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If the universe is expanding uniformly, then wouldn't the rate of expansion of the universe change if you were to move closer to a point that is currently moving away from us faster than light?

For example:

Say A, B and C are all equally far apart. A is moving away from B at just under the speed of light (say 90%), and B is moving from C at the same speed.

But A is moving away from C faster than light (say 110%), but since B is moving away from C at slower than light speed, then someone at point C could reach B. Then, once at B, they could reach A, since A is no longer moving away from the person at faster than light speed?

(Sorry for any poor wording or overcomplicating)

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Yes, in general relativity spacetime can expand faster than light. This is particularly important for uniformly expanding spacetimes like the FRW cosmologies. The relevant point is that matter, fields and the stuff going on in spacetime doesn't get to move faster than light locally. But remote objects may indeed be becoming more remote faster than light.

So were some kind of trick available to move you to a very remote galaxy "instantly" (groan from physicists) you would find yourself in a normal galaxy and everything is expanding away from it. One remote galaxy would be the Milky Way. If they were far enough apart the Milky Way would now be seen as moving away FTL.

Every point in the universe sees the rest of it expanding away from it, faster the further away it is. But the speed is relative to the observer, and intermediate observers will see a different speed.

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"then wouldn't the rate of expansion of the universe change if you were to move closer to a point that is currently moving away from us faster than light?"

How are you going to move closer to a region that is receding faster than the speed of light? Indeed that would require you to move away from your current position at a speed faster than the speed of light (which locally violates special relativity). The restrictions of special relativity apply only to local regions so the existence of FTL regions at very large distances is not a violation.

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  • $\begingroup$ If there's no cosmological constant then it's always possible to reach arbitrarily distant galaxies even if their cosmological recession speed exceeds $c$. In fact they can be reached ballistically with an initial speed less than $c$. See my answer. $\endgroup$
    – benrg
    Nov 11, 2020 at 20:45
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Yes, the recessional speed of a distant galaxy relative to your galaxy is more or less just the sum of the recessional speeds of pairs of adjacent galaxies in a straight line between them. They are just added up, with no "velocity addition formula" involved, so for sufficiently distant galaxies, the sum will exceed $c$. The value $c$ has no special significance when talking about this kind of speed.

If you lived in a very sparsely populated universe, with no cosmological constant, in which the nearest galaxy to yours was moving away at special-relativistic speed of 90% of $c$ (special relativity is approximately valid here because the matter density is so low), then the cosmological recessional speed of that galaxy actually wouldn't be $0.9c$, but around $c \tanh^{-1} 0.9 \approx 1.5c$. The reason is that it's still calculated as a sum of relative speeds of a bunch of imagined intermediate stopping points, and the sum is a straight sum, not special-relativistic velocity addition. This gets you what's called rapidity in the context of special relativity. Despite the recessional velocity being $1.5c$, you can reach that galaxy by accelerating up to around $0.9c$ and coasting. If there's another galaxy beyond that one with the same relative speed, then its cosmological recessional velocity relative to your home galaxy is around $3.0c$, but you can reach it from your home galaxy by accelerating to around $0.994c$ (the special-relativistic "sum" of $0.9c$ and $0.9c$) and coasting.

In the real world, it appears that there is a positive cosmological constant, the expansion is accelerating, and sufficiently distant galaxies are actually unreachable. But this has nothing to do with their current recessional speeds as such. In a universe without a cosmological constant, you can always reach arbitrarily distant galaxies regardless of their recessional speed.

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Special relativity suggests that nothing can move away from anything else at greater than the speed of light, but I'm not sure if that applies to the expansion of space-time.

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    $\begingroup$ Indeed it does not. $\endgroup$
    – Lewis Miller
    Nov 11, 2020 at 15:02

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