Inflating Brane inside hyper-spherically symmetric defects

TL;DR

This paper explores static and inflating brane world models in higher dimensions with topological defects, revealing new regular and periodic solutions influenced by monopoles and bulk cosmological constants.

Contribution

It introduces explicit solutions for inflating branes with topological defects in higher dimensions, including novel regular and periodic configurations.

Findings

New explicit vacuum solutions with non-zero bulk and inflating constants.

Deformation of solutions by global and local monopoles for various dimensions.

Discovery of regular and periodic solutions in the extra dimensions.

Abstract

Static and inflating brane world models are considered in $4+n$-dimensions with a non zero bulk cosmological constant and with a hyper-spherically symmetric topological defect residing in the $n$ extra dimensions. Several vacuum solutions can be constructed explicitely when the bulk and inflating constants are non zero. We study how these solutions are deformed by the presence of a global monopole for generic values of $n$ and a local monopole for $n=3$. New types of solutions, regular and periodic in the radial variable relative to the extra dimensions, are constructed.