  We study the free massive scalar field in de Sitter spacetime with static
charts. In particular, we find positive-frequency modes for the Bunch-Davies
vacuum state natural to the static charts as superpositions of the well-known
positive-frequency modes in the conformally-flat chart. We discuss in detail
how these modes are defined globally in the two static charts and the region in
their future. The global structure of these solutions leads to the well-known
description of the Bunch-Davies vacuum state as an entangled state. Our results
are expected to be useful not only for studying the thermal properties in the
vacuum fluctuations in de Sitter spacetime but also for understanding the
nonlocal properties of the vacuum state.
