  We consider the cosmology of a pair of domain walls bounding a
five-dimensional bulk space-time with negative cosmological constant, in which
the distance between the branes is not fixed in time. Although there are strong
arguments to suggest that this distance should be stabilized in the present
epoch, no such constraints exist for the early universe and thus non-static
solutions might provide relevant inflationary scenarios. We find the general
solution for the standard ansatz where the bulk is foliated by planar-symmetric
hypersurfaces. We show that in all cases the bulk geometry is that of anti-de
Sitter (AdS_5). We then present a geometrical interpretation for the solutions
as embeddings of two de Sitter (dS_4) surfaces in AdS_5, which provide a simple
interpretation of the physical properties of the solutions. A notable feature
explained in the analysis is that two-way communication between branes
expanding away from one another is possible for a finite amount of time, after
which communication can proceed in one direction only. The geometrical picture
also shows that our class of solutions (and related solutions in the
literature) are not completely general, contrary to some claims. We then derive
the most general solution for two walls in AdS_5. This includes novel
cosmologies where the brane tensions are not constrained to have opposite
signs. The construction naturally generalizes to arbitrary FRW cosmologies on
the branes.
