In hypothetical empty space, Bob stays home and Alice flies radially away from home at .9c. In the flat Minkowski coordinates, each determines that the other's clock is running slower than their own. Each determines that the radial distance between them is Lorentz-contracted. Now consider the same scenario, except we change to expanding space in FRW coordinates, with vanishingly small mass density. Now the space has negative (hyperbolic) curvature. Let's say that Alice is very far away, her large recession velocity happens to be exactly comoving with local fundamental observers in the Hubble flow. Each will determine that the other's clock is running at the same rate as their own, i.e. at cosmological proper time. Each determines that the radial proper distance between them is not Lorentz-contracted. It appears to me that the effect of transforming the scenario from Minkowski to expanding FRW coordinates is to: (a) change from flat space to hyperbolic spatial curvature; (b) eliminate Lorentz contraction of the space between them (by exactly offsetting it with hyperbolic spatial curvature), and (c) eliminate time dilation between them (by hyperbolically stretching the time "axis". Mathematically, it appears that the difference between Minkowski and FRW coordinates is that the FRW metric exactly transforms away (or offsets) the effects of SR as between fundamental comovers. Presumably that transformation can be easily demonstrated mathematically, but I haven't done it yet. Anyone know of such a mathematical demonstration?