Junction conditions for Cascading branes

The 6D Cascading DGP model is a braneworld model with infinite extra dimensions which is believed to be able to realize the degravitation phenomenon, thereby explaining why a huge vacuum energy produces only a tiny curvature in our universe. In this model, our universe is a 4 dimensional (4D) brane embedded in a 5D brane, which in turn is embedded in a 6D bulk, both branes being equipped with induced gravity. A transparent study of its phenomenology is however problematic due to the well-known fact that the thin limit of codimension-2 branes is not well-defined.

We show that it is possible to define in a rigorous way the thin limit of this model, by assuming a suitable hierarchy between the overall thicknesses of the two branes. This assumption permits to perform the thin limit equations in two steps, the first step leading to the Israel junction conditions at the 5D brane for the bulk geometry, and the second step leading to new junction conditions at the 4D brane for the geometry of the 5D brane. We comment on the new perspectives that the knowledge of the thin limit equations opens up.