Brane World Models In Critical Gravity And Nonminimally Coupling Gravity Theories

The idea that we live on a brane has received a lot of attention in recent years. Brane world models have revealed new possibilities for addressing the hierarchy problem of particle physics, chirality of neutrinos, dark matter as well as cosmological constant problem.Although in the four-dimensional spacetime, Einstein theory successfully describes our observations, but it has some problems, for example singularities and unrenormaliz-ability. To solve these problems, we need quantum gravity. Although we still don’t know full quantum gravity, modified gravity theories can give us some hints.In this thesis we mainly discuss brane world models in critical gravity and nonmini-mally coupling gravity theories.Firstly, we investigate critical gravity proposed by H. Lii and Pope. Unlike other high-order derivative gravity theories, there can exist thin brane solutions in critical gravity. We give covariant junction conditions for general case. Those conditions become Einstein-Gauss-Bonnet ones if brane is maximal. We also prove that it just modifies propagator of gravitons and scalar perturbation is stable.Secondly, we study five-dimensional nonminimally coupling gravity generated by a single scalar field. We find some new results. Brane can be split into three subbranes and the warp factor can reach its peak beyond the brane. The asymptotic space-time in some cases may be not AdS5. Its tensor perturbation is stable if nonminimally coupling function F(φ) is non-negative, however stability of scalar fluctuation requires that F(φ) is also positive at the infinity.Finally, we consider multi-scalar brane world models which are generalization of single-scalar models. We concentrate on stability of models, especially on scalar pertur-bation. We find that models constructed by single-field and multi-fields are essentially different:for a single field background kink (or other soliton) solution, if there is no ghost field, then the model is always stable, but no such conclusion exists in the latter case. We focus on massless modes and discuss double scalar fields in detail. We find that there is an extra constraint for physical zero mode. For the superpotential background solutions, this constraint is not independent, and there is usually a zero mode which can localize on the brane. Utilizing those results, we find that a special f(R) model is stable.In this thesis analysis of the brane world stability is limited to linear perturbation. In order to compare with results of experiments and observation, especially observation of our solar system, more works on nonlinear analysis are needed.