meteor said:
... observable Universe appears from a point like in the Standard Model or not?
If not, what was the volume of the region that grows to our actual observable universe at the era of the Big Bang? The use of the word "singularity" in the Standard Model is misguiding sometimes in my opinion
since I am not an expert, and have imperfect memory, I have to research before answering but I will tell you my initial reaction to the question.
the volume of some region becomes an operator in the quantum theory, an operator with a spectrum of possible values which it may take.
I am not sure that one would be able to assign a definite number to be the volume of the region you ask about------the region which subsequently expanded to be our observable universe.
I remember reading that there is a maximum density which can be reached during the bounce, and that there is a welldefined quantum operator corresponding to measuring the density, and that it has a spectrum with a maxium possible value. This maximum achievable density, if I remember correctly, is on the order of the Planck density (the Planck energy, or mass, contained in the Planck volume)
but instead of trying to remember, I should really go and look for some LQC papers that are somewhere in my study.
You know meteor, quantum geometry is not completely intuitive, there is for example a geometric "Uncertainty Principle" where if you have two surfaces which INTERSECT then their two area operators do not COMMUTE. that is, the two quantum operators corresponding to measuring the areas of each surface cannot be simultaneously diagonalized!
this is very strange. as if one said that if the area of one surface is measured then the area of the other is poorly defined. this is against normal logic.
However, that said (that one cannot always used common sense) I think your question is very interesting because of this: if one knows the maximum density of a region at some time, and at some later time, then one can think about calculating how much it has expanded and what the volume was at the earlier time. Unfortunately it is not quite simple because there is the trouble with inflation. Inflation creates matter! apparently violating the conservation of energy. So that makes it more complicated. But still some calculation should be possible.
One should be able to get some handle on the volume of the region which has expanded to be the part of the universe which is observable to us at this moment.