Symmetric and asymmetric light dark matter

We examine cosmological, astrophysical and collider constraints on thermal dark matter (DM) with mass m(X) in the range similar to 1 MeV-10 GeV. Cosmic microwave background (CMB) observations, which severely constrain light symmetric DM, can be evaded if the DM relic density is sufficiently asymmetric. Cosmic microwave background constraints require the present anti-DM-to-DM ratio to be less than similar to 2 x 10(-6) (10(-1)) for DM mass m(X) = 1 MeV (10 GeV) with ionizing efficiency factor f similar to 1. We determine the minimum annihilation cross section for achieving these asymmetries subject to the relic density constraint; these cross sections are larger than the usual thermal annihilation cross section. On account of collider constraints, such annihilation cross sections can only be obtained by invoking light mediators. These light mediators can give rise to significant DM self-interactions, and we derive a lower bound on the mediator mass from elliptical DM halo shape constraints. We find that halo shapes require a mediator with mass m(phi) greater than or similar to 4 x 10(-2) MeV (40 MeV) for m(X) = 1 MeV (10 GeV). We map all of these constraints to the parameter space of DM-electron and DM-nucleon scattering cross sections for direct detection. For DM-electron scattering, a significant fraction of the parameter space is already ruled out by beam-dump and supernova cooling constraints.