  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.
