We study the dynamics of branes in configurations where 1) the brane is the edge of a single anti-de Sitter (AdS) space and 2) the brane is the surface of a vacuum bubble expanding into a Schwarzschild or AdS-Schwarzschild bulk. In both cases we find solutions that resemble the standard Robertson-Walker cosmologies although in the latter, the evolution can be controlled by a mass parameter in the bulk metric. We also include a term in the brane action for the scalar curvature. This term adds a contribution to the low energy theory of gravity which does not need to affect the cosmology but which is necessary for the surface of the vacuum bubble to recover four dimensional gravity.

13 pages, uses harvmac, vacuum bubble case corrected and expanded, references added