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We study the linearized metric perturbation corresponding to the radion forthe generalization of the five dimensional two brane setup of Randall andSundrum to the case when the curvature of each brane is locally constant butnon-zero. We find the wave fuction of the radion in a coordinate system whereeach brane is sitting at a fixed value of the extra coordinate. We find thatthe radion now has a mass$^2$, which is negative for the case of de Sitterbranes but positive for anti de Sitter branes. We also determine the couplingsof the radion to matter on the branes, and construct the four dimensionaleffective theory for the radion valid at low energies. In particular we findthat in AdS space the wave function of the radion is always normalizable andhence its effects, though small, remain finite at arbitrarily large braneseparations.Comment: Version which appears in Phys. Rev.

Wave function of the radion in the dS and AdS brane worlds