Inflating baby-Skyrme branes in six dimensions

TL;DR

This paper explores a six-dimensional brane world model with inflating four-dimensional slices, constructed using baby-Skyrme solutions, analyzing their existence, stability, and perturbation spectra.

Contribution

It introduces a numerical construction of baby-Skyrme branes in six dimensions with inflating slices and investigates their stability and perturbation spectra.

Findings

Solutions cease to exist for large brane cosmological constants.

Certain perturbations do not admit localized solutions, indicating stability issues.

Mass estimates for baby-Skyrme and graviton perturbations are provided.

Abstract

We consider a six dimensional brane world model, where the brane is described by a localized solution to the baby-Skyrme model extending in the extradimensions. The branes have a cosmological constant modeled by inflating four dimensional slices and we further consider a bulk cosmological constant. We construct solutions numerically and present evidences that the solutions cease to exist for large values of the brane cosmological constant in some particular case. Then we study the stability of the model by considering perturbation of the gravitational part (resp. baby skyrmion) with fixed matter fields (resp. gravitational background). Our results indicate that the perturbation equations do not admit localized solutions for certain type of perturbation. The stability analysis can be alternatively seen as leading to a particle spectrum; we give mass estimations for the baby-Skyrme perturbation and for the graviton.