Decay of the free-theory vacuum of scalar field theory in de Sitter spacetime in the interaction picture

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.