Spatial averaging and a non-Gaussianity

The spatial averaging used for the splitting of the local scale factor on the homogeneous background and small inhomogeneous perturbation leads to a non-local relationship between locally and globally defined comoving curvature perturbations. We study this relationship within a quasi-homogeneous, nearly spatially flat domain of the Universe. It is shown that, on scales larger than the size of the observed patch, the Fourier components of the locally defined comoving curvature perturbation are suppressed. We have also shown that the statistical properties of local and global comoving curvature perturbations are coincide on a small scale. Several examples are discussed in detail.