Inflationary solutions in the brane world and their geometrical interpretation

We consider the cosmology of a pair of domain walls bounding a five-dimensional bulk space-time with a 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 ( AdS5) space. We then present a geometrical interpretation for the solutions as embeddings of two de Sitter (dS4) surfaces in AdS5, 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) is not completely general, contrary to some claims. We then derive the most general solution for two walls in AdS3. 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.