TalonD said:
hotter and denser but not smaller? ... I mean, do the three dimensions stretch out in all directions infinitely even at the moment of beginning? so in the beginning the singularity was one of density and not of size? or is that wrong? or is it known or unknown?
That is put very clearly. It is a good question. What you present is one possibility---infinite spatial volume filled with infinite matter.
An initial state of very high density. This is the version of the standard cosmic model that is most often used for calculation.
The standard model is LCDM (lambda cold dark matter) and it comes in several versions, most commonly there is the spatially infinite LCDM with overall zero curvature (so-called flat version) and the spatially finite LCDM with slight positive curvature, nearly flat.
If you look in Ned Wright's cosmology FAQ he says clearly
we don't know which is right, all we know is that (finite or infinite) space is really really big.
The easiest version to calculate with and to fit data to is the flat---spatial infinite---version. But the professionals when they fit their data and make their estimates they recognize they don't know so they put extra columns in the table and allow for various cases.
... it must be conceptually ok for a universe to be smaller at some point in the past and yet at the same time be infinite and expanding i.e. getting larger?
it is simpler than that, you don't have to resort to comparing infinities and saying some infinities are larger---that is barking up the wrong tree.
the fact is that when they say universe expanding they mean a pattern of increasing distances that can take place inside a spatial infinite universe with no defined size, and can also take place in a spatial finite universe which has some definite size.
We aren't talking sophisticated set-theoretical infinities, we are talking about ordinary spatial volumes, and an infinite volume has no mathematically defined size---so it cannot get larger.
As cosmologists use the word,
expanding does not mean getting larger----it refers to an internal process of things getting farther apart.
so, in the spatial infinite version LCDM, the thing starts out infinite and stays infinite----meanwhile the density thins out.
in the spatial finite version, there is a well-defined total volume so it makes sense to speak of the volume increasing, so yes in that case it gets larger-----but so far we don't know the volume so we focus on the density thinning out (which it does just like in the infinite case)
