  A free-theory vacuum state of an interacting field theory, e.g. quantum
gravity, is unstable at tree level in general due to spontaneous emission of
Fock-space particles in any spacetime with no global timelike Killing vectors,
such as de Sitter spacetime, in the interaction picture. As an example, the
rate of spontaneous emission of Fock-space particles is calculated in phi^4
theory in de Sitter spacetime. It is possible that this apparent spontaneous
emission does not correspond to any physical processes because the states are
not evolved by the true Hamiltonian in the interaction picture. Nevertheless,
the constant spontaneous emission of Fock-space particles in the interaction
picture clearly demonstrates that the in- and out-vacuum states are orthogonal
to each other as emphasized by Polyakov and that the in-out perturbation
theory, which presupposes some overlap between these two vacuum states, is
inadequate. Other possible implications of apparent vacuum instability of this
kind in the interaction picture are also discussed.
