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 asymmetric one by using a same scalar (kink) with differentpotentials. In this paper, by presenting the mass-independentpotentials of Kaluza-Klein (KK) modes in the correspondingSchrödinger equations, we investigate the localization andmass spectra of various bulk matter fields on the symmetric andasymmetric dS thick branes. For spin 0 scalars and spin 1vectors, the potentials of KK modes in the correspondingSchrödinger equations are the modified Pöschl-Tellerpotentials, and there exist a mass gap and a series of continuousspectrum. It is shown that the spectrum of scalar KK modes on thesymmetric dS brane contains only one bound mode (the masslessmode). However, for the asymmetric dS brane with a largeasymmetric factor, there are two bound scalar KK modes: a zeromode and a massive mode. For spin 1 vectors, the spectra of KKmodes on both dS branes consist of a bound massless mode and aset of continuous ones, i.e., the asymmetric factor does notchange the number of the bound vector KK modes. For spin 1/2fermions, two types of kink-fermion couplings are investigated indetail. For the usual Yukawa coupling ηϕΨ,there exists no mass gap but a continuous gapless spectrum of KKstates. For the scalar-fermion coupling ηsin(ϕ/ϕ0)cos−δ(ϕ/ϕ0)Ψ witha positive coupling constant η, there exist some discretebound KK modes and a series of continuous ones. The total numberof bound states increases with the coupling constant η. Forthe case of the symmetric dS brane and positive η, thereare NL(NL ⩾ 1) left chiral fermion bound states (includingzero mode and massive KK modes) and NL−1 right chiral fermionbound states (including only massive KK modes). For the asymmetricdS brane scenario, the asymmetric factor a reduces the numberof the bound fermion KK modes. For large enough a, there wouldnot be any right chiral fermion bound mode, but at least one leftchiral fermion zero mode.