Bulk spacetimes for cosmological braneworlds with a time--dependent extra dimension

TL;DR

This paper investigates five-dimensional bulk spacetimes for cosmological braneworld models with a dynamic extra dimension, analyzing energy conditions, solving field equations for various matter sources, and demonstrating the viability of such models.

Contribution

It provides new solutions for warped cosmological braneworlds with a time-dependent extra dimension, including analyses of energy conditions and bulk matter sources like scalar fields and dilatons.

Findings

Viable bulk solutions with time-varying extra dimensions are possible.

Energy conditions can be satisfied in these models.

Solutions for scalar, Brans-Dicke scalar, and dilaton bulk matter are obtained.

Abstract

We explore the possibilities of constructing bulk spacetimes in five dimensions for warped braneworld models with a spatially flat Friedmann-Robertson-Walker (FRW) line element on the 3-brane and with a time-dependent extra dimension. Our first step in this direction involves looking at the status of energy conditions when such a bulk line element is assumed. We check these conditions by analysing the relevant inequalities, for specific functional forms (chosen to satisfy certain desirable features) of the warp factor, the cosmological scale factor and the extra-dimensional scale factor. Subsequently, we aim at obtaining solutions with different types of bulk matter sources. We begin with a general analysis of the solution space of non-singular Randall-Sundrum type bulk models with an exponential warp factor and a chosen equation of state. Thereafter, we focus on three specific bulk sources -- the ordinary scalar field, the Brans-Dicke scalar and the dilaton. In each case, we are able to solve the field equations and obtain desirable solutions for which, we once again check the viability of the energy conditions. We also show how one can place branes in the bulk using the junction conditions. The issue of resolution of the bulk singularities which appear in our solutions, using standard methods, is also presented briefly. In summary, we are able to demonstrate, that it is indeed possible to construct viable bulk spacetimes for warped cosmological braneworlds with a time-varying extra dimension and with bulk matter satisfying the energy conditions.