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We consider the cosmology of a pair of domain walls bounding afive-dimensional bulk space-time with negative cosmological constant, in whichthe distance between the branes is not fixed in time. Although there are strongarguments to suggest that this distance should be stabilized in the presentepoch, no such constraints exist for the early universe and thus non-staticsolutions might provide relevant inflationary scenarios. We find the generalsolution for the standard ansatz where the bulk is foliated by planar-symmetrichypersurfaces. We show that in all cases the bulk geometry is that of anti-deSitter (AdS_5). We then present a geometrical interpretation for the solutionsas embeddings of two de Sitter (dS_4) surfaces in AdS_5, which provide a simpleinterpretation of the physical properties of the solutions. A notable featureexplained in the analysis is that two-way communication between branesexpanding away from one another is possible for a finite amount of time, afterwhich communication can proceed in one direction only. The geometrical picturealso shows that our class of solutions (and related solutions in theliterature) are not completely general, contrary to some claims. We then derivethe most general solution for two walls in AdS_5. This includes novelcosmologies where the brane tensions are not constrained to have oppositesigns. The construction naturally generalizes to arbitrary FRW cosmologies onthe branes.Comment: 24 pages, 9 figure

Inflationary solutions in the brane world and their geometrical interpretation