Dark matter from WIMP to FIMP over three regimes: Cosmology versus Colliders

Dark matter models can give rise to specific signatures at particle physics experiments or in cosmology. The details of the cosmological history can also influence the new physics signals to be expected at e.g. collider experiments. In these proceedings, we briefly summarize the case of dark matter weakly to feebly coupled to Standard Model fermions through t-channel portal dividing the discussion into three main regimes. We also underline the interplay between cosmology and particle physics.