  The existence of Dark Matter (DM) has been well established from various
cosmological and astrophysical evidences. However, the particle properties of
DM are largely undetermined and attempts to probe its interactions with the
Standard Model (SM) particles have, so far, not met with any success. The
stringent constraints on the DM-SM interactions, while does not exclude the
standard lore of producing weakly massive interacting particle DM candidates
through thermal freeze-out mechanism in its entirety, have certainly cast
shadow on the same. In this work, we consider non-thermal production of DM
within a simple extension of the SM including an inflaton field and a scalar DM
candidate. Assuming negligible interactions between the SM particles and the
DM, we study the production of the latter at the end of inflation, during the
(p)reheating epoch. In this context, we explore the role of DM
self-interactions and its interaction with the inflaton field, and find that DM
can be over produced in a significant region of the parameter space. We further
demonstrate that large self-interaction of the DM can suppress its abundance
during preheating and to a certain extent helps to achieve the observed relic
abundance via cannibalization.
