  We compute the rate with which unobserved fields decohere other fields to
which they couple, both in flat space and in de Sitter space, for scalar fields
prepared in their standard adiabatic vacuum. The process is very efficient in
de Sitter space once the modes in question pass outside the Hubble scale,
displaying the tell-tale phenomenon of secular growth that indicates the
breakdown of perturbative methods on a time scale parameterically long compared
with the Hubble time. We show how to match the perturbative evolution valid at
early times onto a late-time Lindblad evolution whose domain of validity
extends to much later times, thereby allowing a reliable resummation of the
perturbative result beyond the perturbative regime. Super-Hubble modes turn out
to be dominantly decohered by unobserved modes that are themselves also
super-Hubble. When applied to curvature perturbations during inflation this
observation closes a potential loophole in recent calculations of the late-time
purity of the observable primordial fluctuations.
