Abstract
Modified gravity theories are one of the competing models for explaining the modern accelerated expansion of the universe. These theories are, apparently, the simplest geometric generalization of the general theory of relativity. They are based on replacing the Einstein-Hilbert Lagrangian R by an arbitrary function of the scalar curvature f(R). From a mathematical point of view, the field equations obtained by varying the modified action in the metric have a richer structure of possible solutions, which allows them to be used to obtain new physical results. In this paper, vacuum flat-symmetric solutions in multidimensional modified gravity theories of type f(R)=-aRn, which can be considered as thick branes with codimension =1 in N-dimensional space-time are obtained. These solutions are defined by four parameters. The dependences of the obtained solutions on these parameters are numerically investigated. It is shown that in some cases, when the corresponding parameter tends to infinity, there is saturation. It is shown that the asymptotic behavior of all solutions is antidesitteric.