If I understand it correctly, dark matter has no relevance at all in the expansion. The expansion is attributed entirely to (1) a small amount of non-accelerating distance change that is left over from the earliest days of the universe and (2) a large and accelerating distance change due to whatever it is that we call dark energy.
Before dark energy was discovered, the belief was that the distance change due to (1) would decrease and eventually reverse due to gravity. In fact, as I recall the belief was that the reversal had already started. When it was found that the situation was quite different, with distance changes accelerating, this was attributed to "dark matter" which is a technical term meaning "hey, we have NO idea what's going on but we've got to call it something".