Quantum geometrical current and coherence of the open gravitation system: loop quantum gravity coupled with a thermal scalar field (2012.06114v4)

Abstract: 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.