The structure of f(R)-brane model

Recently, a family of interesting analytical brane solutions were found in f(R) gravity with $$f(R)=R \,+\, \alpha R^2$$f(R)=R+α^R2 in Bazeia et al. (Phys Lett B 729:127 2014). In these solutions, the inner brane structure can be turned on by tuning the value of the parameter $$\alpha $$α. In this paper, we investigate how the parameter $$\alpha $$α affects the localization and the quasilocalization of the tensorial gravitons around these solutions. It is found that, in a range of $$\alpha $$α, despite the brane having an inner structure, there is no graviton resonance. However, in some other regions of the parameter space, although the brane has no internal structure, the effective potential for the graviton Kaluza–Klein (KK) modes has a singular structure, and there exist a series of graviton resonant modes. The contribution of the massive graviton KK modes to Newton’s law of gravity is discussed briefly.