Constant speed of light violates accelerating expansion of universe? My question regards the following:
One of the most fundamental principles of Einstein's GR is that all free bodies move through spacetime with constant velocity $c=1$.
However, in 1998 Hubble showed the expansion of the universe to be accelerating.
Thus, shouldn't all bodies move with constant acceleration (the acceleration of the expanding universe), and thus not have a constant velocity of $c$. This violates Einstein's principle no? Anywhere I've gone wrong?
 A: To quote my answer and comments here:

The limit on speed, the speed of light, affects objects and information within spacetime.  It doesn't apply to changes to spacetime itself, which is what causes the universe's own expansion.  Wikipedia has a decent article on this:



The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not expand "into" anything and does not require space to exist "outside" it. Technically, neither space nor objects in space move. Instead it is the metric (which governs the size and geometry of spacetime itself) that changes in scale......


So the answer is that, we observe and measure the speed of light from inside spacetime. Laws of nature we use day to day, such as whether something is moving at a constant velocity or accelerating, are always against that frame of spacetime as our guide to measure against.
If spacetime itself changes scale, we don't see that in day to day life as an acceleration, because the changes for both space and time are usually far too small on a human timescale. And for distant objects where the scale of space is enough to see things like the Hubble effect and receding objects, we don't see it over long enough time to see acceleration as such, we only see their apparent relative velocity as it is for this million or so years.
A way to think about the expansion of space is this (same answer as above, comment of mine):

I suppose it would be a bit like this: you drive your car from A to B,along a conveniently straight road. Before you set off, you check satnav, A to B is 1000km, car does 100km/h, easy! After an hours drive you recheck satnav. Strangely, A is now 200km behind you, B is now 3000km ahead of you, but the trip computer and speedometer both say you've been doing a steady 100km/h on cruise control the whole time. You drive another 10 hours, convinced you must be there by now, only to find satnav says you've driven 50,000km, got another 1,200,000km to go, and been driving at 100 km/h all the way.


In fact you drive and drive and drive (magic fuel!) and at the latest check, you've been driving 16 years without a break, travelled 4 billion miles from A, got 29 billion miles to reach B, and yet satnav is still adamant you've done exactly 100km/h all the time, and looking out of the window it certainly looks like you're doing 100km/h now. Everything looks.... ordinary. And yet. You never actually reach B. And that's light and the size of the observable universe........

The expansion of spacetime is fundamentally a different kind of thing, than movement (including acceleration) of objects within spacetime. And that's why the two don't conflict. When we discuss "acceleration" we mean the visible, actual or apparent relative movement within spacetime, not the changes to spacetime itself.
A: 
One of the most fundamental principles of Einstein's GR is that all free bodies move through spacetime with constant velocity =1

This is not a fundamental principle of GR. It comes from SR and it is basically just the trivial statement that a unit tangent vector has unit length. In other words, in the geometric concept of SR, an object’s path through spacetime is some curve called a worldline. The four-velocity is the unit tangent vector to that curve, and it’s length is c which is the unit length for speeds in relativity.

Thus, shouldn't all bodies move with constant acceleration (the acceleration of the expanding universe), and thus not have a constant velocity of . This violates Einstein's principle no? Anywhere I've gone wrong?

No, this is wrong in many places. First, even in an accelerating universe not all bodies move with constant acceleration. Second, the spacetime velocity on an accelerating worldline remains c for the same reason that a unit tangent vector remains a unit length even on a curve. Third, this in no way violates any principle.
A: Dale's answer is excellent, but I wanted to clarify a few things.
First of all, when we see the redshift from distant galaxies, the distant galaxies do not have velocity away from us as you would imagine. Instead, the right way to think about it is that the distance between two galaxies is increasing.
Two galaxies can be stationary, but the distance between them and any two points is increasing with time. The galaxies aren't really moving (through space) in this view, and thus they are not accelerating.
In the study of cosmology, the word "acceleration" refers to the change in the distances between points rather than the usual "acceleration" of motion that you would think about in other domains of study. This word is sort of overloaded and means different things in different contexts.
