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Infinite universe in expansion

  1. Sep 21, 2006 #1
    I sometimes read that we know that the universe is in expansion and that we don't know if the universe is finite or infinite. I have some difficulties to understand the notion of "infinite universe" and to see how an infinite universe could be in expansion.

    Assume the universe is infinite.

    Does it mean that the universe has an infinite size?
    Does it mean that the quantities of matter and energie are infinite?
    Therefore there are an infinite number of galaxies, stars...

    How an universe with an infinite size could be in expansion?

    Thanks in advance for any explanations, precisions...

  2. jcsd
  3. Sep 21, 2006 #2


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    Good argument. It suggests it is illogical to assume the universe is both infintely old and contains an infinite number of stars.
  4. Sep 21, 2006 #3


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    Hi fmichel.
    There is no problem for a spatially infinte universe to expand.
    What is ment by "expansion" of space is that the distance between any two objects increases with time.
    To make an analogy: consider a two dimensional toy universe consisting of dots (representing galaxies etc) on an infinitely large paper sheet (so there'll be an infinte number of dots). Now stretch the paper and you'll see that the dots are moving away from each other.
  5. Sep 21, 2006 #4
    There is no problem here. Think of expansion as in expansion in terms of spatial separation.

    For instance consider the infinite set of integers, 0, 1, 2, 3, 4, etc. Each member is separated with a distance of exactly 1. Now expand the scale say 100%. Now we still have the same set but each member is now separated by exactly 2, so we have 0, 2, 4, 6, 8 etc. It is similar with an infinite universe.
  6. Sep 21, 2006 #5
    Ok thank you. I do undestand now how an infinite universe could be expanding.

    About my other question: if the universe has an infinite size, does it mean that there is an infinite number of stars? (instead of the number of stars, I could as well have used the total amount of energy, the total quantity of matter... as infinite values)

    Or does it mean that the size of the universe is infinite, but the number of stars is finite?
  7. Sep 21, 2006 #6


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    If the matter is homogeneously distributed (as it seems to be in our universe), then of course there is an infinte amount of matter in an infinte universe.
    Anyway, one should be careful to speak in terms of what the universe looks like beyond what we can observe. Surely our observable universe, which is the only thing we really can say anything about, is finite.
  8. Sep 22, 2006 #7
    Is that true that at the Big Bag (time t=0), the size of the universe was zero?

    I have difficulties to imagine how the universe can:
    - have an infinite size since t>0
    - has matter at any location in space since t>0
    - was concentrated on one point at t=0

    It would means that there was an infinitely fast expansion from a universe reduced at one point at t=0 to a universe with infinite size at any time t>0. It would mean that the matter has moved at an infinite speed, i.e. quicker than the celerity of ligth which is impossible.

    Moreover, we know that the universe is expanding. Do we know the speed two objects (for example stars) are increasing their distance now? If this speed was infinity at t=0, is should be finite and <c now. Does this speed depend on the distance between the two objects? Is there a formula giving this speed in terms of the distance between the objects?
  9. Sep 22, 2006 #8


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    The simple answer: no!
    According to GR the universe started from a singularity (infinitly dense state), but not necessarily from "one point". But note that we do not know what physics hold at the very earliest time, and hopefully there's some new physics helping to avoid any singularity. The Big Bang singularity just poppes out after using GR in a place were it probably doesn't work very well.
    What the Big Bang theory tells us is that in case the universe is infinite, it once was in a much denser state, but still infinte in size.

    So the lines above should clear these conserns out.

    The speed is propartional to the distance beween the objects, v=Hd, where H is the Hubble parameter. This is called Hubbles law.

    Note that in GR it is perfectly ok for galaxies to move away from us with "speeds" exceeding "c", without contradicting SR. This topic has been discussed frequently here before, so do a search if you're interested.
  10. Sep 22, 2006 #9
    Ok the universe has an infinite size since the beginning, but there was an "infinitely dense state" at t=0. What does it mean?
    Does it mean that all the matter was concentrated in one point?

    In that case, at what time was the matter present everywhere in the infinite space? In the past, was the expansion speed the same as now? In case no, do we have a time-dependant formula for this speed? Is Hubble parameter a known function of the age of the universe?
  11. Sep 22, 2006 #10


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    It means that the energy (matter) density (that is mass per volume unit) was infinite all over space.

    No. (But our observable universe was concentrated to one single point.)

    This reasoning is kind of mindboggling, since what we are doing is sort of adding and subtracting infinites, which not really makes that much sense. But the math of GR is capable of describing the situation.
    One shouldn't though spend too much time thinking about this since fact is we know GR can't hold at the very first times, and thus the prediction of a singularity is pure speculation. Hopefully new physics (perhaps string theory) has a better answer.
    We know the universe once was in a very dense state, but not that it was infinitly dense.

    The Hubble parameter is a function of time.
    Read more here: http://en.wikipedia.org/wiki/Hubble's_law
  12. Sep 22, 2006 #11
    Hi all
    I'm new to the board. Just been kind of reading and learning. Mainly in chemistry though. But this thread intruiged me somewhat. This dimension we call the universe, if it is infinite, by virtue of the definition "infinite" is (let's think of it as) already expanded to a state of infinity and cannot be expanded. This is of course aside from the fact that there is matter in it or not that is spreading apart or not. So if the question is posed "Can or does an infinite universe expand?" the answer has to be in my opinion "no"

    Just my $.02
  13. Sep 22, 2006 #12


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    This might be a problem of the definition of the term "expansion". You seam to assume that expansion has something to do with borders or a dynamics within a embedding space. This is however not the case as was already explained. In cosmology, expansion means the increase of the distance between two points of space. Note that this definition is related only to internal attributes of the universe.
  14. Sep 23, 2006 #13
    Ok according to this article, the Hubble parameter depends on a function H(t) who is unknown.

    I would like to learn more about the possible structure of the universe and about its evolution. Are there interesting books, articles, or documents on the Internet? All suggestions are welcome. Thanks.
  15. Sep 23, 2006 #14


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    Ned Wright's cosmology tutorial:
  16. Sep 23, 2006 #15
    A great book i used for some uni courses was this: Universe 7th edition by Freedman and Kaufmann III. dunno if its avaliable where you are though.

    part of the unit that used this a lot was about cosmic and stellar evolution and this book is jam packed with cool info about it. good, easy read too, well written
  17. Sep 23, 2006 #16


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    As some of you may have noticed, I'm rather found of citing Wikipedia. Although it's sometimes not perfectly complete, and in a few cases even wrong or missleading, it's most of the times a very good source of knowledge for non-experts.
    Hence I recommend you to start with
    and navigate through the links you find interesting.
  18. Oct 18, 2006 #17
    Actually, there is a problem. What if you reversed time and ran the scenario backwards? The dots would all surely merge right? How can an infinite series of dots merge? How would that be physically possible?
  19. Oct 18, 2006 #18


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    I think that the answer is that standard cosmology does not consider t = 0. If you plug t = 0 into the RW metric for any reasonable model of the scale factor you certainly get zero distances between any two points. However, it is known that general relativity does not properly describe the t = 0 state and therefore it is usually assumed that a spatially infinite universe was already infinite at its "origin" (we are able to describe) at an instant after t = 0.
    Last edited: Oct 18, 2006
  20. Oct 20, 2006 #19
    I would think that if the laws of physics work in our visible universe we could talk about the infinite universe as long as we compare them to ourselves, and hold to these laws.

    I was under the impression that singularities pop up in more than one place in GR and that is one of the reasons Dr. Einstein added his constant. Could you go into more details as to where this "place" is.

    But for the duality of motion and matter I could agree with this, because at the same time that your ideal infinite universe reaches its expanded form it is no longer infinite it is now just a part, either as a wave or as matter, of an infinite universe.

    I believe that t = 0 is talking about time, or how we measure motion at t=0 you would have no motion. SR states that there is nowhere in our visible universe that there is absolutely no motion, in an infinite universe there could be more than one. So I would take it as all the mass in our visible universe measured as a volume of space with no motion, at a ratio of 1 meter/1 second.

    Think of fireworks, with the mass of the universe as the fuel, and only one gravity well, now start the burn (motion) at the center of the gravity well. Because we think of the duality of matter we could also think in terms of waves. You could think of the motion starting infinitely small and not needing matter at all in the beginning, because all matter is made up of energy and it could have been formed by motion, but for this you would also need resistance to the expanstion to explain the changes to the motions direction. I like the fireworks because I think the galaxies look like the burning embers expanding out, and because I like to think that we are all just cosmic ash.
  21. Oct 20, 2006 #20
    I understand all of this, but there's one problem: a lot of what I read on quantum fluctuations and inflation seems to suggest the Universe must have originated at a point for it to have appeared through a quantum fluctuation. This I understand with a closed universe but our Unverse is clearly flat - so... does this mean that our cherished ideas about the Universe forming from a quantum fluctuation at a point are wrong?
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