  The braneworld cosmology, in which our universe is imbedded as a hypersurface
in a higher dimensional bulk, has the peculiar property that the inflationary
consistency relation derived in a four-dimensional cosmology persists. This
consistency condition relates the ratio of tensor and scalar perturbation
amplitudes to the tensor spectral index produced during an epoch of slow-roll
scalar field inflation. We attempt to clarify this surprising degeneracy. Our
argument involves calculating the power spectrum of scalar field fluctuations
around geometries perturbed away from the exact de Sitter case. This
calculation is expected to be valid for perturbations which would not cause a
late-time acceleration of the universe. We use these results to argue that the
emergence of the same consistency relation in the braneworld can be connected
with a specific property, that five-dimensional observables smoothly approach
their four-dimensional counterparts as one takes the brane to infinite tension.
We exhibit an explicit example where this does not occur, and in which a
consistency relation does not persist.
