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A passage from a paper:

"If one imagines running the clock backward in time, any given region of the universe shrinks and all galaxies in it get closer and closer until they smash together in a cosmic traffic jam—the big bang"

I can not imagine how this can happen in a flat space, specially when author says in the continue:

"The totality of space could be infinite. Shrink an infinite space by an arbitrary amount, and it is still infinite."

How can a flat space be shrunk at a specific moment to be called Big Bang?

There are many reasons in cosmology that space is flat. When I think of a flat space shrinking, I can not imagine a definitive moment of time when all things smash together. A flat space can never be jammed. With shrinking (thinking backward in time), things certainly smash but that never ends in a certain moment of time. That continues forever! Since the space is flat (it's more like a flat paper sheet instead of a ball), things always can be found in infinitely far distances, and when thinking backward in time, things constantly smash together, but, this will never ends in a specific moment! Unlike the case for a shrinking ball, where all things smash together at a specific moment.

What's the catch?

(Confusion remover: The Big Bang happened everywhere and I do not have a problem with that. My problem is with the moment of Big Bang in a flat space. When you shrink a sphere, everything at the surface comes close to each other until at a specific moment, everything smash together, Big Bang happens everywhere. This is hard to imagine in a flat space.)

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    The big bang doesn't require that all things were in one singular point at some time, it only requires that in the beginning everything was much smaller and that the density and temperature were much higher. How small and how dense and hot that depends on the model for the big bang and we have a number of different ones, we just can't tell them apart with the data that we have. So what's the catch? Generally very poor visualization of the big bang model on tv and in other media which gave you the wrong idea about the assumptions of modern cosmology. – CuriousOne Jun 10 '15 at 08:15
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    This might be useful background reading, though it isn't a duplicate. – John Rennie Jun 10 '15 at 08:20
  • Thank you CuriousOne. My problem is that I can not imagine the moment of Big bang in a flat space. In a closed universe, it is obvious. There is a certain moment of time. But in an open universe, I can not imagine how I get to a specific moment of time where all thing smash together because a flat space essentially never shrinks even if we imagine that the proper distance shrinks with time. –  Jun 10 '15 at 08:23
  • This one might help. http://physics.stackexchange.com/q/4921/ I think, and I say I think cause I'm not an expert, but I think, an infinite universe means an infinite big bang - just, obviously, much much more dense in the beginning. Infinity can stretch or contract and remain infinite the whole time. – userLTK Jun 10 '15 at 08:37
  • I think you are too focused on this popular idea that the universe had to be some tiny spot at some time in the past. That's not necessarily the case. We know that the visible universe was a lot smaller, but that doesn't say anything about the size and shape of the entire universe. The entire universe may not even be homogeneous, let alone flat, we just don't know about it because we can't interact with it. What we do know is that the part we can interact with is, within the precision of our best measurements, consistent with the hypothesis that the visible universe is flat. – CuriousOne Jun 10 '15 at 08:44
  • CuriousOne, do we have an evolution of "shape" in the universe (for example, from closed to open)? If it's flat today, it has been flat any time in the past. –  Jun 10 '15 at 08:53
  • I can't answer that competently. The standard cosmological solution assumes that the universe is so homogeneous that it can be classified this way and this is not contradicted by current cosmological measurements. But if you let go of that assumption, then it might be that we have to look at "swiss cheese" solutions, i.e. some parts look open, some look closed, some are flat and we just happen to live in the flats. But then, again, this is speculation, I am just trying to sensitize you to the fact that cosmology can change on a dime and that it has changed dramatically in the past. – CuriousOne Jun 10 '15 at 09:16
  • @Kamran The curvature of the universe evolves according to the FLRW equations. A flat universe is a unstable fixed point of this equation, meaning that a small deviation from flatness in the past would have render our universe completely open or closed. Such a fine-tuning of flatness in the past was once a big concern (the flatness problem), and it is now solved with inflation. – Bosoneando Jun 10 '15 at 09:22
  • @Bosoneando: Inflation is still purely hypothetical and, to be honest, it's more the flavor of the day than anything. Let me see some serious microscopic inflation models for which observational data exists and we can talk about it moving on to being something of a "solution". – CuriousOne Jun 10 '15 at 09:26
  • @Bosoneando, In the FLRW cosmology, the shape is still unchanging ($k=-1, 0, 1$). Do you mean that the answer to my question is inflation? Does shape change in inflation? –  Jun 10 '15 at 09:30
  • A homogeneous universe cannot toggle between open and closed. And as @userLTK says, if the Universe is infinite now, it was born infinitely large. I think the best way to think of if it is, the whole of the Universe was not at the same point at Big Bang, but any two points separated by an everso-large distance today were at the same point. – pela Jun 10 '15 at 09:33
  • @Kamran Yes, I think that inflation is (according to theoretical models and observational data the most probably) the answer. – Bosoneando Jun 10 '15 at 09:38
  • Your recent edit now makes it clear that your question is answered by Did the Big Bang happen at a point?. If you are asking for an intuitive explanation of what happens at the singularity then I'm afraid you're out of luck as it's fundamentally non-intuitive. In these circumstances we have to go with what the maths tells us. – John Rennie Jun 10 '15 at 09:43
  • I should add that few (if any) physicists believe there really was a singularity at time zero. Instead we believe some quantum gravity effect will come into play and remove the singularity in some way we do not yet understand. So the singularity is a purely mathematical concept that doesn't exist in the real world. – John Rennie Jun 10 '15 at 09:45
  • @John Rennie, I read that page. It's not my question. My problem is with the time of Big Bang in a flat space, not with where it happened. Please, read my question more carefully. When thinking backward in time in a flat space, I never get to a moment when all things smash together. There is still space and therefore, there is still matter yet to come closer, and this never stops. –  Jun 10 '15 at 09:54
  • The point is that the duplicate I have linked explains how the FLRW metric predicts a Big Bang and what happens there. The calculation done in that answer is for a flat universe. The singularity happens at time $t = 0$ by definition i.e. that's the way the metric is defined in the FLRW coordinates. – John Rennie Jun 10 '15 at 09:56
  • I will rewrite the question to make my point more clear. –  Jun 10 '15 at 10:10

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