The consistency relation in braneworld inflation

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.