We argue that the four-dimensional universe on the TeV brane of the Randall
- Sundrum scenario takes the bimetric structure of Clayton and Moffat, wit
h gravitons traveling faster than photons instead, while the radion varies
with time. We show that such a brane world bimetric model can thereby solve
the flatness and cosmological constant problems, provided the speed of a g
raviton decreases to the present day value rapidly enough. The resolution o
f other cosmological problems such as the horizon problem and the monopole
problem requires supplementation by inflation, which may be achieved by the
radion field provided the radion potential satisfies the slow-roll approxi
mation.