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 $\ensuremath{\zeta}$ 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 $\ensuremath{\zeta}$ 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 $\ensuremath{\zeta}$ 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.