If the expansion of the universe is not consistent, what causes the variation?
Einstein's equations are non-linear. The metric expansion of space-time depends on how much matter and energy there is inside that portion of space-time.
Also, quantum fluctuations in the hot dense "quantum soup" before the big bang grew into large scale structures: mass seems to be concentrated in the walls of huge bubbles, as super-clusters of galaxies, with very little mass/energy inside.
At the largest scales, the universe is still homogeneous, so on average, the expansion rate should be constant. But on the scale of the "bubbles", the differences in mass/energy density cause differences in the metric expansion of space-time.
Until recently, this was ignored in simulations, because Einstein's equations are currently impossible to solve exactly at that scale. So now they used better approximations than before, that include this varying metric expansion, and found they don't need dark energy flows to explain some observations. Instead, differences in expansion rates make it appear that some regions "flow" towards other regions, despite everything expanding.
From our point of view expansion appears to be accelerating because of this, causing us to believe that the cosmological constant Lambda (a.k.a. Dark Energy) is not zero. So now it seems they can explain a seemingly accelerating expansion with Lambda=0 using normal metric expansion.