I think our time would have to be slowing different amounts w.r.t. objects at different distances from us. This would imply a Universe-wide effect on the rate o

I think our time would have to be slowing different amounts w.r.t. objects at different distances from us. This would imply a Universe-wide effect on the rate of passage of time which is coincidentally centered on Earth, or at least on our group of galaxies. Universal expansion has the advantage that it doesn't require the Earth to happen to be at a special privileged point in the cosmos.