Wormhole surgery and cosmology on the brane: The world is not enough

We show that the 5-dimensional model introduced by Randall and Sundrum is (half of) a wormhole, and that this is a general result in models of the RS type. We also discuss the gravitational trapping of a scalar particle in 5-d spacetimes. Finally, we present a simple model of brane-world cosmology in which the background is a static anti-de Sitter manifold, and the location of the two 3-branes is determined by the technique of ``surgical grafting''.