Gravitational Kaluza-Klein modes in the string-cigar braneworld

Abstract

In this work we analyze the properties of the gravitational Kaluza-Klein (KK) modes in two stringlike braneworlds, the thin Gherghetta-Shaposhnikov (GS) model and the thick string-cigar model. The string-cigar model is a smooth generalization of the GS model that undergoes a Ricci geometrical flow. We find a new massless mode in both models satisfying the respective Schr\"odinger equations. By means of a numerical analysis, we obtain the complete graviton spectrum and its respective eigenfunctions. The KK spectrum exhibits the usual linear regime for large discrete index $n$ and we find a new decreasing regime for small $n$. Moreover, there is an asymmetric mass gap between the massless mode and the massive KK tower. The mass gap in the GS model is bigger than in the string-cigar model. In addition, the mass gap remains invariant upon the geometrical flow. It turns out that in the string-cigar model the brane structure smoothes and amplifies the KK modes near the brane core. The presence of a potential well in the string-cigar scenario allows the existence of resonant massive gravitons for small masses.