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We study phenomenology of a light scalar dark matter (DM). In the model,there are an inert doublet scalar and a singlet Dirac fermion $\psi$, bothcharged under a global $Z_2$ symmetry. The mass of the lightest inert scalar$H$ can be lighter than 10 GeV by imposing appropriate relations between threescalar quartic couplings. The lightest $Z_2$ odd particle is stable and DM. Inthis paper, focusing on the parameter space where $H$ is lighter than $\psi$and is DM, we discuss DM physics related to relic density, direct detection,indirect detection, collider searches and other cosmological observations. Weclarify differences from the case where $\psi$ is instead DM, which has beenfocused on in the previous works.

Light mass window of inert doublet dark matter with lepton portal interaction