1212.4550 (Elliot Nelson et al.)

Statistical Naturalness and non-Gaussianity in a Finite Universe    [PDF]

Elliot Nelson, Sarah Shandera

We examine the behavior of n-point functions of the primordial curvature perturbations assuming our observed universe is only a subset of a larger space with statistically homogeneous and isotropic perturbations. We show that if the larger space has arbitrary correlation functions in a large family of local type non-Gaussian statistics, sufficiently biased smaller volumes will have statistics from a `natural' version of that family with moments that are weakly non-Gaussian and ordered. Depending on the total size of the universe and the scale-dependence of the power spectrum, typical subsamples the size of our observed volume may be sufficiently biased to make weak non-Gaussianity whose dominant term is consistent with the usual local ansatz very likely, regardless of the statistics of the original field. We also argue that although the dominant shape of the momentum-space correlation functions may not be identical in different volumes, the characteristic behavior of the squeezed limit of the bispectrum is independent of the bias of the subsample.

View original: http://arxiv.org/abs/1212.4550