  We investigate the effect of entanglement between two causally separated open
charts in de Sitter space on the spectrum of vacuum fluctuations. We consider a
free massive scalar field, and construct the reduced density matrix by tracing
out the vacuum state for one of the open charts, as recently derived by
Maldacena and Pimentel. We formulate the mean-square vacuum fluctuations by
using the reduced density matrix and show that the scale invariant spectrum of
massless scalar field is realized on small scales. On the other hand, we find
that the quantum entanglement affects the shape of the spectrum on large scales
comparable to or greater than the curvature radius.
