The observed dark matter abundance in the Universe can be fully accounted for by a minimally coupled spectator scalar field that was light during inflation and has sufficiently strong self-coupling. In this scenario, dark matter was produced during inflation by amplification of quantum fluctuations of the spectator field. The self-interaction of the field suppresses its fluctuations on large scales, and therefore avoids isocurvature constraints. The scenario does not require any fine-tuning of parameters. In the simplest case of a single real scalar field, the mass of the dark matter particle would be in the range $1~{\rm GeV}\lesssim m\lesssim 10^8~{\rm GeV}$, depending on the scale of inflation, and the lower bound for the quartic self-coupling is $λ\gtrsim 0.45$.

9 pages, 5 figures. v2: Minor changes, matches the published version