No 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 p5 = ω 5 ρ with a constant ω 5 . With these static solutions clarified by the parameter ω 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 ω 5 < 0 is interpreted as a thick 1-brane model.

We consider a nonlinear sigma-model-like theory of bulk scalar fields coupled to the five-dimensional Einstein gravity. In Robertson–Walker spacetimes, we find some power-law cosmological solutions for the scale factor when the expansion rate of an extra dimension is proportional to one of our (3+1)-dimensional universe. Among them, the solution with a decreasing warp factor could be related to the one-brane model of Randall and Sundrum.