  The quantum master equation required to describe the dynamics of
gravity-related vacuum decay is still challenging. We aim to study this issue.
Our model consists of the spacetime and scalar field with self-interaction
potential. The environment is chosen as spacetime while the system is formed by
the vacua of the scalar field. 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. Under the
Markovian limit, coherence monotonically decreases with time, leading to the
initial quantum state to decohere into a classical state. This helps the
understanding of the decoherence of the universe. We also highlight that in
certain circumstances, the evolution of the vacuum system may display
non-Markovian dynamics. In specific scenarios, the classical limit of the
quantum master equation is consistent with the classical master equation. In
the steady state, the dominant vacuum corresponds to the smallest cosmological
constant, and various dS vacua can reach equilibrium states.
