Dark matter is one of the bigger mysteries of modern physics. Astronomical data shows that objects and light in space experience additional gravitational effects from something unseen. Though there exist alternative theories for this effect, such as modified gravity, those that propose actual new matter are the least refuted, most popular and most promising. In this masters work, I study one such realization of dark matter, in the form of a weakly interacting massive particle, a copy of the Higgs. This is a natural choice, as we are taking example after a known and proven particle. The realization is called the inert doublet model (IDM), after its primary characteristic - its low reactivity. The goal is to provide an alternative method of calculating the thermally averaged cross-section and consequently also the freezeout relic density of dark matter after the universe cools and expands, such that the dark matter does not react further. The main contributions to the cross-section are analyzed and it is shown how we can apply them.
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