  We argue that, under certain plausible assumptions, de Sitter space settles
into a quiescent vacuum in which there are no dynamical quantum fluctuations.
Such fluctuations require either an evolving microstate, or time-dependent
histories of out-of-equilibrium recording devices, which we argue are absent in
stationary states. For a massive scalar field in a fixed de Sitter background,
the cosmic no-hair theorem implies that the state of the patch approaches the
vacuum, where there are no fluctuations. We argue that an analogous conclusion
holds whenever a patch of de Sitter is embedded in a larger theory with an
infinite-dimensional Hilbert space, including semiclassical quantum gravity
with false vacua or complementarity in theories with at least one Minkowski
vacuum. This reasoning provides an escape from the Boltzmann brain problem in
such theories. It also implies that vacuum states do not uptunnel to
higher-energy vacua and that perturbations do not decohere while slow-roll
inflation occurs, suggesting that eternal inflation is much less common than
often supposed. On the other hand, if a de Sitter patch is a closed system with
a finite-dimensional Hilbert space, there will be Poincare recurrences and
dynamical Boltzmann fluctuations into lower-entropy states. Our analysis does
not alter the conventional understanding of the origin of density fluctuations
from primordial inflation, since reheating naturally generates a high-entropy
environment and leads to decoherence, nor does it affect the existence of
non-dynamical vacuum fluctuations such as those that give rise to the Casimir
effect.
