Study of field fluctuations and their localization in a thick braneworld generated by gravity non-minimally coupled to a scalar field with the Gauss-Bonnet term

TL;DR

This paper presents exact solutions for a 5D warped braneworld with a non-minimally coupled scalar field and Gauss-Bonnet term, demonstrating standard 4D gravity localization and analyzing fluctuation modes.

Contribution

It provides the first exact solutions for such a braneworld scenario, enabling rigorous analysis of gravity localization and fluctuation mode behavior.

Findings

All solutions lead to localized 4D graviton mode.

Scalar and vector modes are not localized on the brane.

The solutions ensure finiteness of the 4D Planck mass.

Abstract

In this work we study a scenario with a warped 5D smooth braneworld with 4D Minkowski geometry builded from bulk scalar matter non-minimally coupled to gravity with an additional Gauss-Bonnet term. We present exact solutions for the full braneworld configuration in contrast to previous results where only approximate solutions were constructed due to the highly non-linear character of the relevant differential equations. These solutions allow us to study the necessary conditions for the finiteness of the 4D Planck mass and additionally, enables us to perform a more rigorous analysis of 4D gravity localization compared to approximate approaches. It is remarkable that all the constructed braneworld configurations lead to standard 4D gravity localization since they contain a localized massless tensor mode (the graviton). We also analyze the localization properties of scalar, vector and tensor fluctuation modes for the constructed field configurations. We show that for the considered backgrounds, only the massless tensor mode, i.e. the 4D graviton, is localized on the brane, while the vector and scalar modes are not confined to the brane.