  We study a Randall-Sundrum cosmological scenario consisting of a domain wall
in anti-de Sitter space with a strongly coupled large $N$ conformal field
theory living on the wall. The AdS/CFT correspondence allows a fully quantum
mechanical treatment of this CFT, in contrast with the usual treatment of
matter fields in inflationary cosmology. The conformal anomaly of the CFT
provides an effective tension which leads to a de Sitter geometry for the
domain wall. This is the analogue of Starobinsky's four dimensional model of
anomaly driven inflation. Studying this model in a Euclidean setting gives a
natural choice of boundary conditions at the horizon. We calculate the graviton
correlator using the Hartle-Hawking ``No Boundary'' proposal and analytically
continue to Lorentzian signature. We find that the CFT strongly suppresses
metric perturbations on all but the largest angular scales. This is true
independently of how the de Sitter geometry arises, i.e., it is also true for
four dimensional Einstein gravity. Since generic matter would be expected to
behave like a CFT on small scales, our results suggest that tensor
perturbations on small scales are far smaller than predicted by all previous
calculations, which have neglected the effects of matter on tensor
perturbations.
