Non-Gaussian Mode Coupling and the Statistical Cosmological Principle
  Local-type primordial non-Gaussianity couples statistics of the curvature
perturbation \zeta on vastly different physical scales. Because of this
coupling, statistics (i.e. the polyspectra) of \zeta in our Hubble volume may
not be representative of those in the larger universe -- that is, they may be
biased. The bias depends on the local background value of \zeta, which includes
contributions from all modes with wavelength k ~< H_0 and is therefore enhanced
if the entire post-inflationary patch is large compared with our Hubble volume.
We study the bias to locally-measured statistics for general local-type
non-Gaussianity. We consider three examples in detail: (i) the usual fNL, gNL
model, (ii) a strongly non-Gaussian model with \zeta ~ \zeta_G^p, and (iii)
two-field non-Gaussian initial conditions. In each scenario one may generate
statistics in a Hubble-size patch that are weakly Gaussian and consistent with
observations despite the fact that the statistics in the larger,
post-inflationary patch look very different.
