generic redshift is characterised (defined) by z = (L-L0)/L0 where L is the wavelength at time of absorption (detection), and L0 was the wavelength at time of emission. for Doppler redshift z = v/c for small (non-relativistic) values of v. assuming the universe is expanding, i've read that the cosmological redshift is (for bodies co-moving with the expansion) directly and strictly related to this expansion of space z = (R0-R)/R where R0 is the scale size at time of absorption (detection), and R was the scale size at time of emission. However the important point here is that the equivalent "recession velocity" does not come into the equation - it is only the expansion of space during the time the photon travels from emitter to absorber which causes the redshift, and NOT the relative velocities of emitter and absorber (both emitter and absorber assumed to be co-moving with space). imagine a "model" universe which is expanding uniformly under a "freely coasting" scenario, ie neither accelerating nor decelerating. let us say the age of this universe (from Big Bang to now) is (for the sake of argument) 10 billion years. Now let us study a stellar object in this universe which is 1 billion light years away from us, ie the light from that object was emitted 1 billion years in the past, ie when the universe was only 9 billion years old and hence only 90% of the size it is now (it is freely coasting, so size is proportional to time). we measure the cosmological redshift of this object - what should we find? well R/R0 = 0.9 hence z = 1/0.9 - 1 = 0.111. This is for an object which is 1 billion light years distant. Let us study another object, which is now 2 billion light years distant. In this case R/R0 = 0.8 hence z = 0.25. Similarly, an object 3 billion light years distant will have R/R0 = 0.7 hence z = 0.429 If we now plot z vs distance, we do not get a linear relationship : D............z 0.1.........0.111 0.2.........0.250 0.3.........0.429 etc i know i must be doing something stupid, but what? where am I going wrong?