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Shape of the universe

  1. Mar 2, 2013 #1
    How certainly is the universe flat? Is is absolutely approved or not?
    If yes, what will cause the big crunch?
  2. jcsd
  3. Mar 2, 2013 #2
    Thanks to WMap our certainty of the shape of the universe is considered flat with an uncertainty of 0.4 % . However as the vacuum energy density is greater than the critical density we are expanding and not predicted for a big crunch. Unless something unpredicted were to happen. Rather were destined for the big whimper.
    The Thread " Look 88 B Years into the future and see the Universe shaping up " posted in the sticky threads above has some powerful tools in the calculators. In the sticky thread on the ballon analogy their is also some good articles covering expansion.
    Last edited: Mar 2, 2013
  4. Mar 2, 2013 #3


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    There are various non-standard models in which the constants vary and different things happen, but the standard consensus model that most cosmologists use and fit the data to, as new observations are made, is the LCDM model. This has no big crunch.

    The overall mean curvature for the LCDM has been measured over the years and the error bar for it has been gradually shrinking down as more and more observational data is acquired.

    I forget the actual latest figures on the curvature---basically, very roughly, it is something like with 95% certainty we think it is zero plus or minus 1%. that is, we do not know that the U is spatially flat, but we are fairly sure that it is very close to flat.

    As I recall a very recent report, from South Pole Telescope, said that with 95% certainty the curvature was not zero but just a wee bit on the positive side of zero! So that while the U is not infinite (according to them) it is so nearly flat that the hypersphere circumference could be as large as 880 billion lightyears. That is, the 3D analog of a sphere so that if you could stop expansion right now and sail off at light speed in some direction you could travel in a straight line for 880 billion years before you found yourself back home. But it might not be that near flat, or that large--there is a range of uncertainty about the mean curvature.

    This finiteness (if it is a fact) does not imply a crunch because we have learned about the acceleration resulting from the small measured value of the cosmological constant Lambda.

    LCDM stands for Lambda cold dark matter.
    Last edited: Mar 2, 2013
  5. Mar 2, 2013 #4
    So far, a flat or near flat ever expanding universe seems like a very good bet.
    Yet we have been fooled many times thru the ages:

    The earth was NOT the center of the universe,

    and up through about the 1920's...

    We thought the universe was our own Milky way galaxy,
    we thought the universe was static...up through the 1920's,
    we thought we knew about 99.9% of the matter in the universe....then up popped 'dark matter'
  6. Mar 2, 2013 #5
    In the thread I mentioned above Marcus is one of the best qualified to explain how to use it.
  7. Mar 3, 2013 #6
    Thanks to everyone for their replies.

    Even as a child I was thinking about the shape of the universe and I thought that it probably won't be determined in my lifetime. Now, I feel really satisfied. In a great time we live.
    I got few more questions if it's not a problem:

    1. When was the shape of the universe approved with the 0.4% uncertainty?
    2. Below is a picture of the flat universe:
    http://img607.imageshack.us/img607/412/55426705.gif [Broken]
    The arrow is pointing towards the smallest dimension of the universe. How wide would it be? It shouldn't be that long (relatively speaking).
    3. Marcus, did you mean in your post that if you reach one end of the universe from your home, you will start at the another end and that way you can return home?
    Last edited by a moderator: May 6, 2017
  8. Mar 3, 2013 #7
    I detect your under a few misconceptions of the answers provided.
    1) a flat universe does not imply closed or open both possibilties in a flat model.
    The strongest data for the shape og the universe was released with WPAPS 7 year survey of thr CMB. I have the findings of WMAP though heavily on technical detail. Many of the posters on this thread have the same.
    Marcus post is in reference to South post findings in favor of a closed universe.

    Remember that flat does not imply closed or open. Open is infinite in size. The post by Marcus describes possibilty of closed but REALLY huge.
  9. Mar 3, 2013 #8
    From which year are these data?

    How would a flat closed universe look like?
  10. Mar 3, 2013 #9
    The resulting shape is 3d 'flat' euclidean w/ .4% uncertainty based from data collected using several methods like subgrading type (large-scale nonsmooth convex). Picking each saddle points of convex-concave in the area of the map; solving its variational inequalities and some techniques for unconstrained minimization of smooth convex functions (Gradient Descent,
    Conjugate Gradients, quasi-Newton methods with restricted memory, etc.). There is a .4% margin of uncertainty where it is impossible to exactly describe the existing state.

    The report was submitted 20 Dec 2012, last revised 30 Jan 2013.

    Here you can play on the values of CMB...

  11. Mar 3, 2013 #10
    Okay, thanks. I need answers to 2 and 3. What is the most approved shape, open or closed?
  12. Mar 3, 2013 #11


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    Yeah, but I wouldn't put any stock in that. Not yet, anyway. That's just not significant enough to say anything.
  13. Mar 3, 2013 #12
    Chemist: try reading here for some background and alternatives......


    Open versus closed is unknown, but maybe if a vote was taken one or the other would be more popular??

    Shape: who knows?? A three space dimensional Mobius strip would be especially fun. Then China would not just be upside down but 'inside out'...[note to police: just a JOKE!!]
    Last edited: Mar 3, 2013
  14. Mar 3, 2013 #13
    If you mean "accepted prior to current/accumulation of data's". It is humongous-ly flat but then again we do have slight positive curvature which give you the impression that it might be huge/closed. Until we have a definitive constraint to what a 'UNI'verse should be. Open or closed remains open to criticism (consequence of that small curve). Till then we rely on mathematical predictions and hope data's fit directly to it. To answer your question. In general. It is 'uncertain' unless you put a probabilistic value to it.
  15. Mar 3, 2013 #14
    The human mind is a funny thing, . It tends to fill in the missing blanks with whatever it desires and then we as sentient beings believe they are true reality and truly there even when they are not, This has been proven in many ways, (the optical illusion, the minds filling in of your optical blind spot in eye sight, filling in personal prejudices, etc), as for survival, our brain lies to us so we may predict and function in life, but we still believe what we see is real . .we also live on limited senses O(only five and each having its limits as well), and limited cognitive ability, . we as inferior mankind through our limited perception of the world, marvel at the impossibility of ideas like "entanglement", the "sole beginning bang of infinite time from nothingness" and even the the philosophical contradiction of the theoretical existence of "totally empty space" . .. like A rat, for example, may learn to navigate a maze that requires it to turn left at every second fork but not one that requires it to turn left at every fork corresponding to a prime number, . we must remember our own mental capacity is also extremely limited in the face of the expanse of the universe, . .. . perhaps in the distant future, after all our scientific experimentation is done, we as humans may find that the universe really, . . does not have any shape at all, . .
  16. Mar 3, 2013 #15
    If the universe is e.g. in the shape of the coat of a cylinder, what would be inside the cylinder?

    Found on wikkipedia: The latest research shows that even the most powerful future experiments (like SKA, Planck..) will not be able to distinguish between flat, open and closed universe if the true value of cosmological curvature parameter is smaller than 10^−4. If the true value of the cosmological curvature parameter is larger than 10^−3 we will be able to distinguish between these three models even now.

    Someone knows the latest info? How much is the cosmological curvature parameter?
  17. Mar 3, 2013 #16


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    We haven't yet definitively detected any deviation from zero. Could be 10^-3, 10^-4, 10^-10, 10^-100.
  18. Mar 3, 2013 #17


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    It's something to watch evolve as information comes in. The next installment will be delivered in just one month from now at a symposium in Holland.
    http://congrexprojects.com/13a11/programme [Broken]
    On 2-5 April, the European Space Agency (ESA) is having its first meeting on the results from the Planck mission.

    Skydive Phil noted that there is also a press conference scheduled for 21 March.

    What WMAP did, with each new release of data, was to roll their data up with other studies to give a combined estimate based on all the available observation (appropriately weighted).
    So WMAP would give its own 95% confidence interval, and also it would give the same thing for WMAP+BAO+SPT+SNe... (i.e. including South Pole Telescope and Supernovae studies etc...)

    So when Planck mission reports a month from now they will probably give their own separate estimates of basic cosmological parameters and also probably give some estimates labeled Planck+WMAP+otherCMB+BAO+... or something like that.

    The talk that cosmologists will be waiting for is at 2PM on the first day:
    Session 2 (Plenary): Main Cosmology results
    14:00 Cosmological parameters from Planck and other experiments
    G. Efstathiou

    So whatever numbers anybody digs up for you on the curvature right now are likely to soon be made obsolete by numbers from Planck combined with "other experiments", as per Efstatiou's talk. That said, I will get some recent numbers nevertheless.

    Last edited by a moderator: May 6, 2017
  19. Mar 3, 2013 #18
    Okay, so all in all, the observable universe is flat with a very very slight deviation that we aren't sure of. On a larger scale (looking far beyond observable universe), if this deviation is high enough, then the universe would be cylinder shaped. If the deviation is small, the universe is open. Either way, the universe will have one dimension much smaller than the others. Are there any estimations of its length (of the smallest dimension)? Did I write everything correct?
  20. Mar 3, 2013 #19


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    A cylinder is geometrically flat (you can bend a piece of paper into a cylinder without tearing).

    If there is a slight positive curvature, then it's like our observable universe is a small piece of a very large sphere. If there's a slight negative curvature, then it's like our observable universe is a small piece of a large saddle-shaped surface.
  21. Mar 3, 2013 #20


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    Chem,what Chally says here is very instructive (even though he dismisses the possibility that the latest data could be telling us something.) We can estimate the CIRCUMFERENCE of the "very large sphere" he mentions--in that case. And imagine "circumnavigating" to get a concrete mental picture of the experience.

    By cosmologists convention, a slight positive curvature corresponds to measuring a slight NEGATIVE value of a number called Ωk.

    ==from the October 2012 SPT report, page 14 equation (21)==
    The tightest constraint on the mean curvature that we consider comes from combining the CMB, H0 , and BAO datasets:
    Ωk =−0.0059±0.0040. (21)

    You can see that the most negative of the 95% confidence interval is Ωk =−0.0099.

    This corresponds to a universe where space is like the 3D analog of the 2D surface of a sphere. Circumnavigating corresponds to heading off at the speed of light in some direction and (assuming expansion could be halted for the duration of your trip) it would take 880 billion years.

    The formula you use is divide 88 billion years by the square root of the number 0.0099.
    That is like dividing 88 billion years by 0.1, so it comes to 880.
    Last edited: Mar 3, 2013
  22. Mar 3, 2013 #21
    I am a little confused now.

    The biggest probability is that the universe as a whole is a sphere or the coat of a sphere?
  23. Mar 3, 2013 #22


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    The 3D coat of a 4D ball.

    So if expansion could be halted to allow this, you could head off straight in some direction and eventually find yourself returning (from the other direction) to your home base.
  24. Mar 3, 2013 #23
    You mean time by the 4th dimension?

    The coat would have a very short dimension. What would happen if someone reaches the end of it?
  25. Mar 3, 2013 #24
    The balloon analagy in the sticky threads above offers some decent descriptions to answer this.
    However if your thinking that the sphere would have an inside or outside that isn't the case.
    One of the easiest ways to avoid confusion though not accurate. Is to think of the inside as the past and the outside as the future.
    This like I said isn' t accurate however its a useful metaphor to avoid the inside-outside confusions that the balloon analogy always leads up to.

    Also keep in mind their is no clear consensus if the universe is open or closed. At this point we can only say that it is flat or extremely close to flat.
    As mentioned in a month as Marcus mentioned. We will be getting further data.
    The sticky thread on the balloon analogy also has tons of useful links. I highly recommend the ones leading to Ned Wrights tutorials. Particularly his FAQ article. Its one of the better articles for those relatively new to cosmology.
    Some things to add on the open closed description. If the universe is closed/finite now then its always finite. Same applies to infinite/open.
  26. Mar 3, 2013 #25


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    As I understand it, what you call the "coat" of a ball is what I would call a sphere.
    in our 3d world, the ball is the solid thing and the sphere is the hollow thing. It has zero thickness. It is a pure 2D surface.

    A dimension is a direction you could point, or move in.
    Or, in the case of a 2D world, it is the direction a 2D animal living in a zero-thickness purely 2D surface could point, or move in.

    As I understand it there is no "very short dimension" because you and I cannot point our fingers in any direction which is the 'thickness" of our 3d space. There is no direction that we can move that we would "reach the end of."
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