Scalar-Tensor Gravity in Two 3-brane System

We derive the effective four-dimensional gravity action in the RandallSundrum scenario in which two 3-branes of opposite tension reside in a fivedimensional spacetime. The dimensional reduction with the Ansatz for the radion field by Charmousis et al., 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 < ω < ∞ (for positive tension brane) and −3/2 < ω < 0 (for negative tension brane). In general the gravity induced a 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. ∗Electronic address: [email protected], JSPS research fellow.