I may have a fundamental misunderstanding of the concept, but I was wondering, how does the accelerating expansion of the universe calculate for the time dilation in light travel? From my understanding, we know that the universe expansion is accelerating because the farthest galaxies that we can see are all red-shifted. However, I also know that due to the speed of light, any light that we see from distant galaxies shows us a representation of what that galaxy looked like in the past. If the galaxies that we see red-shifted are far enough away and closer to the time of the singularity, couldn't it be possible that the red-shift we see is still from the initial expansion and not still currently happening? If it was accelerating away from us several billion years ago, how do we know that it is still accelerating today? Is there an "escape velocity" within a red-shifting galaxy?