Brane versus shell cosmologies in Einstein and Einstein-Gauss-Bonnet theories

We first give a simple example of how, in existing brane cosmological models, the connection of a “bulk” region to its mirror image creates matter on the “brane.” Next, we present a cosmological model with no $Z_2$ symmetry which is a spherical symmetric “shell” separating two metrically different five-dimensional anti–de Sitter regions. We find that our model becomes Friedmannian at late times, like the present brane models, but that its early time behavior is very different: the scale factor grows from a nonzero value at the big bang singularity. We then show how the Israel matching conditions across the membrane (which is either a brane or a shell) have to be modified if more general equations than Einstein’s, including a Gauss-Bonnet correction, hold in the bulk, as is likely to be the case in the low energy limit of string theory. We find that the membrane can then no longer be treated in the thin wall approximation. However, its microphysics may, in some instances, simply be hidden in a renormalization of Einstein’s constant, in which case Einstein and Gauss-Bonnet membranes are identical.