Vacua and infrared radiation in de Sitter quantum field theory

We analyze the asymptotic behavior of quantum fields and perturbative quantum gravity in de Sitter space. We show that the necessary and sufficient condition for the existence of a de Sitter invariant vacuum state in the free theory is if the local field observables commute with the ``memory observable'' on any cosmological horizon. This criterion yields simple, gauge-invariant proofs of the existence of a de Sitter invariant vacuum for the (source-free) massive scalar field, electromagnetic field and linearized gravitational field. However, the massless, minimally coupled scalar does not satisfy this criterion and, consequently, there is no de Sitter invariant vacuum state. In this case, we construct the Hilbert space of normalizable states that have ``square integrable'' distributions in the memory and the conjugate constant mode. This Hilbert space has a unitary representation of the de Sitter symmetry group but no de Sitter invariant normalizable state. However even for free theories with a normalizable de Sitter invariant vacuum we show, by a simple example, that in the presence of a source a large number of infrared particles can be produced if the source interacts with the field for timescales much longer than the Hubble time. In the limit as the source persists forever it emits an infinite number of infrared particles.