  Non-Gaussianity in the inflationary perturbations can couple observable
scales to modes of much longer wavelength (even superhorizon), leaving as a
signature a large-angle modulation of the observed cosmic microwave background
(CMB) power spectrum. This provides an alternative origin for a power asymmetry
which is otherwise often ascribed to a breaking of statistical isotropy. The
non-Gaussian modulation effect can be significant even for typical ~10^{-5}
perturbations, while respecting current constraints on non-Gaussianity, if the
squeezed limit of the bispectrum is sufficiently infrared divergent. Just such
a strongly infrared-divergent bispectrum has been claimed for inflation models
with a non-Bunch-Davies initial state, for instance. Upper limits on the
observed CMB power asymmetry place stringent constraints on the duration of
inflation in such models.
