Abstract
Starting from a completely general standpoint, we find themost general brane-universe solutions for a 3-brane in afive-dimensional spacetime. The brane can border regions ofspacetime with or without a cosmological constant. Making noassumptions other than the usual cosmological symmetries ofthe metric, we prove that the equations of motionform an integrable system, and find the exact solution. The cosmology isindeed a boundary of a (class II) Schwarzschild-AdS spacetime, or aMinkowski (class I) spacetime. We analyse the various cosmologicaltrajectories focusing particularly on those bordering vacuum spacetimes.We find, not surprisingly, that not all cosmologies are compatible withan asymptotically flat spacetime branch. We comment on the role of theradion in this picture.
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