The Vacuum of de~Sitter Space

To resolve infrared problems with the de~Sitter invariant vacuum, we argue that the history of the de~Sitter phase is crucial. We illustrate how either (1)~the diagonalization of the Hamiltonian for long-wavelength modes or (2)~an explicit modification of the metric in the distant past leads to natural infrared cutoffs. The former case resembles a bosonic superconductor in which graviton-pairing occurs between non-adiabatic modes. While the dynamical equations respect de~Sitter symmetry, the vacuum is not de~Sitter invariant because of the introduction of an initial condition at a finite time. The implications for the one-loop stress tensor and the production of particles are also discussed.