Five-Dimensional Warped Geometry with a Bulk Scalar Field

TL;DR

This paper investigates five-dimensional warped geometries with a scalar field, revealing how a parameter influences the warp factor's form, including smooth solutions without singularities, and discusses bounds on the bulk cosmological constant and fundamental scale.

Contribution

It introduces a parameter-dependent family of warped metrics in 5D gravity with scalar fields, including smooth solutions and bounds on physical parameters, connecting to supergravity and M-theory models.

Findings

Warped metric functions are determined by a new parameter.

Smooth, singularity-free solutions are identified for specific parameter values.

Bounds on the bulk cosmological constant and fundamental scale are established.

Abstract

We explore the diversity of warped metric function in five-dimensional gravity including a scalar field and a 3-brane. We point out that the form of the function is determined by a parameter introduced here. For a particular value of the parameter, the warped metric function is smooth without having a singularity, and we show that the bulk cosmological constant have a upper bound and must be positive and that the lower bound of five-dimensional fundamental scale is controlled by both the brane tension and four-dimensional effective Planck scale. The general warp factor obtained here may relate to models inspired by SUGRA or M-theory.