New Localization Mechanism Of Fermions On Braneworlds And Gravitational Resonant States Of F(R)-branes

Extra dimension theory and braneworld scenarios have attracted continuing interest in recent years because they not only show a new viewpoint of spacetime, but also provide new approaches to address some outstanding issues such as the hierarchy problem and the cosmological problem. In order to reconstruct standard model and general relativity in low energy, it is an important problem to localize various material fields on the branes. In this paper we will investigate two problems:one is new localization mechanism of fermions on braneworlds, and another is localization and resonant modes of gravitons in∫(R)-brane model.In Chapter1, we introduce the fundamental knowledge of extra dimension and braneworld theories and the frontier development about localization and resonant modes.In Chapter2. we investigate the localization of spin-half fermions on braneworlds. It is known that a bulk spin-half fermion can be localized on general Randall-Sundrum braneworlds generated by a kink-like background scalar by introducing the Yukawa cou-pling between the fermion and the background scalar. However, this localization mech-anism does not work anymore for Randall-Sundrum braneworlds generated by a scalar whose configuration is an even function of extra dimension. We present a new localiza-tion mechanism for spin-half fermions under such a class of braneworld models. By two examples, it is shown that the new localization mechanism produces interesting results.In Chapter3, we investigate gravitational resonant states of f(R)-branes. Recently, a family of interesting analytical brane solutions were found in f(R) gravity with f(R)=R+aR2in Ref.[Phys. Lett. B729,127(2014)]. In these solutions, inner brane structure can be turned on by tuning the value of α. We investigate how the parameter α affects the localization and the quasilocalization of the tensorial gravitons around these solutions. It is found that the massless graviton (the zero mode) is localized on the brane, so the four-dimensional gravity can be rebuilt. In a range of a, despite the brane has an inner structure, there is no gravitational resonance. This is different from the situation of general relativity where the appearance of gravitational resonances is related to the inner structure of a brane. However, in some other regions of the parameter space, although the brane has no internal structure, the effective potential for the gravitational KK modes has a singular structure, and there exists a series of gravitational resonant modes.