General brane cosmologies and their global spacetime structure

Abstract

Starting from a completely general standpoint, we find the most general\nbrane-Universe solutions for a three-brane in a five dimensional spacetime. The\nbrane can border regions of spacetime with or without a cosmological constant.\nMaking no assumptions other than the usual cosmological symmetries of the\nmetric, we prove that the equations of motion form an integrable system, and\nfind the exact solution. The cosmology is indeed a boundary of a (class II)\nSchwarzschild-AdS spacetime, or a Minkowski (class I) spacetime. We analyse the\nvarious cosmological trajectories focusing particularly on those bordering\nvacuum spacetimes. We find, not surprisingly, that not all cosmologies are\ncompatible with an asymptotically flat spacetime branch. We comment on the role\nof the radion in this picture.\n