle energy and on
particle species, constituting a breakdown of the weak equivalence principle on
sufficiently small scales. This unusual effect comes from the extended nature
of particles confined to a domain-wall brane, and the fact that they feel an
"average" of the bulk spacetime. We demonstrate how to recover the standard
results of brane cosmology in the infinitely-thin brane limit, and comment on
how our results have the potential to place bounds on parameters such as the
thickness of domain-wall braneworlds.Comment: 23 pages; v2 has additional references and reflects journal versio