# Five-dimensional warped product space-time with time-dependent warping and a scalar field in the bulk

## TL;DR

This paper explores a five-dimensional warped space-time with a time-dependent warp factor and scalar field, analyzing how the universe's expansion varies along the extra dimension and how bulk scalar fields influence brane cosmology.

## Contribution

It introduces a model with time-dependent warping and scalar fields in five dimensions, examining their effects on brane expansion and bulk geometry.

## Key findings

- Expansion depends on location in the extra dimension
- Bulk is generally not conformally flat
- Scalar field potential relates to brane Hubble parameter

## Abstract

We have considered gravity in a five-dimensional warped product space-time, with a time-dependent warp factor and a time-dependent extra dimension. The five-dimensional field equations are derived for a spatially flat FRW brane and the energy conditions and the nature of bulk geometry have been examined. It is found that the expansion of the four-dimensional universe depends on its location along the extra dimension and will be different at different locations in the bulk spacetime. At low energies, the trapping of fields within the brane implies a specific correlation between the warp factor and the extra-dimensional scale factor. Generally, the bulk is not conformally flat. At high energies, the bulk is assumed to be sourced by a scalar field with self-interaction. The analysis shows that the potential of the scalar field source of gravity at a given position along the fifth dimension, is related to the Hubble parameter on the brane at that position in the bulk.