  We address the following question: To what extent can a quantum field tell if
it has been placed in de Sitter space? Our approach is to use the techniques of
non-equilibrium quantum field theory to compute the time evolution of a state
which starts off in flat space for (conformal) times $\eta<\eta_0$, and then
evolves in a de Sitter background turned on instantaneously at $\eta=\eta_0$.
We find that the answer depends on what quantities one examines. We study a
range of them, all based on two-point correlation functions, and analyze which
ones approach the standard Bunch-Davies values over time. The outcome of this
analysis suggests that the nature of the equilibration process in this system
is similar to that in more familiar systems.
