Static brane solutions stabilized by nonlinear bulk scalar dynamics

Abstract

We study a nonlinear sigma-model-like theory of a bulk scalar field coupled to the five-dimensional Einstein gravity with a negative cosmological constant. We determine the structure of the non-factorizable spacetime which our Minkowskian brane bounds, when the pressure in the extra dimension is proportional to the energy density of the scalar field as (p) over tilde (5) = omega(5)(rho) over tilde. with a constant omega(5). With these static solutions clarified by the parameter omega(5), we fix the size of the extra dimension in terms of the bulk and brane potentials of the scalar field, imposing the stability condition in the cases of the 2-branes. The hierarchy problem is discussed in their Randall-Sundrum-like limit, and one of the static solutions obtained in the case of a strong bulk potential omega(5) < 0 is interpreted as a thick 1-brane model.