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 non-linear treatment of a recently studied stabilization mechanism for inter-brane spacing. The spacing is uniquely determined after conventional fine-tuning to achieve 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 non-supersymmetric 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.