Localization of scalar field on the brane-world by coupling with gravity

TL;DR

This paper explores how coupling a scalar field's kinetic term with gravity via a function F(R) affects its localization on different brane-world models, showing conditions for zero and massive mode localization.

Contribution

It introduces a novel coupling mechanism between the scalar field and gravity using F(R), analyzing localization in Minkowski, de Sitter, and Anti-de Sitter branes.

Findings

Zero mode always localizes on Minkowski brane.

Massive modes can be localized or quasi-localized depending on the model.

Localization of zero mode on AdS brane requires additional potential considerations.

Abstract

In this paper, we consider a coupling mechanism between the kinetic term and the gravity, in which a coupling function $F(R)$ is introduced into the kinetic term of the five-dimensional scalar field. Based on this scenario, we investigate the localization of scalar fields in three specific braneworld models: the Minkowski brane, the de Sitter brane, and the Anti-de Sitter brane. The brane models considered here are regular with no singularity for scalar curvature. For the Minkowshi brane case, the zero mode can always be localized on the brane, and the massive modes can be localized or quasi-localized on the brane. For the dS$_4$ brane case, two forms of factor $F(R)$ is considered. The zero mode can always be localized, and the massive modes could be quasi-localized on the brane. Besides, with the second coupling factor, the scalar zero mode could be localized on the both sides of the origin of extra dimension, while the massive modes could be quasi-localized on the origin. Lastly, for the AdS$_4$ brane case, the localization of the scalar zero mode requires the consideration of a coupling potential $V(\Phi,\varphi)$, while the massive modes can still be localized on the brane with an infinite number.