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How do the cosmologists account for the time gap of the distant galaxies' images?

First of all I am no phisycist of any kind, I am just a physics enthusiast.
The question that is bugging me in the notion of ever accelerating expantion of the universe is how do we know that the universe is accelerating right now. The images of the furthest galaxies are bilions years old and they are images of the younger universe, a universe that perhaps was 'still exploding', the force that caused the Big Bang was still effecting the matter in the universe. Hence it's only natural that those distant objects appear to be moving away from each other faster than the ones that are closer to us.
We don't and won't know what happens there 'now' and this might be the problem. Not "we're too late to see what happened" but "we're too soon to see what the outcome is/will be".
Please, let me know what is unclear and/or wrong in my reasoning, I'll try my best to lay out my idea.


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