Time-dependent correlations of inflationary perturbations

We show that if the primordial classical perturbations were generated by the gravitational particle creation during inflation, and followed by an evolution of quantum-to-classical transition,the time dependent correlation of these perturbations is long-tailed with a correlation time larger than the Hubble-time. Consequently, the inflationary perturbations are locally scale-scale correlated. Hence, the interaction of the fields during inflation can be explored via the detection of the local scale-scale correlation of the CMB fluctuations.