10 pages, 5 figuresInternational audienceThere are several ways to explain the dark matter relic density other than by the ordinary freeze-out scenario. For example, the freeze-in mechanism may constitute an alternative for generating the correct relic density for dark matter candidates whose predicted freeze-out abundance is too low due to a large total annihilation cross section. Here we show that although such a mechanism could explain why a dark matter candidate has the correct relic density, some candidates may still be ruled out because they would lead to a large gamma ray flux in dwarf spheroidal galaxies or a large elastic scattering rate in direct detection experiments. To investigate this scenario we examine neutralino dark matter...