Polchinski, Quantization of False Vacuum Bubbles: A Hamiltonian Treatment of Gravitational Tunneling, Phys. Guven, Is It Possible to Create a Universe in the Laboratory by Quantum Tunneling?, Nucl. Vilenkin, Quantum Creation of Universes, Phys. Vilenkin, The Birth of Inflationary Universes, Phys. Hawking, Wave Function of the Universe, Phys. Linde, Decay of the False Vacuum at Finite Temperature, Nucl. Linde, Fate of the False Vacuum at Finite Temperature: Theory and Applications, Phys. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Hirvonen, Effective field theory approach to thermal bubble nucleation, Phys. Zhang, Taiji program: Gravitational-wave sources, Int. Kawamura et al., The Japanese space gravitational wave antenna: DECIGO, Class. 5 yr Data Set: Search for an Isotropic Stochastic Gravitational-wave Background, Astrophys. NANOG rav collaboration, The NANOGrav 12. LIGO S cientific and V irgo collaborations, Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. In the steady state, the dominant vacuum corresponds to the smallest cosmological constant, and various dS vacua can reach equilibrium states. In specific scenarios, the classical limit of the quantum master equation is consistent with the classical master equation. We also highlight that in certain circumstances, the evolution of the vacuum system may display non-Markovian dynamics. This helps the understanding of the decoherence of the universe. Under the Markovian limit, coherence monotonically decreases with time, leading to the initial quantum state to decohere into a classical state. We demonstrate that the quantum dynamics of the vacua can be described by the Redfield equation, which can depict the evolution of both coherence and the comoving volume fraction of the vacuum. The environment is chosen as spacetime while the system is formed by the vacua of the scalar field. Our model consists of the spacetime and scalar field with self-interaction potential. The quantum master equation required to describe the dynamics of gravity-related vacuum decay is still challenging.
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