How big is the universe?

[Alex K]

The size of the entire universe is currently unknown, but there doesn't have to be a relationship with the size of the visible universe which is just a result of age+expansion  it could be infinite for all we know. Or at least orders of magnitude larger than what we see.

The problem I'm having with that is the idea that the universe started out roughly the size of a basketball then there occurred Einstein's singularity and it started expanding. If nothing travels faster than light then the expension of the universe would be subject to that limitation, just like if I drive at 70 miles an hour, I can't reach 120 miles from my starting point in half an hour.

It doesn't have to be problematic if we abandon the idea that what we perceive as THE universe is the result of one singularity, but consider the possibility of a multiverse or several Big Bangs. then ours could have happened 13 or so billion years ago while others occurred at various times, accounting for a visible universe that's much larger than what it should be in just the time it's had to expand. Hell, maybe it's these other universes that are moving away from us.

The fact that our universe hasn't had time to reach the size that it has, should make us look for other explanations.

The theory of relativity contains both the speed limit as well as cosmic expansion as built-in features, so you seem to suggest that relativity is inconsistent - but it isn't. It explicitely tells us how cosmic expansion arises from the dynamics of spacetime through a change of all length scales, which is a completely different thing than movement of an object through space. Both phenomena have in common that distances between objects change, but the cause and nature of this change is completely different. Ordinary movement through space only allows an increase in distance of twice the speed of light at maximum, whereas when the universal rulers themselves change as is the case in cosmic expansion, such limits do not apply because the increase in distance does not come from relative movement but from a change of the cosmic rulers built into spacetime (called "the metric" in technical terms). Both phenomena were not postulated separately but are described by the very same theory, Einstein's General theory of relativity, and coexist as two different physical processes.