Holographic time-dependent entanglement entropy in $p$-brane gas geometries

We investigate holographic cosmologies appearing in the braneworld model with a uniformly distributed $p$-brane gas. When $p$-branes extend to the radial direction, an observer living in the brane detects $(p-1)$-dimensional extended objects. On this background, we show that the braneworld model reproduces the expanding universes of the standard cosmology. In an expanding universe with a matter, we investigate the entanglement entropy between the visible and invisible universes across the cosmological (or particle) horizon. We show that, though the visible and invisible universes are causally disconnected, the nonlocal quantum correlation gives rise to a nontrivial time-dependent entanglement entropy relying on the matter.