  The inert doublet model, a minimal extension of the Standard Model by a
second higgs doublet with no direct couplings to quarks or leptons, is one of
the simplest scenarios that can explain the dark matter. In this paper, we
study in detail the impact of dark matter annihilation into three-body final
state on the phenomenology of the inert doublet model. We find that this new
annihilation mode dominates, in a relevant portion of the parameter space, over
those into two-body final states considered in previous analysis. As a result,
the computation of the relic density is modified and the viable regions of the
model are displaced. After obtaining the genuine viable regions for different
sets of parameters, we compute the direct detection cross section of inert
higgs dark matter and find it to be up to two orders of magnitude smaller than
what is obtained for two-body final states only. Other implications of these
results, including the modification to the decay width of the higgs and to the
indirect detection signatures of inert higgs dark matter, are also briefly
considered. We demonstrate, therefore, that the annihilation into three-body
final state can not be neglected, as it has a important impact on the entire
phenomenology of the inert doublet model.
