Bulk Matters on Symmetric and Asymmetric de Sitter Thick Branes

TL;DR

This paper investigates how symmetric and asymmetric de Sitter thick branes in five dimensions localize various bulk matter fields, revealing differences in their mass spectra and bound modes due to asymmetry.

Contribution

It introduces a method to analyze localization and spectra of matter fields on symmetric and asymmetric de Sitter thick branes using mass-independent potentials.

Findings

Symmetric dS branes have one scalar bound mode; asymmetric ones can have two.

Vector fields have a bound massless mode and continuous spectrum on both branes.

Asymmetry reduces the number of bound fermion modes.

Abstract

An asymmetric thick domain wall solution with de Sitter ($dS$) expansion in five dimensions can be constructed from a symmetric one by using a same scalar (kink) with different potentials. In this paper, by presenting the mass-independent potentials of Kaluza--Klein (KK) modes in the corresponding Schr\"{o}dinger equations, we investigate the localization and mass spectra of various bulk matter fields on the symmetric and asymmetric $dS$ thick branes. It is shown that the spectrum of scalar KK modes on the symmetric $dS$ brane contains only one bound mode (the massless mode). However, for the asymmetric $dS$ brane with a large asymmetric factor $a$, there are two bound scalar KK modes: a zero mode and a massive mode. For spin 1 vectors, the spectra of KK modes on both $dS$ branes consist of a bound massless mode and a set of continuous ones, i.e., the asymmetric factor does not change the number of the bound vector KK modes. For spin 1/2 fermions with the scalar-fermion coupling $\eta\bar\Psi \sin(\phi/\phi_0)\cos^{-\delta}(\phi/\phi_0)\Psi$, there exist some discrete bound KK modes and a series of continuous ones. The asymmetric factor $a$ reduces the number of the bound fermion KK modes.