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Follow up to this question here: If the universe is flat, does that imply that the Big Bang produced an infinite amount of energy? As I understand Inflation theory, some time after the Big Bang, the universe was curved and closed. Then, some magical field started up at exactly the right time and made space expand until it was flat.

A flat universe must have a total amount of energy that's infinite (or zero, depending on who you ask). How did we go from the finite amount of energy in the closed universe of pre-Inflation, to an infinite (or zero) amount of energy? Seems like there's a fundamental problem with Thermodynamics.

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    $\begingroup$ A few problems with your question. First, the inflation did not convert the universe from closed to open. As in the answer below, if the universe is infinite, then it started as such. Secondly, if the total energy is zero, it is zero for either infinite or closed universe. (Also, the critical density depends on the age and size and thus approaches infinity in the beginning.) So there really is no question here to answer :) $\endgroup$ – safesphere Jan 8 at 9:17
  • $\begingroup$ I would like to understand how you interpret Inflation then. One of the problems ostensibly solved by Inflation was the Flatness problem. The $\rho_{CRIT}$ required for a flat universe is so finely tuned to a specific value, that it's practically impossible for nature to have selected it randomly. Inflation solves the problem by expanding space exponentially. As I asked below, if the universe started out flat, then what Flatness problem did Inflation solve? $\endgroup$ – Donald Airey Jan 8 at 13:36
  • $\begingroup$ The "flatness problem" refers to the fact that in Lambda-CDM flatness decreases over time. If the universe is flat today, then it must have been many orders of magnitude more flat in the beginning. How did it get so flat back then? One explanation is that initially it may not have been so flat (but still infinite and open). Then the inflation stretched it out so fast and so much that it became very nearly flat. Other cosmological models may not require inflation. For example, in the Milne model, the universe is just always exactly flat. $\endgroup$ – safesphere Jan 8 at 20:02
  • $\begingroup$ For me to understand your answer, you'll need to explain how you get more flat than flat. Either you're geometrically flat (and open and infinite) or you're closed (we'll skip hyperbolic for now). The difference is an infinite amount of energy or a finite amount of energy in the universe, so the difference is pretty significant. $\endgroup$ – Donald Airey Jan 8 at 20:16
  • $\begingroup$ You can't skip hyperbolic. If the universe is infinite and the curvature changes over time, then the universe is hyperbolic (since it cannot remain flat while the curvature changes). The main point though remains that the universe cannot start finite and then become infinite due to inflation or whatever. So there is no difference in energy. $\endgroup$ – safesphere Jan 8 at 22:38
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If the universe is flat, then it is also infinite in extent (barring some exotic topologies).

If the universe is infinite, then it always has been infinite.

I suspect that your question stems from the mistaken assumption that the Big Bang happened at a point. At the moment of the Big Bang, the scale factor was zero, and every point in the already infinite space started expanding.

For more a detailed explanation, see Did the Big Bang happen at a point?

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  • $\begingroup$ I'm not sure why someone downvoted this. This seems like a correct answer to me. $\endgroup$ – Ben Crowell Jan 8 at 1:21
  • $\begingroup$ Then explain how it solved the flatness problem if there never was one, please. It implies that the universe had exactly the mass-energy for critical density from the very first moment which is the same problem people had with General Relativity: the odds are astronomically against it. Even if the universe did have exactly the right mass-energy, quantum fluctuations would have caused some parts to be more or less curved than other parts. $\endgroup$ – Donald Airey Jan 8 at 1:48
  • $\begingroup$ "If the universe is flat, then it is also infinite in extent (barring some exotic topologies)." - A 3-torus is infinitely less exotic than "infinite in extent". Nothing is infinite in reality. Nothing, period. The infinity cannot even be defined without the definition being circular and illogical, but surely cannot be a physical observable. The infinite universe is a perpetuated non-physical nonsense. Meanwhile, a 3-torus (surface of 4-dimensional torus) is a super simple and flat topology very roughly like a room with all 6 walls made of mirrors (not exactly, but just as simple as that). $\endgroup$ – safesphere Jan 8 at 9:05
  • $\begingroup$ @DonaldAirey: Your question didn't ask about the flatness problem. $\endgroup$ – Ben Crowell Jan 9 at 23:21

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