Detecting a small perturbation through its non-Gaussianity

A highly non-Gaussian cosmological perturbation with a flat spectrum has unusual stochastic properties. We show that they depend on the size of the box within which the perturbation is defined, but that for a typical observer the parameters defining the perturbation ``run`` to compensate for any change in the box size. Focusing on the primordial curvature perturbation, we show that an uncorrelated Gaussian-squared component is bounded at around the 10% level by the Wilkinson Microwave Anisotropy Probe (WMAP) bound on the bispectrum, and we show that a competitive bound may follow from the trispectrum when it too is bounded by WMAP. Similar considerations apply to a highly non-Gaussian isocurvature perturbation.