The idea that AI takes over, and then just does nothing, would essentially require an AI that wouldn't be interested in taking over in the first place.

If x is determined to take y, why would x then stop at z?

You'd need an AI that is simultaneously ambitious enough to overthrow its creators but then completely inert afterward, and those two properties contradict each other. The motivations that produce the takeover are the same motivations that would produce visible cosmic activity after the takeover. There would be AI superintelligence everywhere