There is an almost perfect analogy with throwing a ball in the air. If you throw a ball up in the air (= Big Bang) then it will fall back down due to gravity (= universe will eventually re-collapse). However if you throw the ball in the air fast enough, above escape velocity (= expansion rate is fast enough), then the ball will never fall back down again (= will continue to expand forever). However! This would still mean the expansion should slow down over time, slowly grinding to a halt and not reverse. But what we actually see in the universe is that the expansion is accelerating… It’s like throwing the ball upwards and it accelerating away into space.
This seems strange in our ‘Newtonian’ understanding of gravity, where masses attract other masses. But in General Relativity, gravity isn’t necessarily attractive. Certain forms of energy have gravity that pushes things apart. Dark energy (a.k.a. vacuum energy) does exactly this, and is thus thought to be responsible for the accelerated expansion of the universe.
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