  Once dark matter has been discovered and its particle physics properties have
been determined, a crucial question rises concerning how it was produced in the
early Universe. If its thermally averaged annihilation cross section is in the
ballpark of few$\times 10^{-26}$ cm$^3$/s, the WIMP mechanism in the standard
cosmological scenario (i.e. radiation dominated Universe) will be highly
favored. If this is not the case one can either consider an alternative
production mechanism, or a non-standard cosmology. Here we study the dark
matter production in scenarios with a non-standard expansion history.
Additionally, we reconstruct the possible non-standard cosmologies that could
make the WIMP mechanism viable.
