Domain Walls In Noncanonical Scalar Field And In F(R) Gravity

Domain walls are a type of classical topological soliton solutions of scalar field theory.A domain wall connects two degenerated vacua of the system. Domain walls have been applied in many fields of theoretical physics. For instance, in condensed matter, the duality between the two dimensional Sine-Gordon model and the massive Thirring model directly lead to the bosonization method which deal with fermionic systems. In cosmology,the generation and the phenomenological implications of domain walls remain as one of the hottest topics. Recently, the studies on noncompacted extra dimensions attract people to come back to researches on domain walls.Because of their nontrivial configurations, domain walls have many special properties,for instance, they can trap matter fields and gravity in a small domain of the space.This property provides us a theoretical foundation for models with noncompact extra dimensions. In some modern models of extra dimensions, our four-dimensional world might be a domain wall in a five-dimensional space-time. This thesis study static domain wall solutions and their stabilities in two popular effective field theories: the noncanonical scalar field(K-field) and () gravity. We divide our studies into two parts.In the first part, we consider the stability of a class of K-field classical static solutions in cases where space-time is either flat or curved. We obtain the equations for linear perturbations as well as the criterion for stable static solutions. Then we propose the first-order formalism for constructing exactly solvable models in either two-dimensional flat or five-dimensional curved space-time. Using our first-order formalism, it is rather easy to get stable domain wall solutions of a noncanonical scalar field model. In a curved five-dimensional space, the domain wall solution is also a thick brane-world solution, refers to as a thick K-brane. We discuss how the noncanonical kinetic terms affect the linear spectrum of the domain wall, and the localization of fermionic field on the K-brane. Then we study special twinlike models in both two and five dimensions.In the second part, we study domain wall solutions in five-dimensional curved spacetime, i.e., the thick ()-branes. We first consider the pure gravity case. Via conformal transformation, one can rewrite the original pure () gravity action as the action of a canonical scalar field which minimally coupled with Einstein’s gravity. Therefore, one can deal with the stability problem by simply using the results of the first part. We find two exact thick ()-brane solutions, and show that they are stable under linear perturbations. Then we analyze the localization of the gravitational zero mode, and the correction to the Newtonian potential. We also investigate ()-brane models with a single background scalar field, and obtain an exact solution. We show that this solution is stable against tensor perturbation. The localization of the gravitational zero mode and the correction of Newtonian potential are also discussed.