Abstract
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.
Highlights
It has been established that black holes have thermodynamic properties such as temperature and entropy
It is natural to expect an early stage of the universe with w = 1 exists before the radiation dominated universe with w = 1/3. It immediately follows an interesting scenario of the evolution of the very early universe: When the dominate equation of state (EoS) evolves from w = 1 to w = 1/3, the effective description of the universe runs from 1 + 1 dimensional to 3+1 dimensional, along with a remarkable evolvement of the entropy from holographic entropy for Quantum gravitational (QG) particles to normal entropy for radiation
First we review the thermodynamics (1) can be microscopically explained by introducing the so-called QG particles and it is effectively 1 + 1 dimensional [2]
Summary
It has been established that black holes have thermodynamic properties such as temperature and entropy. It is natural to expect an early stage of the universe with w = 1 exists before the radiation dominated universe with w = 1/3 It immediately follows an interesting scenario of the evolution of the very early universe: When the dominate EoS evolves from w = 1 to w = 1/3, the effective description of the universe runs from 1 + 1 dimensional to 3+1 dimensional, along with a remarkable evolvement of the entropy from holographic entropy for QG particles to normal entropy for radiation. The phenomenon of short-distance dimensional reduction was obtained from various approaches to quantum gravity and various definition of effective dimensions. We study the universe filled with a single kind of constituents for simplicity and derive the concerned properties including the entropy inside particle horizon and effective dimension.
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