Quantum entanglement for continuous variables sharing in an expanding spacetime

Detecting the structure of spacetime with quantum technologies has always been one of the frontier topics of relativistic quantum information. Here, we analytically study the generation and redistribution of Gaussian entanglement of the scalar fields in an expanding spacetime. We consider a two-mode squeezed state via a Gaussian amplification channel that corresponds to the time-evolution of the state from the asymptotic past to the asymptotic future. Therefore, the dynamical entanglement of the Gaussian state in an expanding universe encodes historical information about the underlying spacetime structure, suggesting a promising application in observational cosmology. We find that quantum entanglement is more sensitive to the expansion rate than the expansion volume. According to the analysis of quantum entanglement, choosing the particles with the smaller momentum and the optimal mass is a better way to extract information about the expanding universe. These results can guide the simulation of the expanding universe in quantum systems.