  We investigate the entanglement of a quantum field in the expanding universe.
By introducing a bipartite system using a coarse-grained scalar field, we apply
the separability criterion based on the partial transpose operation and
numerically calculate the bipartite entanglement between separate spatial
regions. We find that the initial entangled state becomes separable or
dis-entangled after the spatial separation of two points exceed the Hubble
horizon. This provides the necessary condition for the appearance of
classicality of the quantum fluctuation. We also investigate the condition of
classicality that the quantum field can be treated as the classical stochastic
variables.
