On the Perturbative Stability of Quantum Field Theories in de Sitter
  Space
  We use a 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
$\lambda \phi^4$ theory the vacuum does {\em not} decay, while in
non-conformally invariant models, the vacuum decays as a consequence of a
vacuum wave function renormalization that depends \emph{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 \emph{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 \emph{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.
