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Vacuum Expectation Value Profiles of the Bulk Scalar Field in the Generalized Randall-Sundrum Model

In the generalized Randall-Sundrum warped brane-world model the cosmological constant induced on the visible brane can be positive or negative. In this paper we investigate profiles of vacuum expectation value of the bulk scalar field under general Dirichlet andNeumann boundary conditions in the generalized warped brane-worldmodel.We showthat the VEVprofiles generally depend on the value of the brane cosmological constant. We find that the VEV profiles of the bulk scalar field for a visible brane with negative cosmological constant and positive tension are quite distinct fromthose of Randall-Sundrum model. In addition we show that the VEV profiles for a visible brane with large positive cosmological constant are also different from those of the Randall- Sundrum model.We also verify that Goldberger andWise mechanism can work under nonzero Dirichlet boundary conditions in the generalized Randall-Sundrum model.