Classical and quantum correlations of scalar field in the inflationary universe

We investigate classical and quantum correlations of a quantum field in the inflationary universe using a particle detector model. By considering the entanglement and correlations between two comoving detectors interacting with a scalar field, we find that the entanglement between the detectors becomes zero after their physical separation exceeds the Hubble horizon. Furthermore, the quantum discord, which is defined as the quantum part of total correlation, approaches zero on the super horizon scale. These behaviors support the appearance of the classical nature of the quantum fluctuation generated during the inflationary era.