We consider the possibility of using dark matter particles mass and its interaction cross section as a smoking gun signal of the existence of a Big Bounce at the early stage in the evolution of our currently observed universe. A study of dark matter production in the pre-bounce contraction and the post bounce expansion epochs of this universe reveals a new venue for achieving the observed relic abundance of our present universe. Specifically, it predicts a characteristic relation governing a dark matter mass and interaction cross section and a factor of $1/2$ in thermally averaged cross section, as compared to the non-thermal production in standard cosmology, is needed for creating enough dark matter particle to satisfy the currently observed relic abundance because dark matter is being created during the pre-bounce contraction, in addition to the post-bounce expansion. As the production rate is lower than the Hubble expansion rate information of the bounce universe evolution is preserved. Therefore once the value of dark matter mass and interaction cross section are obtained by direct detection in laboratories, this alternative route becomes a signature prediction of the bounce universe scenario. This leads us to consider a scalar dark matter candidate, which if it is light, has important implications on dark matter searches.
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