This is based on a side discussion in the balloon analogy thread, see #49 and #53. How is the definition of cosmological proper distance ("CPD" from now on) different from the usual definition of distance? Here, I want to discuss the respective defintions, what these definitions "really" mean (i.e. their operational implementation), and how you should interpret the numbers that you calculate. I'm concentrating on the distance of an event/object to an free falling observer in FRW spacetimes. We define the distance of an object "now" in flat spacetime. In that case, you can compare the usual definition (standard coordinates in an inertial system) directly with CPD in an empty FRW universe, as both can be transformed easily into each other. The usual definition is - formally the length of the spacelike geodesic connecting observer and object that is normal to the worldline of the observer at a given event. - operationally the length of a ruler stationary wrt the observer that connects both. The CPD definition is - formally the length of a curve of constant cosmological time connecting both at a given time. (The curve is a geodesic of the subspace defined by fixing the cosmological time.) - operationally the total length of a chain of many small 'comoving' rulers, each in relative motion wrt its immediate neighbour according to the Hubble law, connecting both. Each ruler is supposed to lie end to end with its neighbour at the time you take the measurement. The CPD definition is clearly different from the normal one. It also looks more complicated, but we can make the normal definition also more complicated if we generalize it to curved spacetimes. There it becomes - formally the same as in flat spacetime, but now the geodesic is not simply a staight line. - operationally the total length of a chain of many small 'static' rulers, each at rest wrt its immediate neighbour according to the Hubble law, connecting both. Each ruler is supposed to lie end to end with its neighbour all the time. This definition is compatible to "Normal Coordinates", which represent arguably the next best thing to standard SR coordinates in flat spacetime. Consequences: "Recession Velocity" d(distance)/d(time) Velocity in both definitions is not limited to the speed of light. But there is an important difference: in the absence of spacetime curvature, the normal definition reduces to - you guessed it - the normal SR definition, which is always subluminal. The FRW definition on the other hand is intrinsically different: it is actually no a velocity, but a rapidity, which becomes "superluminal" quite naturally. You don't have to invoke "motion through space" vs "motion of space" to explain that. Operationally: FRW CPD/proper time are locally always the same as the normal coordinates of the fundamental (comoving) observers. Your neighbour moves away from you at dv, and his neighbour moves away from him at dv, too. In normal coordinates, you would use relativistic velocity addition w= dv+dv/(1+dv*dv) to calculate the total velocity. In FRW coordinates, you simply add the velocities, w=dv+dv, the same way you added the lengths of the rulers, even if they were in relative motion. This is not an exotic GR effect due to some miraculous "expansion of space", it is rather very straightforward: Add the dv, you get relative rapidity. Add the dv according to relativistic velocity addition, you get relative velocity. So, first conclusion: what is always called "recession velocity" is actually not a velocity. You don't have to invoke subtle spacetime mechanisms to explain superluminal recession velocities. It's a rapidity, and rapidities go easily "superluminal". Additional information: The different methods of adding small velocities along a curve of constant proper time are addressed in this paper. The "correct" application of the relativistic velocity addition law corresponds to parallel transport of the velocity vector, the algebraic addition to the recession velocity. Both are connected by the tanh function, as the definition of a rapidity requires. I'll have more to say about distances and space curvature, but I'm too tired right now. I hope there's already enough to start a discussion in this post.