Modeling the fifth dimension with scalars and gravity

A method for obtaining solutions to the classical equations for scalars plus gravity in five dimensions is applied to some recent suggestions for brane-world phenomenology. The method involves only first order differential equations. It is inspired by gauged supergravity but does not require supersymmetry. Our first application is a full nonlinear treatment of a recently studied stabilization mechanism for interbrane spacing. The spacing is uniquely determined after conventional fine-tuning to achieve a zero four-dimensional cosmological constant. If the fine-tuning is imperfect, there are solutions in which the four-dimensional branes are de Sitter or anti--de Sitter spacetimes. Our second application is a construction of smooth domain wall solutions which in a well-defined limit approach any desired array of sharply localized positive-tension branes. As an offshoot of the analysis we suggest a construction of a supergravity c function for nonsupersymmetric four-dimensional renormalization group flows. The equations for fluctuations about an arbitrary scalar-gravity background are also studied. It is shown that all models in which the fifth dimension is effectively compactified contain a massless graviton. The graviton is the constant mode in the fifth dimension. The separated wave equation can be recast into the form of supersymmetric quantum mechanics. The graviton wave function is then the supersymmetric ground state, and there are no tachyons.