| In this thesis, we focus on the localization of gravity and various bulk matter fields on the different thick brane-world, and the effective Newtonian gravitational potentials are also discussed by the two typical examples.Firstly, we give an overview of extra-dimensional physics and the braneworld theo-ries. Three important pictures of an extra dimension are reviewed, namely, Kaluza-Klein (KK) theory, ADD model and Randall-Sundrum (RS) model. We then move on to the construction of thick brane and compare it with the thin brane.Secondly, we investigate the localization and the mass spectra of gravity and var-ious bulk matter fields on a thick anti-de Sitter (AdS) brane, by presenting the mass-independent potentials of the Kaluza-Klein (KK) modes in the corresponding Schrodinger equations. For gravity, the potential of the KK modes tends to infinity at the boundaries of the extra dimension, which leads to an infinite number of the bound KK modes. Al-though the gravity zero mode cannot be localized on the AdS brane, the massive modes are trapped on the brane. The scalar perturbations of the thick AdS brane have been analyzed, and the brane is stable under the scalar perturbations. For spin-0scalar fields and spin-1vector fields, the potentials of the KK modes also tend to infinity at the bound-aries of the extra dimension, and the characteristic of the localization is the same as the case of gravity. For spin-1/2fermions, by introducing the usual Yukawa coupling ηΨφΨ with the positive coupling constant77, the four-dimensional massless left-chiral fermion and massive Dirac fermions are obtained on the AdS thick brane.Thirdly, by presenting the mass-independent potentials of the Kaluza-Klein (KK) modes in the corresponding Schrodinger equations, we investigate the localization and mass spectra of various bulk matter fields on an AdS thick brane. For a spin0scalar Φ coupled with itself and the domain-wall-forming field φ via a coupling potential V=(λφ>2-u2)Φ2+τΦ4, the localization and spectrum are decided by a critical coupling constant λ0. When λ>λ0, the potential of the scalar KK modes in the corresponding Schrodinger equation tends to infinite when far away from the brane, which results in that there exist infinite discrete scalar bound KK states, and the massless modes could be trapped on the AdS brane by fine-tuning of parameters. When λ<λ0, the potential of the scalar KK modes tends to negative infinite when far away from the brane, hence there does not exist any scalar bound KK state. For a spin1vector, the situation is same with the scalar with a coupling constant λ>λ0, but the zero mode can not be localized on the brane. For a spin1/2fermion, we introduce the usual Yukawa coupling ηΨφΨ, and find that the localization of the fermion is decided by a critical coupling constant η0For η>η, the four-dimensional massless left chiral fermion and massive Dirac fermions consisted of the pairs of coupled left-hand and right-hand KK modes could be localized on the AdS brane, and the massive Dirac fermions have a set of discrete mass spectrum. While for the case0<η<η0, no four-dimensional Dirac fermion can be localized on the AdS brane.Fourthly, we investigate thick branes with a non-minimally coupled background scalar field, whose solution is a single-kink or a double-kink. The effects of the non-minimal coupling constant ζ on the structure of the thick branes and the localization of gravity, fermions, scalars and vectors are discussed. It is shown that each brane will split into two sub-branes as increasing the non-minimal coupling constant ζ. By investigating the tensor perturbation equations of gravity and the general covariant Dirac equation of fermions, we find that both the gravity zero mode and left-chiral fermion zero mode are localized at the center of the single-kink branes and localized between the two sub-branes generated by the double-kink, which indicates that the constant ζ does not effect the localization of these zero modes. However, the zero mode of scalars is localized on each sub-brane (for both single-kink and double-kink branes) when ζ is larger than its critical value ζ0The effects of the non-minimal coupling constant ζ on the resonances of gravity and fermions with finite lifetime on the branes are also discussed.Finally, the gravity localization and mass spectrum of gravity KK modes on de Sitter and Anti-de Sitter thick branes are investigated. Then, the effective Newtonian gravitational potentials for these bent branes are discussed by the two typical examples. The corrections of the Newtonian potential are turned out to be△U(r)～1/r2at small r for both cases. These corrections are very different from that of the Randall-Sundrum brane model△U(r)～1/r3.
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