cosmology - If the expansion of the universe were to stop, would galaxies continue moving away from each other at a constant speed?

Consider a simple universe consisting of two very distant galaxies (neglect gravity between them). The relative motion between them is such that, if the universe were not expanding, they would be at rest relative to each other. Due to the expansion of the universe, however, the distance between them keeps increasing, at an accelerated rate, suppose.

My general question is: is this "acceleration" literally a kind of (accelerated) motion?

It surely is similar to literal motion in many respects. It can be measured in the same units as literal acceleration. Light reaching each galaxy from the other is suitably red-shifted... Etc.

Yet, it is not like literal motion in other respects. No energy is needed to accelerate either galaxy (I take it that dark energy is postulated only to overcome gravity, not to "cause" the expansion... right?). Relative velocity can (and actually does in some cases) exceed the speed of light, without contradicting SR. No inertial forces are thought to be involved due to their "acceleration" (or are there?). No repulsive force between the galaxies could possibly "cause" this "motion" (at most, a repulsive force would cause the two galaxies to accelerate, in the literal sense). Etc.

So, is it or is it not literally a kind of motion? For example, were the expansion of the universe suddenly to stop, would the two galaxies continue moving away from each other at a constant speed (as they would if it was literally a kind of motion)?

Answer

The universe is expanding overall, and galaxies have relatively small “peculiar velocities” relative to the expanding universe. If you ignore the latter, then if the universe were to stop expanding, the galaxies would stop moving apart.

So the “motion” of galaxies due to the expanding universe is quite different from ordinary “inertial” motion. There are no non-inertial forces arising from the accelerating expansion of the universe.

You really should not think of the galaxies as moving at all. (Again, ignoring their “peculiar motion”.) They are sitting still in an expanding universe, while expanding space causes the distance between them and other galaxies to increase.

Since they are not really moving, this explains why their separation can increase at a rate faster than $c$. There is no speed limit on the expansion of space. There is only a speed limit on how fast objects can move through space.