A Signature of Higher Dimensions at the Cosmic Singularity

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 a simple derivation of the low-energy effective action for braneworlds, highlighting the role of conformal invariance, before showing how the effective action for a positiveand negative-tension brane pair may be improved using the AdS/CFT correspondence. We then solve for the cosmological perturbations in a five-dimensional background consisting of two separating or colliding boundary branes, as an expansion in the collision speed V divided by the speed of light c. Our solution permits a detailed check of the validity of fourdimensional effective theory in the vicinity of the event corresponding to the big crunch/big bang singularity. We show that the fourdimensional description fails at the first nontrivial order in (V/c). At this order, there is nontrivial mixing of the two relevant fourdimensional perturbation modes (the growing and decaying modes) as the boundary branes move from the narrowly-separated limit described by Kaluza-Klein theory to the well-separated limit where gravity is confined to the positive-tension brane. We highlight the implications of this result for cosmology, in particular for the propagation of a scale-invariant spectrum of density perturbations across the bounce in a big crunch/big bang universe. The generation of curvature perturbations on the brane is also examined from a five-dimensional perspective. Finally, as an application of our methods, we develop a new collidingbrane solution of the Hořava-Witten model of heterotic M-theory.