  We study the possibility to describe dark matter in a model of the universe
with two scale factors and a non-standard Poisson bracket structure
characterized by the deformation parameter \kappa. The dark matter evolution is
analyzed in the early stages of the universe, and its relic density is obtained
via the Freeze-In and Freeze-Out mechanism. We show that by fixing \k{appa} and
the initial ratio of energy densities present in the different sectors of the
universe, the space of thermal average annihilation cross-sections and dark
matter masses compatible with the standard cosmology prior to Big Bang
Nucleosynthesis (BBN), is enlarged. This feature of the model is compatible
with non-standard cosmology.
