Bulk Matters on Symmetric and Asymmetric de Sitter Thick Branes

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.