  We discuss the cosmology of a 3-brane embedded in a 5D bulk space-time with a
cosmological constant when an intrinsic curvature Ricci scalar is included in
the brane action. After deriving the `brane-Friedmann' equations for a Z_2
symmetrical metric, we focus on the case of a Minkowski bulk. We show that
there exist two classes of solutions, close to the usual
Friedmann-Lemaitre-Robertson-Walker cosmology for small enough Hubble radii.
When the Hubble radius gets larger one either has a transition to a fully 5D
regime or to a self-inflationary solution which produces a late accelerated
expansion. We also compare our results with a perturbative approach and
eventually discuss the embedding of the brane into the Minkowski space-time.
This latter part of our discussion also applies when no intrinsic curvature
term is included.
