In cosmology, we speak of galaxies racing away from us due to the expansion of the universe. The light from these galaxies appears red-shifted. If the galaxies are far enough, then the space between us actually expands faster than light, and light from these galaxies never reaches us.
My question is what would happen in a Big Crunch universe – where space contracted faster than light.
How would a galaxy getting closer faster than the speed of light appear to us? Would its light be extremely blue-shifted? Would we see photons emitted later arriving first, so it would appear as though it is going back in time, and getting farther away?
Best Answer
In an ideal FLRW recollapsing universe, the collapse is just the time reversal of the expansion. The Doppler shift factor at all times is $a(t_\text{emission})/a(t_\text{detection})$, and during the collapse, that's a blueshift instead of a redshift.
Realistically, the big crunch would be much more chaotic than the big bang, because entropy would continue to increase, and so it wouldn't be well described by FLRW cosmology.
Regardless of the details, though, there is never a "superluminal blueshift" where light arrives backwards.
Recession speeds in cosmology are defined in such a way that the speed $c$ has no special significance. See this answer for more information. Galaxies with a recession speed higher than $c$ aren't traveling faster than light (i.e., outside of the light cone), and it isn't true as a rule that light from them never reaches us. (In ΛCDM, there is a cosmological horizon beyond which we can't see light, but it doesn't coincide with the point at which the recession speed is $c$.)
In a collapsing universe, galaxies can have an approach speed (defined in the same way) that is larger than $c$, but light from those galaxies would still reach us before the galaxy did, and would reach us with a large positive blueshift, not a negative Doppler shift (backwards).