Radion effective potential in the Brane-World

We show that in brane-world scenarios with warped extra dimensions, the Casimir force due to bulk matter fields may be sufficient to stabilize the radion field $\phi$. In particular, we calculate one loop effective potential for $\phi$ induced by bulk gravitons and other possible massless bulk fields in the Randall-Sundrum background. This potential has a local extremum, which can be a maximum or a minimum depending on the detailed bulk matter content. If the parameters of the background are chosen so that the hierarchy problem is solved geometrically, then the radion mass induced by Casimir corrections is hierarchycally smaller than the $TeV$. Hence, in this important case, we must invoke an alternative mechanism (classical or nonperturbative) which gives the radion a sizable mass, to make it compatible with observations.