Cosmology on a brane in Minkowski bulk

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 Z2 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–Lemaı̂tre–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.