  We compute the rate with which super-Hubble cosmological fluctuations are
decohered during inflation, by their gravitational interactions with unobserved
shorter-wavelength scalar and tensor modes. We do so using Open Effective Field
Theory methods, that remain under control at the late times of observational
interest, contrary to perturbative calculations. Our result is minimal in the
sense that it only incorporates the self-interactions predicted by General
Relativity in single-clock models (additional interaction channels should only
speed up decoherence). We find that decoherence is both suppressed by the first
slow-roll parameter and by the energy density during inflation in Planckian
units, but that it is enhanced by the volume comprised within the scale of
interest, in Hubble units. This implies that, for the scales probed in the
Cosmic Microwave Background, decoherence is effective as soon as inflation
proceeds above $\sim 5\times 10^{9}$ GeV. Alternatively, if inflation proceeds
at GUT scale decoherence is incomplete only for the scales crossing out the
Hubble radius in the last ~ 13 e-folds, of inflation. We also compute how
short-wavelength scalar modes decohere primordial tensor perturbations, finding
a faster rate unsuppressed by slow-roll parameters. Identifying the parametric
dependence of decoherence, and the rate at which it proceeds, helps suggest
ways to look for quantum effects.
