  We explore the possible cosmological consequence of the gravitational
coupling between the inflaton and axion-like fields. In view of the forthcoming
cosmic microwave background (CMB) polarization and lensing data, we study the
sensitivity of the CMB data on the cross-correlation between the curvature and
axion isocurvature perturbations. Through a concrete example, we illustrate the
explicit dependence of the scale dependent cross-correlation power spectrum on
the axion parameters.
