  We study the time evolution of entanglement entropy in expanding universes
with various matters. To describe expanding universes holographically, we take
into account a braneworld moving in an asymptotic AdS space involving a uniform
$p$-brane gas. In the braneworld model, an observer living in the braneworld
detects the bulk motion of the braneworld as an expanding universe. We show
that the entanglement entropy of expanding universes increases by the volume
law in the early time and by the area law in the late time. We further consider
the cosmological horizon, which is the border of the visible and invisible
universe, and then investigate the time-dependent quantum entanglement between
them across the cosmological horizon.
