  We propose a simple mechanism of light dark matter (DM) production from the
decay of the oscillating inflaton condensation. If the reheating temperature
after inflation is higher than the inflaton mass, which is of the same order of
the momentum of the DM at the time of the production, the DM momentum can be
suppressed compared to the temperature of the thermal plasma if the interaction
of the DM is weak enough. Consequently, the DM can be cold enough to avoid the
observational constraints on the warm DM, like the Lyman-$\alpha$ bound even if
the DM mass is small. We study the bosonic and fermionic DM production from the
inflaton decay, taking into account the effect of the stimulated emission and
Pauli blocking, respectively. In both cases, the DM can be cold and abundant
enough to be a viable candidate of the DM. We also apply our mechanism to the
production of isocurvature-problem-free axion DM and Dirac sea DM of
right-handed neutrino consistent the seesaw relation for the active neutrino
masses.
