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According to the WMAP data in the past years we can say that our universe is considered flat or at least nearly flat and we also know that flat universe is allowed to be both infinite or finite in size depending on his topology. Now my question is:

Considering the first case where is flat like an euclidean space (so I'm not talking about a hypothetical closed finite universe torus shaped universe) we can describe it infinite just because the fact that due his expansion nothing can ever reach a any kind of boundary traveling according to the laws of physics (i.e. the speed of light limit) or I am missing something else?

Can we just say that's growing to infinity in an infinite time? If someone could HYPOTHETICALLY see the "big picture " (i.e. the all amount of space created from the Big Bang at the same time ,so not considering other reference frames) will find out the the space is still finite?

I'm more interested in the way of reasoning that sits behind this if I'm wrong than in the answer itself.

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have a read through Did the Big Bang happen at a point? as this provides important background.

If, as you say, you are considering only a simply connected universe, so it isn't finite due to its topology, then the assumption we make when solving Einstein's equations is that the universe is the same everywhere - the technical terms are isotropic and homogeneous. So the universe has been infinite for as long as it has existed. The expansion doesn't mean it is expanding into anything, it just means the distance between things in the universe is increasing with time.

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  • $\begingroup$ Thanks for the reading,it was really intresting! By the way i understand that even in a classical flat universe there can't be any type of real "edges" because it's homogeneous "behavior "but the concept of an infinite space it's still pretty hard to swallow..even harder to imagine an infinite density at the beginning..As the paper you posted quantum mechanics seem to "protect" Nature from some kind of infinities at some level, but it's still an hard concept.. Do you personally think that the open infinite flat universe is still the favourite one these days ? $\endgroup$
    – Andrea Scaglioni
    Commented Nov 5, 2015 at 15:46
  • $\begingroup$ @AndreaScaglioni: I would guess that few physicists believe in a simple infinite flat universe. It seems more likely that the universe is inflating, and the bit we see is a flat region within the inflating universe. See eternal inflation for the details. $\endgroup$
    – John Rennie
    Commented Nov 5, 2015 at 15:49
  • $\begingroup$ @jonh rennie Yeah i know ..that's why i talked about the fact that the universe is expanding..Till now i Always had in my mind this picture of huge expanding bubble universe (far larger than our Hubble region)..with nontrivial boundiaries of course..but still finite ..Thanks anyway for your time. $\endgroup$
    – Andrea Scaglioni
    Commented Nov 5, 2015 at 15:59

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