High Dimension F(R) Modal

Recent observations of type Ia supernovae (SNe Ia)indicate that the expansion of the Universe is accel-erating at present time. But the hot big bang model based on the ordinary matter component denotes that the expansion of universe would be decelerating, which is not consistent with the observation. In order to explain the expansion of our Universe, we have to modify it properly. People have proposed many kinds of theories to explain the acceleration, for example dark energy models, f(R) theory, and high-dimensions theory,from above theories, in this paper,we discuss the theory of high-dimensions f(R) theory. Firstof all, we introduce the background knowledge of modern cosmology, including hierarchy problem, fine-tuning problem, then we introduce several dark energy models.Second, we introduce the background knowledge of high-dimension theory, there are three famous theo-retical models-ADD, RS, DGP models.Furthermore, we introduce the background knowledge of f (R) theory, f(R) gravity with arbitrary coupling between matter and geometry are derived.Finally, the metric f(R) theories of gravity are generalized to five-dimensional spacetimes. By assuming a hypersurface-orthogonal Killing vector field representing the compact fifth dimension, the five-dimensional theories are reduced to their four-dimensional formalism.Then we study the cosmology of a special class of models in a spatially flat FRW spacetime. It is shown that the parameters m and n can be constrained to a certain range by the current observed deceleration parameter, and its lower bound corresponds to the Kaluza-Klein theory.