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Is the Universe Closed, Flat or Open?

  1. Aug 12, 2004 #1
    Just wondering what the general scientific community thinks about this topic.
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  3. Aug 12, 2004 #2


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    Last edited: Aug 12, 2004
  4. Aug 12, 2004 #3
    Apparently though, in a closed Universe, the mass and the gravitational attraction in the Universe cancel out to give zero total energy. Does that mean that this does not hold anymore in our Universe if it is flat?
  5. Aug 12, 2004 #4
    I would think that an "open" universe would imply a boundary. Otherwise, you would be talking about the instantaneous existence of infinite space. That would deny any attempt to find the cause and thus the logical consistency of existence.

    I suppose, therefore, that the universe started with a closed structure, with dimensions that curl back upon themselves so that you end up where you started - that the universe grew larger and larger with this closed structure. And then space may have tore or ripped to form a boundary to spacetime so that now it may be possible that it forms an open universe. Or maybe not.
  6. Aug 12, 2004 #5
    Flat is the common consensus, though I was reading Roger Penroses's "The large, the small and the human mind" and he believes that the universe is open (hence hyperbolic geometry), but this book was written before the results of WMAP
    Last edited: Aug 12, 2004
  7. Aug 12, 2004 #6
    And what exactly does "flat" mean? Every particle that has mass begins to curve space close to its center. Does flat only a reference to the space between particles? Is it a comment about how much empty space there is between particles that appears flat? If so, then wouldn't things appear flat even with small distances and continue to be flat at large distances?
  8. Aug 13, 2004 #7
    All the evidence seems to point at the universe been flat but I believe most scientists believe that it really is closed and they're searching for evidence.
  9. Aug 13, 2004 #8


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    I don't think that about the scientists is so; where is your evidence?
  10. Aug 13, 2004 #9


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    I think both you and Self Adjoint are correct in some ways. If there is a bias, it is for a good reason. As we are curiously (considering all possible values) above the 1% mark in known matter/energy in the universe to hit the "flat" spot, we are forced to look ever more closely at sources of dark (unknown) matter and energy. We aren't going to go backwards in our numbers (i.e. lower). In other words, we might discover more but we can't discover less. Scientists would be negligent if they assumed the universe was open and stopped looking. Therefore, they must "adopt" the concept that the universe is flat/closed so they can look for sources of missing energy. Agreeing also with the other side, I don't think scientists will be too surprised if/when it is concluded that the universe is open.

    Recent cosmology strongly suggests the observable portion of the universe will "shrink" (even though the total volume of space continually increases) in the future due to the ongoing expansion of the universe. Galaxies we can see today will start to recede from us faster than the speed of light (just as recently observed high red shift objects currently do). Eventually, the Andromeda galaxy will be the only observable galaxy from the Milky Way. I think that experimental result implies an open universe by itself, not entirely sure.
    Last edited: Aug 13, 2004
  11. Aug 13, 2004 #10


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    Euclidean geometry on large scales.
  12. Aug 13, 2004 #11


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    this will show my age some and reveal a little nostalgia, but I want to emphasize the point (which some on this thread have referred to or know already)

    When I was first introduced to closed-flat-open in beginning astronomy, things were in a way simpler. There were only 3 main possibilities

    closed---space finite---positive largescale curvature----eventual crunch

    flat----space infinite----zero largescale curvature---- just barely keeps expanding forever, borderline case

    open---space infinite---negative largescale curv.----expands forever always decelerating but doesnt slow down as much as in flat case

    Little Warning: a torus can have a flat geometry on it, so technically the flat case included a toroidal possibility where space was not infinite, but you didnt think about that much.

    To put it simply there were just these 3 possibilities people talked about back then:

    closed---space finite---crunch
    flat---space infinite----no crunch
    open---space infinite---no crunch

    then 1998 happened and people saw some type IA supernovas which were not redshifted as much as they should have been at that distance
    (in other words they were dimmer than they should have been at that redshift).

    this caused great excitement

    Now there dont seem to be just those 3 simple possibilities any more.

    In particular it seems that we could have a U in which Omega > 1,
    that is one where space is positively curved and finite but still has no crunch

    I am not saying what I think we do have. I trying not to put any personal bias on it at all. I am just saying that the logical possibilities have changed and are more complex-----because of allowing for a nonzero Lamda.

    People used to assume Lamda was zero (unless they were being obsessively rigorous they usually just took it for granted) but now they dont automatically do that.

    If we have a postive Lambda (and right now there seems to be this huge happy agreement about that) then there is this closed crunchless case to consider. That sounds like a contradiction.
    I mean the case where the U is finite (Omega >1, positive curv.) but still does not end in a crunch but keeps on expanding.

    Words and their connotations get rooted in the brain. I am still not comfortable calling a U that expands forever by the name "closed"---
    closed still has for me the residual connotation of crunch. The term
    "closed", even if it is technically correct, sounds poorly chosen and misleading to me. Maybe we are hitting a little linguistic turbulence and eventually some new words will emerge for the possibilities.
  13. Aug 14, 2004 #12
    OK, thanks for the answers everybody. So, marcus, does this means that this closed crunchless Universe is now becoming the option scientists prefer when discussing about the Universe or is it just another possibility that has not gained a lot of popularity?
  14. Aug 14, 2004 #13


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    Hi Curious,
    first thing to note is that they use the Friedmann equations to model the universe, and a metric called the FRW metric (Friedmann Robertson Walker)

    this is the "standard model" for cosmology, and it includes some parameters which can be measured and assigned plus/minus confidence intervals

    I dont know how familiar you are with mathematical models which contain measureable parameters and from which you derive stuff to compare with observations----or how familiar with this particular model with its parameters like Omega and Lambda and H(t) the hubble parameter.

    But for me to respond, you dont have to be familiar with any of the details.
    the interesting, almost a little funny, thing is that when you use that model
    you dont have to decide what you think about whether it is finite or not.

    there is an unobtrusive little parameter k which appears in the FRW metric and in the Friedm. eqns. which has only 3 possible values k = -1,0,1
    and a cosmologist can do his calculations working with all three cases at once and leave it undecided

    And the numbers that you predict are not dramatically different between a spatially finite very nearly spatially flat universe
    (technically something like Omega = 1.01)
    and a spatially infinite perfectly flat universe (Omega = 1.00000 exactly).

    Omega has been measured to be 1.02 +/- 0.02
    but this is unsatisfactory and hopefully preliminary
    this was done using the satellite WMAP and I believe another satellite is
    supposed to go up that will hopefully do it better. And WMAP which by any
    objective standard is one of the great human accomplishments even tho it didnt distinguish between the two cases, is still collecting data AFAIK.

    Ned Wright (check his site!) is one of the WMAP directors. Watch his "News of the Universe" page at his site for signs of what working cosmologists think.

    Here is my take: just out of laziness because it is a lot easier they often assume spatially flat infinite (Omega = 1 exactly, k=0) when the are calculating something. Because it gets rid of the k parameter, simplifying things, and it makes very little numerical difference!
    You get the same numbers (to compare with observations) as you would in a slightly positive curved finite case----a big balloon is almost flat.

    But Ned Wright has some page at his site where he kind of takes a sidelong glance at the possibility that Omega might be, say 1.01 or slightly more than exactly 1. And he fits such a case to some data and says hmmmm.
    doesnt look too bad. But he doesnt draw any conclusion---why should he?
    The data doesnt warrant deciding between the cases.

    Some other people here at PF may have different opinion about what working cosmologist think------there are some theoretical reasons why it ought to be this or that (but theoretical reasons are thin ice).

    right now I personally am beginning to guess it might be finite but just very large (crunchless closed)

    and I cant really speak for what "most cosmologists think"

    but I will take a guess and say that they are mostly undecided
    because to do their work they dont have to decide on what they believe
    about that particular issue
    Last edited: Aug 14, 2004
  15. Aug 14, 2004 #14


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    I don't know if there is a majority consensus among theorists, but, a number of them, including Hawking, favor a finite but boundless model of the universe. An eternal, infinitely voluminous and massive unverse should look very much the same everywhere at all times. The one we live in does not.
  16. Aug 15, 2004 #15
    OK, thanks for the answers!!!
  17. Aug 15, 2004 #16


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    I was looking back to post #1, 2, and 3 of this tread to see what the main thing is. First Curious asked a clear direct question. then Chronos gives a clear valid answer----which we never really improved on!

    then in post #3 Curious raises another issue which seems very basic (now, to me as I look back) which we didnt ever address. How can the total energy of the universe be zero or nearly zero?

    Can someone please explain in a simple physical way how this can be?

    this answers the original question, but then Curious asks further:


    Note that Alan Guth, a noted authority on inflation, often makes the point that the total energy can be zero or nearly zero because the gravitational potential energy (a deficit, a negative, a being-down-in-the-hole) can cancel the positive energy of the existence of the matter.

    But how can one imagine the universe bootstrapping itself into existence always keeping the total or net energy nearly zero? Can someone offer a physical way of imagining this? Or point us to a better than usual explanation on line?

    I will try to respond to curious second question: Curious I think this can work whether it is spatially finite or infinite. If you can imagine positive and negative nearly canceling in a finite U then probably you can imagine the same thing happening in a sufficiently large finite piece of an infinite U.
    Then, altho there is no total mass-energy for an infinite U, you can say that the mass-energy per cubic lightyear is balanced by the negative gravitational potential energy per cubic lightyear. the cancelation could happen in large finite volumes---which seems to be the same thing.

    the difficulty (for me) is to imagine how it happens in the first place, even for the finite universe.

    EDIT: I see now there is a separate thread about this.
    Chronos has offered a link
    this is to a brief non-technical explanations by two good astronomers.
    Alex Filippenko BTW was on the first team that found the TypeIA supernova data for accelerating expansion and postulated a positive cosmological constant (dark energy) to explain it.
    Last edited: Aug 15, 2004
  18. Aug 15, 2004 #17


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    In this thread:


    we touched upon this issue, but took it no further.

    Our question appears to be: "If the net energy of the universe is zero, how can it remain so perfectly balanced across all this time and across all the space in the universe?" On what scales must this self-correction occur?
    Can it happen over very large portions of the universe, with the net energy in some areas being very large, but cancelled out on a larger scale? In that case, would we need to invoke superluminal "communication" of some type to mediate this self-correction? That seems problematic.

    Must the self-correction occur over very short scales (in which case, each particle exists only because of the existence of an equal but conterbalancing particle or quanta of energy)? This would allow the net energy to stay balance over all the universe, even though the far-flung parts of it cannot communicate with each other. This idea brings to mind the old Superman comics and the Bizzaro world, where there are negative analogs for things that exist in the real-world. :smile: That of course is just an entertaining plot device, but if we are to expect that the universe keeps itself balanced at the Planck scale, where are these equal-but-opposite energies expressed? How can they be intimately connected to every particle and wave in our universe, but be separated in such a way that they do not self-annihilate?
  19. Aug 15, 2004 #18


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    If you solve the Laplacian for electrical potential you find there is both global neutrality and local charge conservation so long as the universe does not 'leak'. I would expect the same to be true of gravity.
  20. Aug 15, 2004 #19
    None of the above. :tongue2:

    It is impossible for me (and I would think everyone else) to see and understand the ultimatum of the universe our current knowledge.
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