Correlation of isocurvature perturbation and non-Gaussianity

We explore the correlations between primordial non-Gaussianity and isocurvature perturbation. We sketch the generic relation between the bispectrum of the curvature perturbation and the cross-correlation power spectrum in the presence of explicit couplings between the inflaton and another light field which gives rise to isocurvature perturbation. Using a concrete model of a Peccei-Quinn type field with generic gravitational couplings, we illustrate explicitly how the primordial bispectrum correlates with the cross-correlation power spectrum. Assuming the resulting f_NL ∼ (1), we find that the form of the correlation depends mostly upon the inflation model but only weakly on the axion parameters, even though f_NL itself does depend heavily on the axion parameters.