Thick brane in Palatini formalism with a non-minimally coupled bulk scalar field

TL;DR

This paper constructs a stable thick brane model in Palatini gravity with a non-minimally coupled scalar field, demonstrating gravity localization and analyzing the spectrum of gravitational fluctuations.

Contribution

It introduces an analytic thick brane solution in Palatini gravity with a non-minimal scalar coupling, ensuring stability and gravity localization.

Findings

Stable brane configuration with localized graviton zero mode

Absence of tachyonic modes ensuring stability

Massive modes delocalize into the bulk

Abstract

We study a thick brane scenario within the Palatini formulation of gravity, where the metric and affine connection are treated as independent variables. By introducing a non-minimal coupling between a bulk scalar field and the Ricci scalar, we obtain analytic solutions under a flat, four-dimensional Poincar\'e-invariant metric with a kink-like scalar configuration. The warp factor exhibits a bell-shaped profile, while the scalar potential forms a symmetric volcano-like structure, characteristic of a finite-thickness brane. The corresponding energy density is regular and localized, featuring a central peak with symmetrically placed negative minima. Through the analysis of linear tensor perturbations, we derive a Schr\"odinger-like equation with supersymmetric factorization, ensuring the absence of tachyonic modes and thus the stability of the background configuration. The effective potential also takes a volcano-like form that supports a localized graviton zero mode, confirming the recovery of four-dimensional gravity on the brane. A numerical study of the massive Kaluza--Klein spectrum reveals the progressive delocalization of massive modes into the bulk. Our results demonstrate a stable and physically consistent thick brane configuration within the Palatini gravity framework, offering new insights into gravity localization and braneworld phenomenology.