I know that the known universe is roughly 27 billion light years in diameter, but what about theunknownuniverse - that is, the universe even beyond what is visible?

I used to assume it just wasn't known how big it was until I came across a chart the other day depicting the rate of expansion of the early universe. It was like this:

Time: size:

10^-40s 1mm

10^-30s 100m

10^-20s Earth

10^-10s solar system

1s 10 Ly

Now I'm not sure how reliably we can extrapolate this chart to today's universe. The rate of expansion has been changing after all. From what I understand according to the inflationary theory, the universe started out by accelerating, then decelerated, and is now into an accelerating phase once again.

But given that physicists seem to have some kind of grasp on its rate of expansion and size at various points in its history, and that we know the age of the universe, can we estimate with any confidence its size today?