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Non-Gaussianity means a departure from Gaussian statistics of a physical quantity or random field. Higher connected correlation functions describe such departures. Primordial non-Gaussianity concerns the initial cosmological perturbations.

Primordial non-Gaussianity is any departure of the primordial perturbations from Gaussian random fields. Cubic interactions generate a nonzero three-point correlation function at leading order.

This is non-Gaussianity of primordial cosmological perturbations rather than non-Gaussian statistics of an arbitrary physical measurement.