Gravity in the brane-world for two-branes model with stabilized modulus

We present a complete scheme to discuss linear perturbations in the two-branes model of thr: Randall and Sundrum scenario with the stabilization mechanism proposed by Goldberger and Wise. We confirm that under the approximation of zero-mode truncation the induced metric on the branes reproduces that of the usual 3-dimensional Einstein gravity. We also present formulas to evaluate the mass spectrum and the contribution to the metric perturbations from all the Kaluza-Klein modes, We also conjecture that the model has tachyonic modes unless the background configuration for the bulk scalar held introduced to stabilize the distance between the two branes is monotonic in the fifth dimension. (C) 2000 Elsevier Science B.V, All rights reserved.