Is there critical density for universe so that universe expansion begin to accelerate ?

If I am correct, the present view is that in the early stages of the universe - for a less than 5 billion year after big bang - universe was decelerating, due to gravity, then begin to accelerate due to dark energy become dominant force over the gravity. Gravity turned weaker due to expansion of the Universe. Then onwards universe is accelerating due to dark energy for which Cosmologists use Cosmological Constant which actually Einstein proposed once and then abandoned. That means is this cosmological constant tells us about the critical density of the Universe? Is there any critical density - the minimum density - below which dark energy turned dominant and make the universe expand with acceleration? If so what is that equation relates density of the universe ?