  We study the linearized metric perturbation corresponding to the radion for
the generalization of the five dimensional two brane setup of Randall and
Sundrum to the case when the curvature of each brane is locally constant but
non-zero. We find the wave fuction of the radion in a coordinate system where
each brane is sitting at a fixed value of the extra coordinate. We find that
the radion now has a mass$^2$, which is negative for the case of de Sitter
branes but positive for anti de Sitter branes. We also determine the couplings
of the radion to matter on the branes, and construct the four dimensional
effective theory for the radion valid at low energies. In particular we find
that in AdS space the wave function of the radion is always normalizable and
hence its effects, though small, remain finite at arbitrarily large brane
separations.

High Energy Physics - Theory