Why does an open universe expand forever even without dark energy?

I have very little basics in Physics. I have read old posts but still confused.

Why would an open universe without dark energy expand forever, since there is no repulsive force(dark energy) but only attractive force(gravity) ?

Please explain how my thinking is flawed. Thanks :)

Suppose you saw a ball in mid air. Balls don't just hover in mid air, so if you see a ball in mid air you know that someone must have thrown it. You could do things like measure the ball's velocity, and this would tell you whether the thrown ball is on the way up or on the way down. Or if the ball's velocity was upwards and very high you could tell if the ball was going to escape Earth's gravity never to return.

This is the situation we find ourselves in when we observe the universe. We see a large number of stars, galaxies etc, but they can't just be hanging there because that isn't a stable configuration - they must be moving. And when we measure the velocities of galaxies we find they are all moving away from us, so the universe is like the ball on its way up.

Knowing the current positions and velocities of all the galaxies we can extrapolate backwards in time, and when we do so we find that as we work backwards in time the velocities get higher and higher until 13.7 billion years ago they become infinite. That is of course the moment of the Big Bang.

The analogy with the thrown ball is actually pretty close. At the instant of the Big Bang the galaxies all started out with very high velocities, just as the thrown ball started out with a high velocity, and for the first few billion years the mutual gravity of all those galaxies was slowing them down, just as the ball slows down as it moves upwards. If dark energy didn't exist the galaxy velocities would continue to decrease. We think the universe is flat, which is analogous to the ball having exactly escape velocity, so the galaxy velocities would tend asymptotically to zero given infinite time.

But ...

The problem is that we know why the ball started out with a high velocity because someone threw it. But we don't know why the galaxies all started out with high velocities because our theories don't go back in time far enough to describe the Big Bang. We hope that some future theory of quantum gravity will explain why the universe started out as it did 13.7 billion years ago.

• Thank you very much for your explanation. But I still don't understand about the expansion. From what I understand(might be wrong), the universe's expansion is the expansion of space, not galaxies moving with velocities right? If so, when the inflation ended, why wouldn't the universe without dark energy start to contract immediately, since it's the space that expands (not galaxies moving with velocities). Oct 20, 2017 at 6:58
• @parker: We usually say it's space expanding because that's the way the expansion is described in general relativity i.e. we use a coordinate system called comoving coordinates in which the galaxies are stationary but the distance between them increases. But it's also perfectly reasonable to say that in our coordinate system the galaxies have a velocity away from us. The lesson of general relativity is that spacetime and matter are inextricably linked. Space is only expanding because it's full of matter. In an empty universe space wouldn't be expanding. Oct 20, 2017 at 7:10
• Minor quibble, but "At the instant of the Big Bang the galaxies all started out with very high velocities" galaxies take a little while to form ;) Still, nice use of a simple analogy that is actually pretty accurate. Oct 20, 2017 at 7:27
• @KyleOman: yes, I realised that as I was writing but decided in the interests of simplicity to ignore it :-) Oct 20, 2017 at 7:29
• @parker: when the scale factor goes to zero. Inflation doesn't really change the behaviour because all it does is introduce another term into the mass/energy distribution that causes the scale factor to increase exponentially for a brief period. The equations that govern the expansion are still basically the same. You should note we have no idea what caused inflation, and there are physicists who doubt inflation ever happened. Honestly, we have no idea what happened at such small times after the time zero. Nov 6, 2017 at 7:51

A similar phenomenon already exists if we consider only the Earth and some rocket, both alone in the universe: we launch the rocket from the Earth surface by firing its engine for only a short time, as usual, so as to give it some initial velocity, and then we leave it entirely to the Earth gravity. There is a velocity threshold such that if this initial velocity is higher than that, the rocket will never fall back on Earth: it will keep moving farther and farther. It will move slower and slower because of Earth gravitational pull, sure, but that won't be enough to stop the rocket and make it fall back. This threshold velocity is what is called escape velocity for an obvious reason I hope.

The situation is qualitatively similar for the universe without dark energy: the big bang imparted enough initial "speed" to spacetime itself that gravity will not be able to stop the expansion. The expansion will go ever slower, as the rocket, but it will never stop. For the universe, the threshold is not given in term of an initial speed as I did for the rocket. It is instead given in term of a threshold for the mass of the universe. You can understand that with my rocket by imagining we vary the mass of the Earth, which in turn would vary the gravitational pull on the rocket. There is an Earth mass threshold such that above it the gravitational pull will be strong enough to stop the rocket in a finite time and make it fall back on Earth. Similar idea for the entire universe, only qualitatively of course, because you need General Relativity.