Evolution of the Universe with Flat Extra Dimensions
  Evolution of a universe with homogeneous extra dimensions is studied with the benefit of a well-chosen parameter space that provides a systematic, useful, and convenient way for analysis. In this model we find a natural evolution pattern that entails not only stable extra dimensions in the radiation-dominated era, thereby preserving essential predictions in the standard cosmology, but also the present accelerating expansion while satisfying the limit on the variation of Newtonian gravitational constant. In this natural evolution pattern the extra dimensions tend to be stabilized automatically without resorting to artificial mechanisms in both the radiation-dominated and the matter-dominated era, as a wonderful feature for building models with extra dimensions. In addition, the naturalness of this evolution pattern that guarantees the late-time accelerating expansion of a matter-dominated universe presents a solution to the coincidence problem: why the accelerating phase starts at the present epoch. The feasibility of this evolution pattern for describing our universe is discussed. 
Je-An Gu, W-Y. P. Hwang, Jr-Wei Tsai