We develop a fully covariant, well-posed $5D$ effective action for the $6D$ cascading gravity brane-world model, and use this to study cosmological solutions. We obtain this effective action through the $6D$ decoupling limit, in which an additional scalar degree mode, $\pi$, called the brane-bending mode, determines the bulk-brane gravitational interaction. The $5D$ action obtained this way inherits from the sixth dimension an extra $\pi$ self-interaction kinetic term. We compute appropriate boundary terms, to supplement the $5D$ action, and hence derive fully covariant junction conditions and the $5D$ Einstein field equations. Using these, we derive the cosmological evolution induced on a 3-brane moving in a static bulk. We study the strong- and weak-coupling regimes analytically in this static ansatz, and perform a complete numerical analysis of our solution. Although the cascading model can generate an accelerating solution in which the $\pi$ field comes to dominate at late times, the presence of a critical singularity prevents the $\pi$ field from dominating entirely. Our results open up the interesting possibility that a more general treatment of degravitation in a time-dependent bulk, or taking into account finite brane-thickness effects, may lead to an accelerating universe without a cosmological constant.

• Received 12 January 2010

DOI:https://doi.org/10.1103/PhysRevD.81.084020