Brane Worlds In Higher-Order Theories Of Gravitation And Related Issues

Theories with extra dimensions provide new ideas for solving some fundamental problems in theoretical physics.As a significant development of extra-dimensional theories,the brane world scenario provides alternative interpretations for problems such as gauge hierarchy,cosmological constant,dark energy,and dark matter.The brane world models with warped extra dimensions are the main interest of this thesis.Thick brane worlds and related issues in higher-order theories of gravitation are considered in this thesis,including the linear stability of perturbations,brane world solutions,and the correction of the gravitational potential on the brane.Besides,the possibility of generating thick branes from spinor fields in general relativity is considered.Its stability and the localization of zero modes of various types of perturbations are also explored in this thesis.In this thesis,analytic solutions of thick brane worlds are studied under different gravitational theories.In order to study the configuration of different thick brane worlds under higher-order theories of gravitation,new analytical solutions of the background fields are found in this thesis using a reconstruction technique.Stability is a prerequisite for the existence of the system,so the linear stability of the brane world model under perturbation is a key element of this study.In this thesis,in order to investigate the properties of different gravitational theories in the framework with a warped extra di-mension,the effect of different gravitational theories on the Newtonian potential on the brane is analyzed after deriving the Schr（?）dinger-like equation satisfied by the graviton Kaluza–Klein（KK）modes.Further,the relationship between the effective gravitational action on the brane and the gravitational action in the bulk is analyzed to reveal the relationship between higher-dimensional gravitation and our four-dimensional world.First,this thesis gives a brief introduction to the extra dimension theory from the early KK theory to the modern brane world models with large extra dimensions and warped extra dimensions.Several typical extra-dimensional models are briefly intro-duced separately.Second,we consider that the Lagrangian density of gravitation depends only on an arbitrary function of the curvature scalar,namely the f（R）theory of gravitation.Specif-ically,a special class of D（=4+1+d）-dimensional anisotropic background spacetimes is investigated under f（R）theory,where the metric of the background spacetime is a non-factorizable metric that can describe the brane world.The stability of an asymptot-ically anti-de Sitter（Ad S）background spacetime under tensor perturbations is investi-gated in the case of f（R）gravity without ghost states.For this special class of spacetime structures,new brane worlds solutions are found in the six-dimensional case using a re-construction technique,and the arbitrary dimensional generalization of these solutions is also illustrated.The localization of the graviton zero mode is further investigated,and the effective potential of the graviton KK modes is also discussed.Third,we consider the extended gravitational Lagrangian density f（R,φ,X）.It is an arbitrary function of the scalar curvature R,the scalar fieldφand its kinetic term X,and is therefore a generalized higher-order gravity.In this thesis,we consider f（R,φ,X）gravity in a five-dimensional asymptotically Ad S spacetime and investigate the thick brane and related issues under such higher-order gravity,including perturbative stability and brane world solutions.The stability of the brane system under tensor perturbation is studied when the condition_?^{（?）f（R）,_Rφ,X}>0 is satisfied.Using a reconstruction technique,a class of brane world solutions consisting of non-canonical scalar fields is found directly in the higher-order frame.In addition,the graviton KK modes are investigated.Whether the Newtonian potential can be recovered on the brane is discussed,and the magnitude of the correction of the Newtonian potential is analyzed qualitatively.At last,the possibility of thick branes with spinor fields is explored in warped five-dimensional bulk.We study solutions of a real spinor field coupled to gravitation in five dimensions.We find that the nonlinear spinor fields support a class of soliton configu-rations which could be viewed as a wall embedded in five dimensions.We begin with an illuminating solution of spinor fields in the absence of gravitation.In a further inves-tigation,we exhibit three sets of solutions of spinor fields with non-constant curvature bulk and three kinds of solutions corresponding to three kinds of constant curvature bulk spacetimes.We discuss the energy density distributions and these solutions of spinor fields result in the regular warp of the five-dimensional bulk spacetime.Therefore,con-figurations of these walls can be interpreted as spinor walls which are interesting spinor field realizations of domain walls.In order to investigate the stability of these spinor walls,the linear perturbations of the spinor walls are studied.The localization of the zero modes of various perturbations is also discussed.As an example,the domain wall-like solution of this spinor field is used to discuss the localized properties of a test scalar field.