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

TL;DR

The work tackles vacuum stability for interacting fields in de Sitter spacetime by examining spontaneous emission in the interaction picture. It computes the amplitude for producing four quanta in a conformally coupled scalar theory with a quartic interaction and derives a nonzero emission rate per unit volume that is enhanced by horizon scale modes. The key finding is that the in vacuum evolves into a state orthogonal to the out vacuum, signaling that in-out perturbation theory is inadequate in this setting. The results also connect to observer dependent pictures, suggesting interpretations in terms of a Gibbons-Hawking bath and hinting at transitions to de Sitter invariant but infinite norm states, with implications for higher order and quantum gravity theories.

Abstract

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.