When we say the universe expands, we mean that all distances in the universe become larger with time. Moreover, they all become larger at the same rate, everywhere in the universe. We can measure this rate of expansion of space by asking ourselves: “How long will it take until all distances become twice as long?”.
Nothing in the observable universe is moving away from us at or greater than the speed of light with the expansion of space, but the current understanding is that the tiny bit of space that expanded to become what is now the observable universe was a very small part of what formed at the Big Bang event. It then seems likely that there are parts of this vast space that are moving away from us at greater than the speed of light. Anything in the parts of space that are moving away from us faster than the speed of light are impossible to observe, and that makes this idea hypothetical but still constant with what we know about the part of the universe that we can see.
The answer turns out to be a bit complicated. However, if we make some simplifying assumptions, most importantly that a parameter called the Hubble parameter is constant and will remain constant forever, we can get the following answer:
At the current rate of expansion, distances in the universe will become twice as long in approximately 9 billion years.
The universe itself will become 8 times as large, because it’s 3-dimensional, and each dimension will become 2 times as large. .
Notice that this means the farther away a galaxy is from us, the faster it would seem to move. Why? Let’s see:
- A galaxy that is 1 million light years from us now will be 2 million light years from us in 9 billion years. So it would seem to move 1 million light years during that time.
- Another galaxy, that is now 2 million light years from us, will be 4 million light years from us in 9 billion years. So it would seem to move 2 million light years during that same time.
- Yet another galaxy, that is now 4 million light years from us, will be 8 million light years from us in 9 billion years. So it would seem to move 4 million light years during the same amount of time as the other two!
This observation, that farther away galaxies move faster from us, is called Hubble’s law.
Of course, in the simple examples I gave above I didn’t take into account that the galaxies are, in fact, already moving. However, their speeds at such close distances are small enough that it wouldn’t matter.
What about the relation to the speed of light? Well, all the galaxies that currently less that roughly 14 billion light years from us all move slower than light with respect to us.
However, Hubble’s law says that galaxies farther away move faster, so galaxies that are currently more than 14 billion light years from us move faster than light with respect to us.
Is there a contradiction with relativity here? No, because nothing is actually moving faster than light. There’s a “loophole” here that comes from the fact that speed is something that you measure relative to space, but in this case space itself is expanding, so speeds are no longer meaningful.
It’s like standing on a moving sidewalk (usually found at airports). You can be perfectly still, and not move at all with respect to the moving sidewalk, but the sidewalk itself is still moving.
In conclusion: Space is expanding at a constant rate, not a speed. Things in space, like galaxies, move because space itself is expanding. Their speed relative to us is proportional to their distance from us. So if they’re far enough (namely more than 14 billion light years), they move faster than light. They move at that speed whether they want to or not, because space itself is moving.
(For anyone interested in how I arrived at 9 billion years, and knows some cosmology: I solved the equation where is the cosmological scale factor and is the Hubble parameter. Assuming that is constant, the solution is . This means that doubles itself after a time , which evaluates to roughly 9 billion years.)