  Open quantum systems interacting with the environments often show interesting
behaviors, such as decoherence, non-unitary evolution, dissipation, etc. It is
interesting but still challenging to study the open quantum gravitation system
interacting with the environments. In this work, we develop a general
parameterized theoretical framework for the open quantum gravitation system.
Under the Born-Markov approximation, we derived the quantum master equation
with a new method which determines the evolution for certain types of open
quantum gravitation system. Finally, we studied a specific model where the real
scalar field plays the role of the environment and the spacetime is assumed to
be homogeneous and isotropic. We quantize the spacetime through the loop
quantum gravity. We show that the scalar field can induce the quantum geometry
in the equilibrium state when the scalar field is under the thermal
equilibrium. For the non-steady state, the quantum geometry flux emerges. We
point out that the quantum geometry flux and the coherence can drive the
evolution of the spacetime geometry. This provides us a new view on the
evolution of the spacetime geometry. Our results shown that the coherence of
the spacetime monotonically decreases as the temperature of the bath decreases.
This indicates that a classical cold universe can emerge from an initial hot
quantum universe. We found in this model that the entanglement entropy of the
gravitation system is related to the average volume of the space. We take the
continuous limit for studying the loop quantum cosmology and approximately
obtain a tunneling probability of the spacetime from the zero volume state to
the finite volume state.
