Is light thermal scalar dark matter possible?

We study a light thermal scalar dark matter (DM) model with a light scalar mediator mixed with the standard model Higgs boson, including both the theoretical bounds and the current experimental constraints. The thermal scalar DM with the mass below a few GeV is usually strongly constrained by the observation of CMB and/or indirect detection experiments because the leading annihilation mode is S-wave. However, we find that two parameter regions still remain, which are the resonant annihilation region and the forbidden annihilation region. For the both cases, higher partial waves dominantly contribute to the annihilation at the freeze-out era, and the constraint from the cosmological observation is weaker. We consider typical cases of these regions quantitatively, mainly focusing on the mixing angle and the mass of the new particles. Finally, we also discuss the testability of this model at future experiments.