Nonlinear interactions of the radion field

We study the Randall-Sundrum model with two branes. The Standard Model fields are localized on the brane with a negative tension, the gravitational field and scalar Goldberg-Wise field propagate in the multidimensional bulk. For this model we construct the Lagrangian for the scalar fluctuations of the gravitational and scalar fields above a background solution. We obtain an effective four-dimensional Lagrangian, which contains nonlinear self-interaction terms of the radion field up to the fourth order and nonlinear interactions of the radion and the Standard Model fields