General properties of the self-tuning domain wall approach to the cosmological constant problem

We study the dynamics of brane worlds coupled to a scalar field and gravity , and find that self-tuning of the cosmological constant is generic in theo ries with at most two branes or a single brane with orbifold boundary condi tions. We demonstrate that singularities are generic in the self-tuned solu tions compatible with localized gravity on the brane: we show that localize d gravity with an infinitely large extra dimension is only consistent with particular fine-tuned values of the brane tension. The number of allowed br ane tension values is related to the number of negative stationary points o f the scalar bulk potential and, in the case of an oscillatory potential, t he brane tension for which gravity is localized without singularities is qu antized. We also examine a resolution of the singularities, and find that f ine-tuning is generically reintroduced at the singularities in order to ret ain a static solution. However, we speculate that the presence of additiona l fields may restore self-tuning. (C) 2000 Elsevier Science B.V. All rights reserved.