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On the infinity of the Universe

  1. Mar 20, 2012 #1
    Okay, now this question has been asked over and over, and all that stuff, so I am not going to ask whether the universe is infinite or not. Actually, my physical intuition says that it probably is, and so do two very intelligent people I admire, namely Eliezer Yudkowsky (a mere AI programmer, just look him up) and the physicist Max Tegmark.

    Actually, Tegmark starts his paper called 'Parallel Universes' assuming that the universe is flat (the WMAP experiment seems to point in that general direction), that distribution of matter is ergodic and so that it is spatially infinite. And while they could likely be wrong, it still appeals to me to imagine an infinite universe, so bear with me.

    My question is not 'whether,' it's 'how.' Let's assume for a second that the Universe is spatially infinite, with all its far reaching consequences (including the multiple copies of yourself who are at most 10^10^115 metres away from you). How could that be so?

    I mean, there's this place here which states that the Big Bang was not the origin of The Universe, but rather the origin of the Observable Universe, and as such The Universe actually is infinite. Then the forum's FAQ seems to corroborate, and that's just fine by me.

    Now I have also read that the Big Bang's Singularity actually held an infinite amount of energy.

    That's my problem, really. Where does all that energy come from? I was under the impression that the amount of energy was constant and finite in The Universe, not merely in the observable one. And let me reiterate that I'm okay with the idea that there is infinite energy in the universe, really. I just want to know.

    Okay, I'm repeating myself, but I just want to be very clear: does the property 'spatially infinite' not imply 'energetically infinite'? How is that? Is the Big Bang not the origin of The Universe (capital T and U), but merely of the observable universe (lower-case o and u)?

    Also, from what I understood of Tegmark's paper, the Big Bang was in fact the origin of The Universe, which is but one stable bubble of the inflationary bubbles that are created all the time, each infinite in volume. If each bubble is infinite in volume, should they not also have infinite energy? This is the problem I have, really, the relationship between energy and volume.

    I know I'm not being clear, it's past midnight as I'm posting here, but this has been annoying me for the past few weeks, because I'd never given it too much thought before.

    Thank you for your patience :)
  2. jcsd
  3. Mar 20, 2012 #2


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    In a spatially infinite and homogenous universe you are forced to concede it includes an infinite amount of energy/matter. One spatially infinite universe, however, appears to be enough. An infinite number of other spatially infinite universes that are causally disconnected does not make much sense to me.
  4. Mar 21, 2012 #3
    Not making sense is not the same as not being true, one should be reminded. We have Savannah-optimised brains that are not even supposed to deal with the actual fabric of reality, so that sort of intuition isn't very reliable.

    And the model of chaotic cosmic inflation (which appears to be backed up by some considerable amount of evidence plus it's quite elegant) does seem to suggest the existence of causally disconnected bubbles outside the universe. Also, of course, since the actual universe is bigger than the observable one, one should expect that we are causally disconnected from a number of events (infinite number, maybe?) within our own universe, so it should come as no surprise to have other causally disconnected universes.

    Another struggle I have with infinite energy is its conservation. If ∞ + 1 = ∞, what's to prevent energy from being created out of nowhere? If the amount of energy in the universe is infinite, it shouldn't matter. I'd thought Conservation laws only applied fully to isolated systems, which is exactly what our Universe is, but if it is an isolated system with infinite energy... you can see where I'm going with this, I suppose.
  5. Mar 21, 2012 #4
    If the universe is infinite and homogenous then it has an infinite mount of energy and an infinite amount of matter.

    If the universe is finite and homogenous then it has a finite mount of energy and a finite amount of matter.
  6. Mar 21, 2012 #5


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    Not necessarily. One possibility is that the total energy content of the universe is exactly zero, and that the large positive energy content associated with matter and radiation is balanced by the large negative energy content of the gravitational fields See, for example, the following book by Lawrence Krauss:

  7. Mar 21, 2012 #6
    It's what it seems, but I am not discussing whether it's infinite or not, I am using the assumption that it is in fact infinite and flat a priori, and speculating about its energetic contents. More than that, though, I am speculating about how Conservation Laws apply in a Universe with infinite energy/matter, and how infinite energy/matter could be contained in a singularity such as the one at t=0 and yet expand enough to create finite Hubble volumes in a finite time.

    And actually one of my questions was whether the singularity at t=0 is the origin of our spatially infinite Universe or just the observable Universe. I understood it was the latter, and as I said, Tegmark seems to agree with that, and I respect his opinion a lot, even though I still haven't even started my physics major to understand enough (I'm waiting until after I finish Engineering for that).

    Hm, that is interesting. And that would justify infinite energy in a spatially infinite universe, if it was cancelled out by the negative energy of gravitational fields. I'm still stumped on the topics I mentioned above, though...
  8. Mar 21, 2012 #7


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    Energy conservation is a local constraint, it does not hold globally and is in fact not a requirement in general relativity. This is a well-known issue that is related to the lack of uniquely defined sense of time translation that holds globally. I can't think of a good reference now, but googling "energy conservation in general relativity" should return some good results.

    EDIT: Here's an article I came across a while back that I believe should address some of your issues: http://astronomy.case.edu/heather/151/davis.pdf [Broken]
    Last edited by a moderator: May 5, 2017
  9. Mar 21, 2012 #8
    Okay, that makes sense. It all adds up to normality, I suppose.

    So, from these answers, I gather that yes, indeed, The Universe, assuming it is infinite, ergodic and flat, has infinite positive energy - which may or may not be cancelled out by the total gravitational energy, which would be in fact a very elegant solution, in my opinion.

    Now... what about the Big Bang, then? Is it the origin of The Universe or the Observable Universe? Did it have infinite energy stored in the singularity, or just zero energy that, because of quantum fluctuations, happened to inflate into its own zero-energy Universe?
    Last edited by a moderator: May 5, 2017
  10. Mar 21, 2012 #9
    Well if the BB is the origin of the Universe then by default it is the origin of the OU.

    We cannot assume the Big Bang as a "beginning" of anything, remember when we talk about the Big Bang we are talking about T>plancke time and not t=0.

    I think isotropy has a large role to play here, but when we start discussing homogeneity with respect to an infinite Universe then isotropy meaning becomes less important. Maybe 1 in a trillion, trillion hubble volumes is completely void of any mass - this would not invalidate homogeneity on the extremely large scales.

    Personally I think all BB's were the same Bang and that time/space are infinite and flat in all directions - even though we are causally disconnected from anything outside our own OU.

    All very interesting!!
  11. Mar 21, 2012 #10


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    It's important to point out that what we refer to as the "hot big bang" within the context of chaotic inflation is very different from the moment related to the origin and subsequent evolution of THE universe. While chaotic eternal inflation does not obviate the initial singularity (it's not "past eternal"), what us observers perceive as the hot big bang is really the reheating phase occurring in our local Hubble patch at the end of inflation. In this sense, there are necessarily many hot big bangs occurring in the chaotic inflationary universe, each one corresponding to the reheating of individual, causally disconnected "observable universes". The proposition that we live in an eternally inflating universe renders questions regarding the initial singularity essentially unverifiable.
  12. Mar 21, 2012 #11
    Yes, yes, of course, we're talking about extremely large scales.

    Let's be clearer when we talk about universe.
    When I say The Universe, I mean the inflationary, spatially infinite, flat, ergodic bubble within which our Observable Universe/Hubble Volume (for the purpose of this discussion let's assume they're the same thing) lies. And then there's the other Universes with possibly different physical constants and dimensionality that are inflating elsewhere (other possible ground states, true vacuum, not sure of the terms here).

    With that in mind... the 'hot big bang' you mention would be the end of the inflation period of our Universe (inflationary bubble, ground state)... or just Observable Universe/Hubble Volume?

    And once again, where does all that energy come from? I mean, how can an infinite amount of energy expand to an infinite volume in a finite inflation epoch in our own Universe?
  13. Mar 21, 2012 #12


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    OK. Within the context of chaotic eternal inflation that I was referring to above, there is one Universe (infinite or not) according to your definition, comprised of a large number of separate "pocket" universes (Hubble volumes) that have stopped inflating and have undergone reheating (had separate hot big bangs). There could of course be entirely separate other Universes undergoing eternal inflation as well, but I am not referring to these, since we don't need them to set up an effective multiverse of the kind I just described. However, you mention the possibility of different Universes with different physical constants; this can happen even within a single Universe, where instead each pocket universe has a different vacuum and with different physical parameters.

    In chaotic internal inflation, you have a Universe that is undergoing inflation. Assume it is infinite for the sake of argument. Different regions of this Universe will stop inflating at different times, leading to the percolation of non-inflationary Hubble patches (what I called pocket universes above). So the picture is of an infinite inflationary universe with non-inflationary bubbles being constantly percolated -- it's called eternal inflation because there are always regions of the Universe that are inflating, despite the fact that non-inflationary patches are percolating out (in fact, the fractional volume of the Universe that is inflating is increasing into the future). These non-inflationary patches reheat and begin to evolve according to the standard hot big bang model. So...to clarify, the hot big bang to which I refer is the end of inflation in one of the Hubble volumes.

    I'm not sure I follow this. If the universe is infinite, it was always infinite. Our observable universe is finite and inflated for a finite period of time.
  14. Mar 21, 2012 #13
    Okay, what you are saying is fundamentally different from what I am saying. From what I read (more specifically from Tegmark, here, who was the guy that made my thinking on this subject restart), these 'pockets' you mentioned are what I call the Universe, are themselves spatially infinite, and our Hubble Volume is but a fraction of a single pocket. So what I call 'The Universe' is one of those pockets.

    When I say different universes I mean different pockets. I'm saying that out pocket is much larger than our Hubble Volume, and is what we should call our Universe because it comprises everything that behaves in the same way as our own Hubble Volume, and in principle everywhere inside it reachable (if it stops expanding acceleratedly), whereas different Pockets are in principle unreachable.

    Hmmm... in short: the impression I got from Tegmark's paper was that the Pocket Universe you mentioned is not our Hubble Volume, it is much bigger than our Hubble Volume, it is in fact infinite, and within it there are infinite other Hubble Volumes, with one Hubble Volume exactly equal to ours down to the last photon at most 10^10^115 metres away.

    In his paper, he calls these other Hubble Volumes that are within our own Pocket Universe 'Level I Parallel Universes.' Then, he calls the other Pocket Universes (with different physical constants but probably the same laws) caused by inflation 'Level II Parallel Universes,' which are the 'in principle unreachable' ones I mentioned above.
  15. Mar 21, 2012 #14


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    Perhaps I was not careful with the term "pocket universe." What I mean is Hubble volume.
  16. Mar 21, 2012 #15
    Okay, let's be more specific here, then, with our names. What Tegmark calls Level IV and Level III Parallel Universes are irrelevant to this discussion, so we have three levels I'm concerned about:
    • There's the big, infinite, continually inflating universe, within which there are many pocket universes, each with its constants and dimensionality. We shall call that universe the Fractal Universe.
    • There's then our bubble within that universe, which is flat and infinite (that was my a priori assumption), and which we will call Universe, or the patch, or the pocket.
    • Finally, there's the Hubble Volume within which we reside, which consists of only the parts of the Universe that we can see. I will use Hubble Volume or Observable Universe to refer to that, never mind the subtle differences between both.

    So, I'm okay with the Fractal Universe undergoing eternal inflation, with patches of it that stop inflating. Now, what I want to understand is, if the Big Bang is the end of the inflationary epoch of our patch, how can the patch be infinite and possess infinite energy?

    ...although, looking at this, I'm thinking that maybe I understand. Let me get my facts straight.

    According to chaotic inflation theory, the end of the inflationary period of the Universe coincides with that moment that, in previous Big Bang models, was at t = 10^-43s after the singularity. Is that correct?

    If that is so, then was there no singularity at all?
  17. Mar 21, 2012 #16


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    It could be. There are inflation models that reheat at much lower temperatures too, though. For example, I've seen models constructed that reheat just above the scale of electroweak symmetry breaking. So, as far as our observable universe is concerned, our "hot big bang" might never have emerged through a Planck era at all, or really been all that "hot".

    In the chaotic inflation scenario, no, not a singularity in the past of our Hubble volume. But, since even eternal inflation has an initial singularity, the Universe must still contend with it (or "bounce" around it, or what have you).

    I also apologize if I'm telling you things you already know as if you're hearing them here for the first time -- that's not my intent. It's sometimes difficult to gauge people's levels of knowledge here.
  18. Mar 21, 2012 #17
    No need to apologise, I can imagine that :)

    And one thing you said is really new for me, which is the fact that even eternal inflation had an initial singularity, and that... sort of goes back to my original point. How can that be so? I mean, I can picture a finite amount of energy trapped in an infinitesimal point, but how could an infinite amount of energy such as the one contained within the Fractal Universe be enclosed in an infinitesimal singularity? I mean, if that was the case shouldn't this singularity sort of "create" energy eternally, since it would take literally forever for all the energy trapped inside it to be "released into the wild"?

    One of my original problems had been infinite energy in a singularity, and so... it's back :P
  19. Mar 21, 2012 #18


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    That's just about the definition of a sticky problem. Of course, it's likely that there is no singularity to speak of, and that quantum gravitational effects smooth things out at a finite energy scale. Would this avert the conceptual difficulty that you see?
  20. Mar 21, 2012 #19
    Erm... not really. What quantum gravitational effects would do anything there? I'd thought quantum gravity was still in the limbo of unfinished theories...
  21. Mar 21, 2012 #20
    It seems counter-intuitive, but is very much possible.

    Here's a video of Alan Guth explaining that a "bubble" universe arising from inflation can still appears to be infinite:

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