Dark matter candidates in a broad class of non-thermal models produce primordial isocurvature perturbations and non-Gaussianities. We discuss the model dependence of such scenarios. In particular, fermionic superheavy dark matter requires non-gravitational interactions to be observationally interesting. We also present a general mathematical result regarding the cross correlation between the primordial isocurvature perturbations and curvature perturbations. This last result is of general interest for isocurvature phenomenology. Download the slides