Thick Brane Worlds Arising From Pure Geometry

TL;DR

This paper explores a non-Riemannian 5D geometric framework with Weyl integrable structure, producing thick brane solutions that address the hierarchy problem and ensure a stable, quantized Kaluza-Klein spectrum.

Contribution

It introduces a novel non-Riemannian geometric approach to thick brane models, demonstrating a natural resolution of the hierarchy problem and a stable KK spectrum without tachyons.

Findings

Thick brane solutions with localized gravity are obtained.

The model naturally resolves the hierarchy problem.

The KK spectrum is quantized and free of tachyonic modes.

Abstract

We study a non-Riemannian modification of 5-dimensional Kaluza-Klein theory. In our proposal the Riemannian structure of the five-dimensional manifold is replaced by a Weyl-integrable one. In this context a 4-dimensional Poincar$\grave{e}$ invariant solution is studied. Spacetime structures with thick smooth branes separated in the extra dimension arise. We focus our attention, mainly, in a case where the massless graviton is located in one of the thick branes at the origin, meanwhile the matter degrees of freedom are confined to the other brane. Due to the small overlap of the graviton's wave-function with the second thick brane, the model accounts for a resolution of the mass hierarchy problem a la Randall-Sundrum. Although, initially, no assumptions are made about the topology of the extra dimension, the solution found yields an extra space that is effectivelly compact and respects $Z_2$ symmetry. Unlike some other models with branes, a preliminary study (not including the effect of scalar perturbations) shows that the spectrum of massive Kaluza-Klein states is quantized and free of tachyonic modes.