  We discussed a mechanism that allows the universe to start from lower
dimension ($d < 4$) in its very early era and evolves to four dimension at the
end of the process. The mechanism is generated by a nonminimal derivative
coupling of scalar field, where derivative terms of the scalar field coupled to
curvature tensor. We solve the Einstein equations for a limit of large and
nearly constant Hubble parameter and analyze the evolution of the Hubble
parameter in this limit. The lower-dimensionality in early universe has
advantages in the context of unification theory.
