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A common view now in the physics community is that the Universe is infinite in extent (which makes Hubble sphere an infinitely small part of the Universe). On the other hand, there is the Big Bang theory which states that the Universe began about 14 billion years ago. So, how can the Universe be both infinite and have a beginning? Or does the Big Bang only apply to the Hubble sphere?

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The solution arises during the inflationary epoch. It is hypothesised that some sort of phase transition during the first moments of the universe drove a tremendous expansion/inflation of space by many, many orders of magnitude. A few details are in the link. I'm not sure that an "infinite" universe is the prevailing view; just very much larger than the observable universe.

The thing is that this faster-than-light, exponential expansion of space effectively isolates different parts of the original universe meaning that our little patch is just part of a much greater whole. It simultaneously explains why the universe is "flat", and highly isotropic and homogeneous, and most importantly for this question, addresses the "horizon problem".

The first section of the wikipedia entry on the exponentially growing scale factor during the inflationary epoch would be useful reading.

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  • $\begingroup$ So then you are saying that the Universe in fact does have a curve? Because if it is completely flat AND finite, that would imply an edge. Which would be weird and violate the assumption that there are no "special" places in the Universe. $\endgroup$ – David Jan 27 '15 at 2:49
  • $\begingroup$ @David It's "flat" (in the sense of spacetime curvature) to about 1%. The 2d analogy is to imagine a grid on the surface of a ballon. If you massively inflate the balloon, the grid square you live in looks flat to you. But there is no edge. $\endgroup$ – Rob Jeffries Jan 27 '15 at 3:39
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    $\begingroup$ en.wikipedia.org/wiki/Shape_of_the_universe "Many textbooks erroneously state that a flat universe implies an infinite universe; however, the correct statement is that a flat universe that is also simply connected implies an infinite universe. For example, Euclidean space is flat, simply connected and infinite, but the torus is flat, multiply connected, finite and compact." $\endgroup$ – David Jan 28 '15 at 4:13
  • $\begingroup$ @David What's your point? We don't know that we live in an exactly flat universe. The sentence from wikipedia simply means that even if we did you could not say that the universe was infinite. $\endgroup$ – Rob Jeffries Jan 28 '15 at 7:51
  • $\begingroup$ I think I was just answering my own question :) But your response is the best I got it. Response accepted. $\endgroup$ – David Jan 29 '15 at 13:33
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If the Universe is infinite, then it had instantly grew from zero to infinity at the moment of Big Bang.

Note, that this is a possible model from General Relativity (GR).

But most probably GR is not applicable at the moment of Big Bang, because it contains singularity.

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  • $\begingroup$ Hasn't the universe always been infinite in extent? Even when all the stuff in it was in the same place? $\endgroup$ – RedGrittyBrick Dec 6 '14 at 0:09
  • $\begingroup$ I don't think it's true, Dims. What you said violates the basic tenets of Big Bang and Inflationary theories. Namely that after the Big Bang but before the inflation, the universe was microscopic. Right after the inflation it became visible to the naked eye, but still smaller than a basketball. $\endgroup$ – David Dec 6 '14 at 2:09
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    $\begingroup$ The Universe could be microscopic, if it was finite. But FLRW metric tells it can be both finite or infinite. Observations tell it is most probably infinite, hence it never was microscopic. But any length unit, like 1 megaparsec, if propagated back it time, was microscopic. $\endgroup$ – Dims Dec 6 '14 at 11:42
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First of all, the universe is not infinite. There is enough reason to disprove an infinite universe model. In such a case, the universe can have a beginning. Reasons to why the universe simply cannot be infinite are as old as the time of Isaac Newton. The problem is gravity. In an infinite universe, the total gravity of the mass it contains would be infinite and the whole universe would collapse into a space of infinite density, a black hole. On the case of expansion, modern theories such as of inflation, accurately describe certain features what we observe, such as the CMBR (Cosmic Microwave Background Radiation).

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    $\begingroup$ This is wrong. The force of gravity would not be infinite, because gravity gets weaker over distance. (I also would not recommend using Newtonian gravity to model the universe.) Furthermore, measurements (e.g. from WMAP) support the theory of an infinite (or at least very large) universe. $\endgroup$ – HDE 226868 Nov 14 '15 at 14:35

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