Cosmic variance in inflation with two light scalars

We examine the squeezed limit of the bispectrum when a light scalar with arbitrary non-derivative self-interactions is coupled to the inflaton. We find that when the hidden sector scalar is sufficiently light (m ≲ 0.1 H), the coupling between long and short wavelength modes from the series of higher order correlation functions (from arbitrary order contact diagrams) causes the statistics of the fluctuations to vary in sub-volumes. This means that observations of primordial non-Gaussianity cannot be used to uniquely reconstruct the potential of the hidden field. However, the local bispectrum induced by mode-coupling from these diagrams always has the same squeezed limit, so the field's locally determined mass is not affected by this cosmic variance.