Generalizations of the Randall-Sundrum model containing a bulk scalar field $\Phi$ interacting with the curvature R through the general coupling $Rf\left(\Phi \right)$ are considered. We derive the general form of the effective 4D potential for the spin-zero fields and show that in the mass matrix the radion mixes with the Kaluza-Klein (KK) modes of the bulk scalar fluctuations. We demonstrate that it is possible to choose a nontrivial background form ${\Phi }_0\mathrm{}\left(y\right)\mathrm{}$ (where y is the extra dimension coordinate) for the bulk scalar field such that the exact Randall-Sundrum metric is preserved (i.e. such that there is no back reaction). We compute the mass matrix for the radion and the KK modes of the excitations of the bulk scalar relative to the background configuration ${\Phi }_0\mathrm{}\left(y\right).$ We find that for any (consistent) ${\Phi }_0\mathrm{}\left(y\right)\mathrm{}$ the expected mass for the radionlike eigenstate is suppressed relative to the Planck scale by the standard warp factor needed to explain the hierarchy puzzle, implying that $\sim 1\mathrm{TeV}$ is a natural order of magnitude for this mass. The general considerations are illustrated in the case of a model containing an $R{\Phi }^2$ interaction term.

• Received 5 May 2003

DOI:https://doi.org/10.1103/PhysRevD.68.055002