de Sitter Thick Brane Solution in Weyl Geometry

TL;DR

This paper presents a de Sitter thick brane model in Weyl geometry, analyzing its gravitational stability, KK spectrum, and Newtonian potential corrections, revealing a stable graviton zero mode and unique potential features.

Contribution

It introduces a novel de Sitter thick brane solution in Weyl integrable geometry and studies its gravitational perturbations and stability properties.

Findings

Single bound zero mode graviton indicates a stable 4D gravity

Mass gap exists between zero mode and KK modes

Newtonian potential correction differs from volcano-like models

Abstract

In this paper, we consider a de Sitter thick brane model in a pure geometric Weyl integrable five-dimensional space-time, which is a generalization of Riemann geometry and is invariant under a so-called Weyl rescaling. We find a solution of this model via performing a conformal transformation to map the Weylian structure into a familiar Riemannian one with a conformal metric. The metric perturbations of the model are discussed. For gravitational perturbation, we get the effective modified P$\ddot{\text{o}}$schl-Teller potential in corresponding Schr$\ddot{\text{o}}$dinger equation for Kaluza-Klein (KK) modes of the graviton. There is only one bound state, which is a normalizable massless zero mode and represents a stable 4-dimensional graviton. Furthermore, there exists a mass gap between the massless mode and continuous KK modes. We also find that the model is stable under the scalar perturbation in the metric. The correction to the Newtonian potential on the brane is proportional to $e^{-3 r \beta/2}/r^2$, where $\beta$ is the de Sitter parameter of the brane. This is very different from the correction caused by a volcano-like effective potential.