We derive the second variation Lagrangian of the Randall -Sundrum model with two branes, study its gauge invariance and diagonalize it in the unitary gauge. We also show that the effective fourdimensional theory looks different on different branes and calculate the observable mass spectra and the couplings of the physical degrees of freedom of 5-dimensional gravity to matter.

We consider brane world models with interbrane separation stabilized by the Goldberger-Wise scalar field. For arbitrary background, or vacuum configurations of the gravitational and scalar fields in such models, we construct the second variation Lagrangian, study its gauge invariance, find the corresponding equations of motion and decouple them in a suitable gauge. We also derive an effective four-dimensional Lagrangian for such models, which describes the massless graviton, a tower of massive gravitons and a tower of massive scalars. It is shown that for a special choice of the background solution the masses of the graviton excitations may be of the order of a few TeV, the radion mass of the order of 100 GeV, the inverse size of the extra dimension being tens of GeV. In this case the coupling of the radion to matter on the negative tension brane is approximately the same as in the unstabilized model with the same values of the fundamental five-dimensional energy scale and the interbrane distance.

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We consider brane world models, which can be constructed in the five-dimensional Brans-Dicke theory with bulk scalar field potentials suggested by the supergravity theory. For different choices of the potentials and parameters we get: (i) an unstabilized model with the Randall-Sundrum solution for the metric and constant solution for the scalar field; (ii) models with flat background and tension-full branes; (iii) stabilized brane world models, one of which reproduces the Randall-Sundrum solution for the metric and gives an exponential solution for the scalar field. We also discuss the relationship between solutions in different frames -with non-minimal and minimal coupling of the scalar field.

Brane world gravity looks different for observers on positive and negative tension branes. First we consider the well-known RS1 model with two branes embedded into the AdS_5 space-time and recall the results on the relations between the energy scales for an observer on the negative tension brane, which is supposed to be "our" brane. Then from the point of view of this observer we study energy scales and masses for the radion and graviton excitations in a stabilized brane world model. We argue that there may be several possibilities leading to scales of the order 1-10 TeV or even less for new physics effects on our brane. In particular, an interesting scenario can arise in the case of a "symmetric" brane world with a nontrivial warp factor in the bulk, which however takes equal values on both branes.Comment: 15 pages, corrected typos, enlarged conten