We show that scale-scale correlations are a generic feature of slow-roll inflation theories. These correlations result from the long-time tails characteristic of the time dependent correlations because the long wavelength density perturbation modes are diffusion-like. A relationship between the scale-scale correlations and time-correlations is established providing a way to reveal the time correlations of the perturbations during inflation. This mechanism provides for a testable prediction that the scale-scale correlations at two different spatial points will vanish.
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