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)?