  We compute the relative entropy between the vacuum and a coherent state for a
massive scalar field in de Sitter spacetime, using Tomita-Takesaki modular
theory and the Araki-Uhlmann formula for the relative entropy. Embedding de
Sitter spacetime as a hyperboloid in the ambient Minkowski space, we can
restrict the Minkowski wedge and the corresponding modular operator to de
Sitter, and we verify that this construction gives the correct modular flow. We
check that the relative entropy is positive and jointly convex, relate it to
the Noether charge of translations along the trajectories of the modular flow,
and determine the local temperature as seen by an observer that moves along
these trajectories.
