In this thesis we study the dynamics of higher-dimensional gravity in a universe emerging from a brane collision. We develop a set of powerful analytic methods which, we believe, render braneworld cosmological perturbation theory solvable. Our particular concern is to determine the extent to which the four-dimensional effective theory accurately captures the higher-dimensional dynamics about the cosmic singularity. We begin with an overview of the generation of primordial density perturbations, both in inflation and in the ekpyrotic mechanism, followed by an introduction to braneworld cosmology. A simple derivation of the low-energy effective action for braneworlds is presented, highlighting the role of conformal invariance. We then solve for cosmological perturbations in a five-dimensional background consisting of two separating or colliding boundary branes, as an expansion in the collision rapidity. We show that the four-dimensional effective description fails at first non-trivial order in this expansion, and highlight the implications for cosmology. Finally, we extend our methods to find a colliding brane solution of heterotic M-theory.