Brane World Models With Bulk Scalar Fields

TL;DR

This paper explores five-dimensional brane world models with bulk scalar fields, focusing on avoiding singularities, stabilizing branes, and achieving small cosmological constants and mass hierarchies.

Contribution

It introduces methods for constructing nonsingular, stable brane models with bulk scalar fields that naturally produce small cosmological constants and hierarchies.

Findings

Randall-Sundrum warp factor is recovered asymptotically.

Nonsingular expanding models are possible with specific scalar field conditions.

A class of solutions with small cosmological constant and hierarchy is found.

Abstract

We examine several different types of five dimensional stationary spacetimes with bulk scalar fields and parallel 3-branes. We study different methods for avoiding the appearance of spacetime singularities in the bulk for models with and without cosmological expansion. For non-expanding models, we demonstrate that in general the Randall-Sundrum 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.