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

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. We studied a specific model where a 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 if the scalar field is in the thermal equilibrium state, the spacetime geometry will reach the equilibrium state after the transient relaxation. For the non-steady state, the quantum geometry current emerges. We point out that the quantum geometry current and the coherence can together drive the evolution of the spacetime geometry. This provides us a new view on the evolution of the spacetime geometry. Our results show that the coherence of the spacetime monotonically decreases as the temperature of the bath decreases. It helps the understanding of how a classical cold universe can emerge from an initial hot quantum universe.

Quantum master equation for the vacuum decay dynamics

“…Typically, as one part of the universe, the system interacts with the environment and can not be seen as an isolated one. Thus, the general covariance does not constrain the (effective) Hamiltonian of the system to be equal to zero [36]. Or in other words, the general covariance does not constrain dρ/dt to be equal to zero.…”

“…Or in other words, the general covariance does not constrain dρ/dt to be equal to zero. Therefore, one can use equation (2.6) to describe the quantum dynamics of the system [36].…”

“…Some of the physical quantities, such as the coherence and the entanglement entropy, will change over time. This means that dρ/dt ̸ = 0, even for the systems related to gravity [36]. Extracting all the quantum dynamic information of the universe seems to be blocked by the general covariance according to the Wheeler-DeWitt equation (2.3), yet we can still obtain partial dynamical information of the quantum universe according to equation (2.6).…”

“…All of the above arguments indicate that it should be reasonable to use equation (2.6) to describe the quantum evolution of the open gravitational system. The more general form of this equation can be found in [36]. Next, based on equation (2.6), we will derive the quantum master equation for describing the vacuum decay quantum dynamics.…”