  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.

High Energy Physics - Theory;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology