On Symmetric and Asymmetric Light Dark Matter

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I will discuss cosmological, astrophysical and collider constraints on thermal dark matter with mass in the range 1 MeV to 10 GeV. CMB observations can be evaded if the DM relic density is sufficiently asymmetric, while collider constraints generally require sufficiently light mediators. These light mediators can give rise to significant DM self-interactions, and I will describe bounds on such interactions from dark matter halo shapes. Finally, I will describe how these constraints map onto the parameter space of DM-electron and DM-nucleon scattering cross sections for direct detection.