On the perturbative stability of quantum field theories in de Sitter space
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We usea field theoretic generalization of the Wigner-Weisskopf method to study the stability of the Bunch-Davies vacuum state for a massless, conformally coupled interacting test field in de Sitter space. We find that in λϕ 4 theory the vacuum does not decay, while in non-conformally invariant models, the vacuum decays as a consequence of a vacuum wave function renormalization that depends singularly on (conformal) time and is proportional to the spatial volume. In a particular regularization scheme the vacuum wave function renormalization is the same as in Minkowski spacetime, but in terms of the physical volume, which leads to an interpretation of the decay. A simple example of the impact of vacuum decay upon a non-gaussian correlation is discussed. Single particle excitations also decay into two particle states, leading to particle production that hastens the exiting of modes from the de Sitter horizon resulting in the production of entangled superhorizon pairs with a population consistent with unitary evolution. We find a non-perturbative, self-consistent “screening” mechanism that shuts off vacuum decay asymptotically, leading to a stationary vacuum state in a manner not unlike the approach to a fixed point in the space of states.