Why does General Relativity with no dark energy, no cosmological constant, predict that the universe should expand? All the matter in the the universe causes collapse of spacetime, not expansion. So, where does the "expansion" come from? An intuitive answer is appreciated.

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    $\begingroup$ "General Relativity with no dark matter, no cosmological constant, predict[s] that the universe should expand" [citation needed]. $\endgroup$ – AccidentalFourierTransform Feb 1 '18 at 15:07
  • $\begingroup$ @AccidentalFourierTransform I saw it on a video @ Youtube, PBS Studios Spacetime. Sorry can't remember the video. $\endgroup$ – PhyEnthusiast Feb 1 '18 at 15:22
  • $\begingroup$ I answer that question with a trivial question : You throw a ball vertically in the air. Gravity wants to bring the ball to the floor. Yet, the ball is rising. Where does the vertical "expansion" comes from ? $\endgroup$ – Cham Feb 1 '18 at 16:44
  • $\begingroup$ @Someone this site is intended for everyone who loves physics to help everyone else who loves physics in the hope of making the world a better place for physicists. We are all enthusiasts here. Would it have been so much trouble to expand your answer a bit to make it a bit more helpful to a beginner? $\endgroup$ – John Rennie Feb 1 '18 at 17:30
  • $\begingroup$ @JohnRennie, PhyE asked for an intuitive answer. I think that this query is much easier when reformulated as a classical (i.e. newtonian) equivalent. $\endgroup$ – Cham Feb 1 '18 at 17:40

It isn't strictly true to say that GR predicts the universe should expand. What GR predicts is that a static universe cannot be stable.

This is a lot simpler than you might think. Suppose you see a stone in mid air. Experience tells us that stones don't hover in mid air, so someone must have thrown the stone and it must be on its way up or on its way down. If we measure the velocity of the stone we can tell which of these is the case.

Likewise if you see space full of galaxies this can't be a stable configuration because if the galaxies are all stationary they would attract each other. If the galaxies are there it's because some thing threw them (we'll get back to what I mean by threw in this context). By measuring the velocities of the galaxies we can tell if they are on the way up or on the way down, and if we measure the velocities we find they are on the way up i.e. the galaxies are all receding from each other.

What GR does is make this quantititative i.e. with a few simplifying assumptions we can calculate how the density of matter behaves with time. And when we do this we find in order to get where it is right now all the matter must have started out infintely dense and moving away from all the other matter infinitely fast, and that happened 13.7 billion years ago. Obviously, this moment is the Big Bang.

The key point is that GR isn't the reason the universe is expanding. It's an experimental observation that the universe is expanding, and starting with this observation GR gives us the means to calculate how the universe behaved in the past and how it will behave in the future.

The reason the universe is expanding is because of whatever happened at the Big Bang but GR can't explain that. Hopefully some theory of quantum gravity will explain why the Big Bang happened, but until then we just haveto accept that it did and use GR to calculate what happened next.

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    $\begingroup$ But, I heard a story of Einstein having finished his theory and as it stood it predicted expansion, but to make it a static universe, he added the cosmological constant. Hubble finds the expansion, no need for the constant and it's Einstein's biggest blunder. Then they find its accelerated expansion, dark energy and cosmological constant back again $\endgroup$ – PhyEnthusiast Feb 1 '18 at 15:31
  • $\begingroup$ @PhyEnthusiast the story you've heard is incomplete. When Einstein applied his theory to the universe he discovered it couldn't be static i.e. it must be expanding or contracting. This was a problem because at that time people thought the universe was static. Hence Einstein had to add a CC (effectively add some dark energy) to make the universe static. $\endgroup$ – John Rennie Feb 1 '18 at 15:34
  • $\begingroup$ I have two stones circling each other in space. Is there an easy explanation why GR also rules out a static rotationg configuration? $\endgroup$ – lalala Feb 1 '18 at 16:03
  • $\begingroup$ @lalala do you mean a static rotating universe? $\endgroup$ – John Rennie Feb 1 '18 at 16:17
  • $\begingroup$ so is every gravitational system unstable? $\endgroup$ – PhyEnthusiast Feb 1 '18 at 17:02

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