  We revisit the generation of dark matter isocurvature perturbations in the
curvaton model in greater detail, both analytically and numerically. As
concrete examples, we investigate the cases of thermally decoupled dark matter
and axionic dark matter. We show that the radiation produced by the decay of
the curvaton, which has not been taken into account in previous analytical
studies, can significantly affect the amplitude of isocurvature perturbations.
In particular, we find that they are drastically suppressed even when the dark
matter freeze-out (or the onset of the axion oscillations for axionic dark
matter) occurs before the curvaton decays, provided the freeze-out takes place
deep in the curvaton-dominated Universe. As a consequence, we show that the
current observational isocurvature constraints on the curvaton parameters are
not as severe as usually thought.
