Measuring the size of the observable universe

[g.lemaitre]

The size of the observable universe usually gets put at 93 trillion light years, though some people believe it is infinite, though I'm not sure which camp is in the majority. Those who believe it is 93 trillion light years across are they just assuming that the size of the universe at the first Planck time was finite, I'm guessing 10^-35 m? And they are just using Hubble's constant, along the evidence of the extent to which Hubble's constant has sped up and slowed down over time, to calculate the size of the universe? I've read quite a few times that some physicists believe the universe was a centimeter across after inflation, hence finite. Again, let me state my question more succinctly, is the idea that the universe is finite just an assumption or is there some equation which requires it?

 

[mfb]

The size of the observable universe usually gets put at 93 trillion light years, though some people believe it is infinite

I would expect this "infinite" refers to the total universe, not just the observable part. Otherwise, can you provide a source for this claim?
The same is true for the size of the observable universe (which is not the size of the total universe) after inflation.

The universe can be finite or infinite - if it is small enough, it can be possible to measure its size, but we cannot distinguish between "really large" and "infinite" with current experiments and models.