2009年，Oda、Suyama和Yokoi (OSY)在一类非标准的标量-张量模型中构造了第一个Randall-Sundrum-1 (RS-1)型厚膜模型。该模型有望解决标准模型的层次问题，同时又能避免传统RS-1模型中存在的奇异性问题。本项目将从求和规则和线性稳定性两方面进一步分析OSY模型是否能成为一个可行的RS-1型厚膜模型。如果不能，则在目前已知的运动方程为二阶的最广泛的标量-张量理论，即Horndeski理论中寻找新的RS-1型厚膜模型。本项目还将在Horndeski理论中构造新的RS-2型厚膜模型，利用解析和数值方法分析Horndeski理论中的微分耦合项对厚膜性质的影响。本项目有望建立起新的RS-1和RS-2型厚膜模型，同时也对认识Horndeski理论中微分耦合项对厚膜性质的影响有重要的理论价值。

In 2009, Oda, Suyama and Yokoi (OSY) constructed the first Randall-Sundrum-1 (RS-1) type thick brane model in a non-standard scalar-tensor model. This model may be used to solve the hierarchy problem, while at the same time, evade the singularity problem of the traditional RS-1 model. In this project we analyze if the OSY model is a viable RS-1 type thick brane model by considering the sum rules and the stability issues. If it is not, we will construct new RS-1 type thick brane models in the Horndeski theory, which is the most general scalar-tensor theory whose equations of motion are second order. We will also construct new RS-2 type thick brane models, and analyze how the derivative coupling terms affect the properties of thick brane solutions by using analytical and numerical methods. This project will construct new RS-1 and RS-2 types of thick brane models, and will have an important theoretical value in understanding how the derivative coupling terms of the Horndeski theory could affect the properties of thick branes.