  In this paper, we suggest that the early universe starts from a
high-energetic state with a two dimensional description and the state recovers
to be four dimensional when the universe evolves into the radiation dominated
phase. This scenario is consistent with the recent viewpoint that quantum
gravity should be effectively two dimensional in the ultraviolet and recovers
to be four dimensional in the infrared. A relationship has been established
between the running of effective dimension and that of the entropy inside
particle horizon of the universe, i.e., as the effective dimension runs from
two to four, the corresponding entropy runs from the holographic entropy to the
normal entropy appropriate to radiation. These results can be generalized to
higher dimensional cases.
