Investigation Of Multi-Kink Branes In Gauss-Bonnet Gravity

In the extra-dimensional theory,our universe is described as a four-dimensional hypersurface called 3-brane embedded in higher dimensional spacetime called bulk.Braneworld is widely studied as our real world.Gauss-Bonnet(GB)term does not contribute to the equations of motion in four-dimensional spacetime because of the full differential form,but it is nontrivial in extra-dimensional models.In order to study the influence of GB term,the properties of multi-kink thick brane generated by bulk scalar field in five-dimensional GB gravity are studied.Firstly,we mainly introduce the proposal and development of the extra-dimensional theories: the Kaluza-Klein(KK)theory,the domain wall model,two important thin brane models: The Arkani-Hamed-Dimopoulos-Davli(ADD)model and Randall-Sundrum(RS)model,as well as thick braneworld model which is more consistent with our real world.In addition,this thesis introduces the research status of the GB gravity and brane world models in the extra dimensional theories,the characteristics of GB item will be revealed through the properties of thick branes.Secondly,we construct thick brane generated by bulk scalar field in five-dimensional GB gravity.Two methods are introduced to obtain the brane solution.The superpotential method reduces the equations of motion to the first-order formulas,we can obtain thick brane solution with a suitable superpotential.On the other hand,the scalar field and scalar potential can be obtained by selecting an extended polynomial warp factor.A series of multi-kink thick branes are obtained with the first method by choosing five superpotentials.We analyse the parameter space of thick branes,the result shows that the GB term and the configuration of superpotential play an important role in regulating the structure of multi-kink thick brane.We construct an extended polynomial warp factors with the second method and obtain a series of double-kink branes.These thick branes only have single-kink and double-kink structures when GB coupling parameter goes to zero(in the general relativity case).Finally,we study the stability and localization of gravitons of the thick brane system by considering the tensor fluctuations,as well as gravitational resonances in multikink thick brane.We derive the linear equation of tensor fluctuations of braneworld model in GB gravity and prove that the brane system is linearly stable under tensor fluctuations,there doesn't exist ghost state.Gravitational zero mode is localized on the multi-kink thick brane in this paper and so four-dimensional Newtonian potential can be recovered.In order to reveal the interaction of gravitational field to brane,we analyse and obtain a series of gravitational resonances.The influence of GB invariant on gravitational resonances of thick brane is obtained by comparing the properties of these thick branes under different GB coupling parameters.