  We demonstrate that local, scale-dependent non-Gaussianity can generate
cosmic variance uncertainty in the observed spectral index of primordial
curvature perturbations. In a universe much larger than our current Hubble
volume, locally unobservable long wavelength modes can induce a
scale-dependence in the power spectrum of typical subvolumes, so that the
observed spectral index varies at a cosmologically significant level (|\Delta
ns | ~ O(0.04)). Similarly, we show that the observed bispectrum can have an
induced scale dependence that varies about the global shape. If tensor modes
are coupled to long wavelength modes of a second field, the locally observed
tensor power and spectral index can also vary. All of these effects, which can
be introduced in models where the observed non-Gaussianity is consistent with
bounds from the Planck satellite, loosen the constraints that observations
place on the parameters of theories of inflation with mode coupling. We suggest
observational constraints that future measurements could aim for to close this
window of cosmic variance uncertainty.
