According to the standard model, which gives a pretty good fit to the data, the acceleration is not as you imagine it.
People get fooled by the word "acceleration".
If you pick a definite length, like a million lightyears, the speed distances of that length are destined to grow is supposed to DECLINE.
In the future, any given length will be growing MORE SLOWLY than it is today.
Nothing will be pulled apart, a "sea of quarks" will not be created. I'm talking about the standard LambdaCDM cosmic model that cosmologists use. There are some wild scenarios that people used to write more about in the early 2000s. But they write less about that now. Fewer researchers are interested. The data continues to confirm that Lambda the cosmological constant is, well, constant
So our experience of expansion will only get milder rather than more severe. No "big rip".
When astronomers talk about "acceleration" of distance growth they mean something different. It's like money in a savings account where the bank pays you a rate of interest that slowly declines over time say down to some basic floor rate. If the decline is slow, your account can still grow almost exponentially because each year the PRINCIPAL is bigger, so you get more interest on you account (even though the percentage rate may have declined slightly).
So if you watch a particular distance between two observers at rest relative to background, that distance will grow like a bank account with a slowly declining rate of interest and it will therefore accelerate.
Even though the interest paid on some definite amount, like $100, declines over time.
Sizes of ordinary things, like books, stars, or galaxies are not affected in any significant way by this expansion. However INTERGALACTIC distances, if they are large enough, and span between objects essentially at rest wrt background, are effected according to the standard expansion pattern. So far in the future our galaxy will have very few neighbors!
You could say that this makes the place cold and lonely. But the main trouble with the longterm future, I think, is that stars eventually burn out.
If it weren't for that, the future would look pretty much like the present (except you wouldn't see galaxies thru a telescope---astronomy wouldn;t be as much fun.)