if you need to think of something "driving" the pattern of expanding distances, try thinking that general relativity is driving.
And think of GR not as a theory of gravity but as a theory of dynamic geometry. It explains why we observe the geometric relations we do, where we do, and how geometry changes.
It explains, for example, why in most places and situations, the sum of the angles is 180, and pythagoras, and stuff like that. And explains why and how distances between apparently stationary things can increase, when GR says, and decrease when they have to. All this contained in the idea of curvature.
The main GR equation tells how geometry evolves. And once it gets started expanding, the equation makes it continue (although the eq. allows it to speed up gradually or slow down, depending on stuff etc.)
Try thinking that way, as dynamic geometry. See how it works.
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Try saying to yourself "geometry is autonomous."
You should realize that except for small random motions the galaxies are not moving.
Most galaxies we can see have redshift z > 1.7. And if a galaxy has redshift over 1.7 then the distance to it is increasing at a rate faster than c. So the distance to a typical galaxy is increasing faster than c. But the galaxy is not going anywhere, it is not ordinary motion where the galaxy would be approaching some destination. It is simply distances between stationary objects changing as required by the Law of Geometry. (the main GR equation, that is)
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In school, 14-year-olds learn pythadoras and that triangles add up to 180 degrees, which is approximately true at least in this neighborhood of space, and a very useful approximation---what it says is that locally our space is approximately FLAT.
But they aren't told why it is flat.
It is flat because the density is about right for flatness. The main GR equation explains what makes it flat, and what the critical density has to be.
At the present epoch the average largescale density has to be about 0.86 nanojoules per cubic meter. If it were significantly different then you wouldn't have pythagoras or 180 degrees.
GR says there are reasons for basic features of how things are, why are that way. Off hand you have no right to expect some things to be true that you learn as a 14 year old, without something causing them to be that way.
And you can't expect distances to stay the same, because they evolve according to a pattern as part of autonomously evolving geometry. (which the initial conditions and the density of matter does influence!)
