  This is a technical note on the $i\epsilon$ prescription in cosmology where
we consider a self-interacting scalar field in the Poincare patch of the de
Sitter space whose Hamiltonian has explicit time dependence. We use both path
integral and operator formalisms to work out the evolution of states from
asymptotic past infinity with $i\epsilon$ prescription, which becomes
nontrivial even in the free theory, and explicitly show how arbitrary states
are projected onto the vacuum. We establish that in perturbation theory the
$i\epsilon$ prescription can be implemented in Weinberg's commutator formula by
just inserting $\epsilon$ dependent convergence factors that make the
oscillating time integrals at infinity meaningful.
