Super cosmic variance from mode-coupling: A worked example

Abstract

If the entire post-inflationary patch is large compared to our Hubble volume even a small level of non-Gaussianity can cause statistics of the primordial curvature field in our Hubble volume to be biased by mode-coupling. We explicitly compute the variation of locally measured statistics of the primordial curvature $\zeta$ from non-Gaussian mode coupling within a specific inflationary scenario: the curvaton model with a quadratic curvaton potential. This "super cosmic variance" is calculated in two ways: (i) as a super observer who has access to the curvature perturbation field across the entire post-inflationary patch and therefore sees local statistics as biased by mode coupling and (ii) as a local observer who sees the statistics of $\zeta$ determined by the local values of quantities in their Hubble patch. The two calculations agree and show that in the quadratic curvaton model patch-to-patch differences in statistics of $\zeta$ can be interpreted entirely as a shift in the value of the curvaton field at freeze out. Applying the same arguments to single-field slow-roll inflation gives a simple picture of how non-Gaussian mode-coupling between the curvature perturbations on very different physical scales must vanish in the attractor limit.