Quantum entanglement in inflationary cosmology

We investigate the time-dependent entanglement entropy in the AdS space with a dS boundary which represents an expanding spacetime. On this time-dependent spacetime, we show that the Ryu–Takayanagi formula, which is usually valid in the static spacetime, provides a leading contribution to the time-dependent entanglement entropy. We also study the leading behavior of the entanglement entropy between the visible and invisible universes in an inflationary cosmology. The result shows that the quantum entanglement monotonically decreases with time and finally saturates a constant value inversely proportional to the square of the Hubble constant. Intriguingly, we find that even in the expanding universes, the time-dependent entanglement entropy still satisfies the area law determined by the physical distance.