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I've heard from renowned astrophysicists that we don't yet know whether or not the Universe is infinite. How is that possible regarding the big bang theory is accepted (as they all do)? Are they referring to the existence of other Universes when they say it could be infinite, or what?

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Please clarify: why do you think that Big Bang theory and an infinite universe are somehow incompatible? Are you imagining that an infinite universe is incapable of expanding, perhaps? Or is it something else? –  Stan Liou Apr 23 at 2:09
    
What I mean is, even if it is capable of expanding, if everything originated at the big bang how can that space turn to be infinite in a finite time - the age of the universe. –  harogaston Apr 23 at 2:19

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What I mean is, even if it is capable of expanding, if everything originated at the big bang how can that space turn to be infinite in a finite time - the age of the universe.

In the standard ΛCDM model of the Big Bang, the universe is infinite and has always been such. The Big Bang singularity happened everywhere, in the sense that far back enough in time, the density diverges to infinity at every place.

But this is just a particular model--it assumes that the universe if spatially flat and is globally homogeneous and isotropic. There are extended models in which it is not exactly flat, and so could be finite even if it is still homogeneous and isotropic (if the curvature is even slightly positive). And of course we don't actually know whether it is homogeneous and isotropic at scales much larger than we actually see. Some inflationary models imply that it isn't.


To clarify: the ΛCDM model uses the assumes a spatially flat FLRW solution of general relativity, in which space is the Euclidean $3$-space The Euclidean $3$-space is the only flat homogeneous and isotropic $3$-manifold, so there no way to make it finite without violating at least one of those modeling assumption (e.g., a flat torus could have the same form for the metric, but would not be globally isotropic).

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I don't see how this model implies that the universe is infinite. Taken from the wikipedia page you referred to: "The model includes a single originating event, the "Big Bang" [...], which was not an explosion but the abrupt appearance of expanding space-time [...]. This was immediately (within 10−29 seconds) followed by an exponential expansion of space by a scale multiplier of 1027 or more, known as cosmic inflation." "expanding space-time" doesn't seem infinite to me. I'm not implying you are wrong, but I understand a different thing from that article. –  harogaston Apr 23 at 2:58
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@harogaston: "expanding space-time" says nothing about either finiteness or infiniteness, but I've edited the answer to point to the specific part of the model that implies the universe is infinite (if we take the model more literally than is justifiable, anyway). –  Stan Liou Apr 23 at 3:32

It is known that the universe that we can see in our telescopes is less than the total universe. Since we cannot see what is beyond the visual edge, we cannot determine if the universe is infinite or finite.

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Sorry, that doesn't answer my question. Even if we cannot see beyond our observable universe, if everything originated at the big bang how can that space turn to be infinite in a finite time - the age of the universe. –  harogaston Apr 23 at 2:14

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