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Accounts of the early stages of the big bang say that it began as an infinitely small size which began expanding and cooling. This was not an expansion into empty space, but was an expansion of 3 dimensional space itself. The progress of the universe can then be described - at this time the size was so big, the average temperature was this, and this was what was happening with fundamental particles, formation of structure, etc.

All this is challenging to understand, but makes sense to me.

But if I focus on a different question, the size of the present universe, I find that there is conjecture whether it is finite or infinite. I understand that, depending on the total mass/energy of the universe and the cosmological constant, the universe may be either closed (it will eventually collapse back), open (it will expand forever) or flat (it will slow down and reach a static state at time infinity). And I understand that if the universe is closed, then it is finite in size, but if it is open, then it is infinite in size.

I further understand that the best scientific measurements so far indicate the universe is very close to flat, but could still be open or closed. I am not here concerned about which is the case. But rather, that if it turns out that the universe is open, and infinite, this seesm to contradict what I learned about the big bang and the growth of the universe from small to large, but still finite and measurable.

So my questions are:

1. Does the scientific account of the big bang include a finite universe of measurable or calculable size?

2. Do some current understandings suggest (though not prove) that the universe might be infinite in size?

3. If both of these are true, how are they compatible? Did the size of the universe pass from finite to infinite at some stage in the 14 billion years since the beginning of the big bang? (I find that quite bizarre!)

Thanks for any light you can shed.