Different Prospects of the Universe Depending on Dark Energy and/or a New Kind of Extra Dimension

Abstract: Generally making the cosmological scale factor $R$ be a function of the coordinate of the extra dimension $\sigma $ that is also a function of time $t$, we achieve a new kind of cosmic acceleration mechanism depending on extra dimension. We give the constraints on $\sigma $ under four different prospects of the universe, and indicate that dark energy is not required for both the small extra dimension and the accelerating expansion of our universe. This results in this paper show that the accelerating expansion of our universe may come from both dark energy and the achieved new mechanism here, or the latter alone.