We examine several different types of five-dimensional stationary space-times with bulk scalar fields and parallel 3-branes. We study different methods for avoiding the appearance of space-time singularities in the bulk for models with and without cosmological expansion. For nonexpanding models, we demonstrate that in general the Randall-Sundrurn warp factor is recovered in the asymptotic bulk region, although elsewhere the warping may be steeper than exponential. We show that nonsingular expanding models can be constructed as long as the gradient of the bulk scalar field vanishes at zeros of the warp factor, which are then analogous, to the particle horizons found in expanding models with a pure Ads bulk. Since the branes in these models are stabilized by bulk scalar fields, we expect there to be no linearly unstable radion modes, As an application, we find a specific class of expanding, stationary solutions with no singularities in the bulk in which the four-dimensional cosmological constant and mass hierarchy are naturally very small. (C) 2001 Elsevier Science B.V. All rights reserved
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