If the whole universe were rotating with respect to the central axis of the universe wouldn't this "look" the same as if the universe were radially expanding explosively from a single point?
Both scenarios represent motion, one radial and the other tangential, which would cause the light from distant sources to be red-shifted due to time dilation.
One would be transverse red-shifting (rotating scenario) and the other would be doppler-like red-shifting (radially expanding scenario).
Without any extra-universal (outside the universe) reference points we could not tell if the universe were rotating except by following a similar train of thought as done in this post: The Fastest Clock.
If the universe were rotating as a whole and it were contracting then, due to conservation of angular momentum, the respective tangential velocities of the galaxies would increase which would cause the source-redshift to increase which would imitate an expanding radial universe because it would seem that since the redshift is increasing then the objects must be accelerating away ...
... but in reality the universe is collapsing.
This thread is now open for discussion.