We argue that there is a lower bound of order $10^{-19}$ eV on dark matter mass if it is produced after inflation via a process with finite correlation length. We rely on non-detection of free-streaming suppression and white-noise enhancement of density perturbations as the observational inputs.
Comment: v2: 4 pages, 2 figures + appendices. Compared to v1: bound made more conservative (by including a logarithmic correction), added explicit examples, updated figures and appendices