  We study the effect of the early kinetic decoupling in a model of fermionic
dark matter (DM) that interacts with the standard model particles only by
exchanging the Higgs boson. There are two DM-Higgs couplings, namely
CP-conserving and CP-violating couplings. If the mass of the DM is slightly
below half of the Higgs boson mass, then the couplings are suppressed to obtain
the measured value of the DM energy density by the freeze-out mechanism. In
addition, the scattering processes of DM off particles in the thermal bath are
suppressed by the small momentum transfer if the CP-violating DM-Higgs coupling
is larger than the CP-conserving one. Due to the suppression, the temperature
of the DM can differ from the temperature of the thermal bath. By solving
coupled equations for the number density and temperature of the DM, we
calculate the DM-Higgs couplings that reproduce the right amount of the DM
relic abundance. We find that the couplings have to be larger than the one
obtained without taking into account the difference in the temperatures. A
consequence of the enhancement of the DM-Higgs couplings is the enhancement of
the Higgs invisible decay branching ratio. The enhancement is testable at
current and future collider experiments.
