Scalar-tensor gravity in a two 3-brane system

We derive the low-energy effective action of four-dimensional gravity in the Randall-Sundrum scenario in which two 3-branes of opposite tension reside in a five-dimensional spacetime. The dimensional reduction with the Ansatz for the radion field of Charmousis. Gregory, and Rubakov, which solves five-dimensional linearized field equations, results in a class of scalar-tensor gravity theories. In the limit of vanishing radion fluctuations, the effective action reduces to the Brans-Dicke gravity in accord with the results of Garriga and Tanaka: Brans-Dicke gravity with the corresponding Brans-Dicke parameter 0 < omega < infinity (for positive tension brane) and -3/2 < omega < 0 (for negative tension brane). In general the gravity induced brane belongs to a class of scalar-tensor gravity with the Brans-Dicke parameter which is a function of the interval and the radion. In particular, gravity on a positive tension brane contains an attractor mechanism toward the Einstein gravity.