https://physics.stackexchange.com/questions/376343/time-dilation-due-to-space-expansion
From the physicist on this link:
"There is no reason to expect cosmological Doppler shifts to be analyzable into factors like the ones you used for your argument for the longitudinal Doppler shifts in SR. Actually GR doesn't have a way to define the relative velocities of distant objects, so there would be no way to define a β. When people talk about cosmological expansion in terms of the velocities of distant objects relative to us, that's just a popularized explanation."
They just continue to underestimate its effects because they are using c as the parameter, when the expansion began faster than c and has continued to increase.... They do so because they don't understand why c is always c regardless of velocity.
I really don't know where you get this. The expansion did NOT start 'faster than c'. During the inflationary epoch, it *was* faster than c', but it was slower both before and after that epoch. In particular, the rate of expansion was *decreasing* until about 5 billion years ago, when it started to increase again.
Or that people are not trying to figure it out?
Dark energy explained by relativistic time dilation? – Astronomy Now
Absolute Loentz Transformation. Right. OK.