We examine cosmological , astrophysical and collider constraints on thermal dark matter ( DM ) with mass m _ { X } in the range \sim 1 \leavevmode \nobreak { MeV } -10 \leavevmode \nobreak { GeV } .
Cosmic microwave background ( CMB ) observations , which severely constrain light symmetric DM , can be evaded if the DM relic density is sufficiently asymmetric .
CMB constraints require the present anti-DM to DM ratio to be less than \sim 2 \times 10 ^ { -6 } ( 10 ^ { -1 } ) for DM mass m _ { X } = 1 MeV ( 10 GeV ) with ionizing efficiency factor f \sim 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 } \gtrsim 4 \times 10 ^ { -2 } \mbox { MeV } ( 40 \mbox { 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 .