If you accelerate every particle in the whole universe, would it slow down universe expansion? Perhaps an odd question, but 
(Proposition): say I want to slow down everything that is happening in the universe, I believe this could be done by accelerating everything to a velocity close to the speed of light. The universe should be invariant to translations, so this should be fine. 
(Question): If this can be done and does in fact slow down every event, would it also affect the expansion of space itself?
(Bonus Question): In the case that the expansion itself would be halted, is there any telltale sign that could indicate "btw, everything in the universe is translating"
 A: As a warm-up, let's think about this in the context of a Newtonian cosmology, such as the one that Newton originally envisioned, with a uniform mass distribution that stays in (unstable) equilibrium because all forces cancel by symmetry. You're proposing setting the whole universe in translational motion. However, this is an unobservable thing. Newton can say that the whole universe is in translational motion in a certain direction, with some huge speed. That's just a choice of a frame of reference.
As a second warm-up, consider the earth, described in special relativity. Its state of motion can be anything you want, depending on your frame of reference. We can say it's going at 99.999999% of the speed of light in the direction of the constellation Sagittarius. This doesn't cause any observable effects. We don't feel like time is going slow, because what would we compare with?
When we get to GR-based cosmology, there is an additional issue because GR doesn't have global frames of reference, nor does it have things like translation operators: How do frames of reference work in general relativity, and are they described by coordinate systems?
But, interestingly, it is possible for the universe to rotate: What if the universe is rotating as a whole? In these models, the universe is still homogeneous, however, so there is no observable time dilation between one galaxy and another.
