Brane Worlds In Gravity With Auxiliary Field And Nonlocal Gravity

The theory of extra dimension provides a new way to understand our universe and has made a great progress in solving the hierarchy problem. On the other hand, in order to solve the problems such as singularity, nonrenormalizability, dark energy, and dark matter in general relativity, modified gravity theories have been presented and investigated widely. In this thesis, we study the braneworld model in gravity with auxiliary fields and nonlocal gravity. Further, based on our study we propose a new kind of braneworld model to solve the hierarchy problem.Firstly, Pani, Sotiriou, and Vernieri explored a new theory of gravity by adding non-dynamical fields, i.e., gravity with auxiliary fields [Phys. Rev. D 88,121502(R) (2013)]. In this gravity theory, higher-order derivatives of matter fields generically appear in the field equations. In this thesis, we extend this theory to any dimensions and discuss the thick braneworld model in five dimensions. Domain wall solutions are obtained numeri-cally. The stability of the brane system under the tensor perturbation is analyzed. We find that the system is stable under the tensor perturbation and the gravity zero mode is localized on the brane. Therefore, the four-dimensional Newtonian potential can be realized on the brane.Secondly, we propose a new description of the (4+N)-dimensional Arkani-Hamed-Dimopoulos-Dvali (ADD) model in a (4+1)-dimensional warped geometry to solve the gauge hierarchy problem. It has the same KK spectrum as in the ADD model and recovers its phenomena that do not involve the interaction among the graviton KK modes. There is no hierarchy between the fundamental length and the size of the extra dimension. An explicit realization is constructed in the nonlocal gravity theory to give a warped description of the six-dimensional ADD model. Remarkably, the number N of the extra dimensions in this description may be non-integral, which provides a new mechanism to escape the experimental constrains.Finally, based on our former result that thin brane can not localize the gravity zero mode when the size of the extra dimension is infinite, we consider the thick braneworld in the nonlocal gravity theory. We find improper choice of the nonlocal term will destroy the localization of gravity zero mode. We use the reconstruction procedure to find some properties that the nonlocal term should possess to ensure the localization of gravity zero mode. We also find that extra conditions should be imposed on the scalar field and we calculated it in detail in our setup.