Thick Branes With Inner Structure

The Randall-Sundrum-2(RS-2)model tells us that Newtonian gravitational potential can be recovered in four-dimensional space-time even if our world has an infinitely large extra spatial dimension.Thick brane models are extra-dimensional models developed on the basis of the RS-2 model combined with the domain wall model.The main difference between them and the RS-2 model is that the warp factors of thick brane models are smooth,and the thick branes have rich inner structure.This thesis will mainly focus on the discussion of thick branes with inner structure,how to obtain the thick brane models with inner structure,and explore their physical properties.Due to the inner structure of thick branes,the resonant spectrum of tensor perturbation and their evolution properties will be more abundant.The modification of these resonances to the four-dimensional Newtonian potential is also studied.First,we study the thick brane under mimetic f(R)gravity.Since this gravity contains more degrees of freedom,it is possible to obtain a thick brane model with inner structure by setting the warp factor instead of the scalar field.Considering the transverse and traceless tensor perturbation of the thick brane,we obtain the Schr?dinger-like equation of the Kaluza-Klein(KK)graviton,and analyze the stability of the thick brane under the tensor perturbation.Based on such Schr?dinger-like equation,we solve the massive KK graviton resonances of the thick brane.The relationship between the structure of the thick brane and the resonance is further analyzed,and we also studied the massive KK gravitons on the thick brane resonant in the sub-brane.Second,we study thick brane with inner structure generated by a multi-kink scalar field under general relativity.We use the superpotential method and the conformal scalar field method to get the thick brane solutions with a multi-kink scalar field.It is found that it is easier to obtain a thick brane model with inner structure by using the conformal scalar field method.Furthermore,we investigate the stability of these thick brane models by calculating tensor perturbation and scalar perturbation.And we then study the resonances of these thick branes with inner structure.The Newtonian gravitational potential corrections from resonances are also calculated with different inner structure.In previous investigation on resonances,one usually only solved the stationary Schr?dinger equation,and obtained a time-independent resonance,without considering the evolution of the resonances with time.Therefore,a complete dynamical analysis of the resonance requires further study of their evolution with time.On the basis of the previous thick brane solutions,we re-decompose the equation of the gravitational tensor perturbation,and obtain the time-dependent Schr?dinger-like equation.By taking the original resonance wave function as the initial value of this equation to evolve under the maximum dissipation boundary condition,we obtain the behavior of the resonances decaying with time.We also study the relationship between the evolution of the off-resonances and the resonances.Finally,we study the gravitational echo effect on thick branes by firing a test wave packet into the thick branes.We select initial test wave packets with different shapes and inject them into thick brane from different positions to study their evolution with time.It is shown that gravitational echo effects exist in thick branes with inner structure.The gravitational echoes of different initial wave packets will be different in the frequency domain.And these gravitational echoes are closely related to resonances.Both of them can reflect the characteristics of thick branes.