Bulk Matters on Symmetric and Asymmetric de Sitter Thick Branes

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 Schrödinger equations, we investigate the localization and mass spectra of various bulk matter fields on the symmetric and asymmetric dS thick branes. For spin 0 scalars and spin 1 vectors, the potentials of KK modes in the corresponding Schrödinger equations are the modified Pöschl-Teller potentials, and there exist a mass gap and a series of continuous spectrum. 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, 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, two types of kink-fermion couplings are investigated in detail. For the usual Yukawa coupling ηΨ̄φΨ, there exists no mass gap but a continuous gapless spectrum of KK states. For the scalar-fermion coupling ηΨ̄ sin( φ φ0 ) cos −δ( φ φ0 )Ψ with a positive coupling constant η, there exist some discrete bound KK modes and a series of continuous ones. The total number of bound states increases with the coupling constant η. For the case of the symmetric dS brane and positive η, there are NL(NL ≥ 1) left chiral fermion bound states (including zero mode and massive KK modes) and NL − 1 right chiral fermion bound states (including only massive KK modes). For the asymmetric dS brane scenario, the asymmetric factor a reduces the number of the bound fermion KK modes. For large enough a, there would not be any right chiral fermion bound mode, but at least one left chiral fermion zero mode.