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Open quantum systems interacting with the environments often show interestingbehaviors, such as decoherence, non-unitary evolution, dissipation, etc. It isinteresting but still challenging to study the open quantum gravitation systeminteracting with the environments. In this work, we develop a generalparameterized theoretical framework for the open quantum gravitation system.Under the Born-Markov approximation, we derived the quantum master equationwith a new method which determines the evolution for certain types of openquantum gravitation system. Finally, we studied a specific model where the realscalar field plays the role of the environment and the spacetime is assumed tobe homogeneous and isotropic. We quantize the spacetime through the loopquantum gravity. We show that the scalar field can induce the quantum geometryin the equilibrium state when the scalar field is under the thermalequilibrium. For the non-steady state, the quantum geometry flux emerges. Wepoint out that the quantum geometry flux and the coherence can drive theevolution of the spacetime geometry. This provides us a new view on theevolution of the spacetime geometry. Our results shown that the coherence ofthe spacetime monotonically decreases as the temperature of the bath decreases.This indicates that a classical cold universe can emerge from an initial hotquantum universe. We found in this model that the entanglement entropy of thegravitation system is related to the average volume of the space. We take thecontinuous limit for studying the loop quantum cosmology and approximatelyobtain a tunneling probability of the spacetime from the zero volume state tothe finite volume state.

Quantum geometrical current and coherence of the open gravitation system: loop quantum gravity coupled with a thermal scalar field