Thoughts on the scale of the universe?

[Darkstar]

But unless the expansion rate is infinite, wouldn't it take an infinite amount of time for the universe to become infinitely large, assuming it was even capable of doing so?

No. The universe could have been infinite to start with, before it even expanded. Think of a progenitor universe that consist of infinite number of little units of space. This progenitor universe is infinitely large. Then something happened to it, a phase transition, say. So all of a sudden every one of the infinite number of little unit of space expanded greatly. The universe is still infinite, and consist of infinite number of space units. But each unit has now expanded enormously at its own rate of expansion.

The universe was infinite, still is infinite, but the unit of space we are in expanded greatly at its own finite rate of expansion.

How can something that is infinitely large get bigger? Wouldn't the infinite number of spaces, no matter how small each one was, take up an infinite amount of space and leave no room for expansion? Infinite is not just 'big beyond comprehension', it is everything, that is why we cannot assign a value to infinity-10^99999999; it would still be too large. If they could still expand, that would suggest that the 'space' the universe is expanding into was bigger than infinity, which is impossible. If you said that an infinite amount of potential space was contained in the singularity, but not infinite mass, and that space was simply becoming less dense with matter as it expanded, being infinite all the way, I'd be willing to believe that much.