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On the general curvature of space.

  1. Aug 22, 2004 #1


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    What is actually commonly accepted in the cosmologist society regarding the model of the universe? Do they think C=0 or > 0 or < 0 ? And what makes them think that?

    Also, how do one get the shapes related to each posibility for C from the equations of GR?
  2. jcsd
  3. Aug 23, 2004 #2
    I'm not sure I understand your question. People think (actually they know) that c= 3.00 x 10^8 m/s.
  4. Aug 23, 2004 #3
    Last edited: Aug 23, 2004
  5. Aug 23, 2004 #4


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    I should have specified that I had the following equation in mind while writing the question...

    [itex] C=k(\rho + \Lambda) - H^2 [/itex]

    Where [itex] C [/itex] is the overall curve of space (C = 0 meaning a flat universe, C > 0 meaning a closed universe and a C < 0 meaning a universe shaped like a sadle),
    [itex] k [/itex] is a constant meant to make the dimensions from the right hand side of the equation match the dimensions of the left hand side.
    [itex] \rho [/itex] is the density of matter
    [itex] \Lambda [/itex] is the cosmological constant (or density of the vacuum)
    [itex] H [/itex] is Hubble's constant.
  6. Aug 23, 2004 #5
    We all know that the universe is flat, because of basic reasons. For example, parallel lines dont intersect, the angles of a triangle add up to 180 degerees, ect. If we lived in a curved universe, none of this would be true.
  7. Aug 23, 2004 #6


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    We know that those facts are true locally. They might not hold up if you examine a larger region of the universe.
  8. Aug 23, 2004 #7
    I think there are two different problems trying to be solved by one theory that doesn’t apply to either.

    The first question is the physical curve of the universe.

    If the universe started out from the Big Bang then it expanded in all directions and forms and has always formed a sphere, or a curved surface.

    This is a three dimensional hypersphere. If you examine the universe from this point of view you must come to the conclusion that the universe is a geometrical curve.

    The second question is the nature or the forces of the expansion.
    This is where the concept of open, balanced, or closed universe comes into play.

    Not going into my personal theory, there is no explanation for the expansion except the result of an initial explosion and the law of inertia.

    The law of inertia states that bodies in motion continue in motion unless acted on by a force.

    With out a slowing force the universe would expand at the same rate forever. This is the open universe.

    If the force of gravity is able to act on the expanding universe then the question is, will it slow the universe expansion and create a closed universe.
  9. Aug 23, 2004 #8


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    In the book I took the formula from, they say it can be shows that if, at any time, the universe had a positive/negative/zero C, then it has always been so and will always be. In other words, the universe CANNOT change from open to flat to closed.

    Another thing that's bugging me is, if the vacuum has density, then it should be subject to gravitationnal attraction, shouldn't it? I never heard anyone mention that though.
  10. Aug 23, 2004 #9
    You have to look for the perfect solution for the vacuum(bubble nucleation/topology)? :smile:

    Also you must understand why the universe is flat. Temperature is very important attribute that helps you consider?
  11. Aug 23, 2004 #10


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    WMAP data indicates it is as flat as a pancake.
  12. Aug 23, 2004 #11
    Why does everyone try to make a simple problem so difficult?

    >WMAP data indicates it is as flat as a pancake.<

    The background radiation observation only tells you that, the universe if uniform to a high degree except for clumping. You will see the same result if the universe has a flat or curved geometry.

    Everyone is always trying to make the universe fit his or her theory. It must in the end be the other way around

    You must first decide if you accept the idea of the Big Bang.

    If you don’t then you have the problem of explaining all the observations that support the Big Bang theory. Up to this point I have seen no other theory that works.

    If you accept the Big Bang theory then you accept the concept of expansion outward from the Big Bang. With out going into detail about the early universe and the resulting mass.

    You must then accept that the mass that is the result of the Big Bang moved outward from the center in all directions. This resulted in a three dimensional spatial sphere. If you problem is not being able to visualize a three dimensional sphere you are not alone. The lack of visualization does not change the way the universe is.

    If you think the universe is geometrically flat then you must explain how the edges where able to move faster from the center of the BB to form a flat surface. That same surface must also be a three dimensional surface. You have not eliminated the three dimensional surface.

    There is no problem with mass affecting the shape of the universe. All the mass of the universe moved out uniformly in all directions and only affected mass space in local areas. This is observed by the uniform distribution, over a large area, of objects in the sky. You note that I use the term mass space. Mass only affects the force of mass, gravity. Mass does not affect the electric force and the electric force does not affect mass. Therefore mass does not curve space it only curves space that affects mass.

    >Another thing that's bugging me is, if the vacuum has density, then it should be subject to gravitational attraction, shouldn't it? I never heard anyone mention that though.<

    The vacuum density, aether, or all prevailing medium APM. Or what ever you want to call it is not a mass construct. Just as the electric charge has a different force than mass. The APM is not required to have any force at all.

    There is nothing wrong with an open universe. The universe will just fade away until all energy differentials are below the Planck level.

    There is more problem with a closed universe. What happen to the idea of escape velocity? The force of gravity decreases a square, as the increase of expansion is linear.
  13. Aug 23, 2004 #12


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    the run of mill working cosmologists think it is absolutely flat or just slightly positive curvature

    with your equations you are basically saying
    Is the actual density (including cosm. const Lambda) bigger than or equal to or less than the critical density?

    the customary thing for cosmologists is not to take the difference in the densities and say is it positive zero or negative but to take the ratio
    real-rho divided by critical-rho
    and call that ratio Omega
    and then ask is Omega bigger than 1 or just exactly equal 1 or less.

    (you can see it is different way of saying same thing)

    and then the WMAP data is saying so far that
    Omega = 1.02 +/- 0.02

    do you want a link to the WMAP report?

    so you can see it is not conclusive. Omega could be exactly 1, or it might be slightly bigger. (spatial flatness or slight positive curvature)
  14. Aug 23, 2004 #13
    What were the chances of that happening ( 1.02 +- 0.02) ?
    Unlucky if you like a clear outcome.
  15. Aug 24, 2004 #14

    The 3D Universe

    Open ([tex]\omega[/tex]<1) Hyperbolic geometry

    Flat (([tex]\omega[/tex]=1) Euclidean geometry

    Closed ([tex]\omega[/tex]>1) Spherical geometry
    Last edited: Aug 24, 2004
  16. Aug 24, 2004 #15


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    I think omega is exactly 1. Observational evidence leans toward a slightly larger value [e.g., an open universe], but, if you apply thermodynamic laws to the universe as a whole [blackbody], 1 is the only result that is consistent with both thermodynamics and relativity, as far as I can see.
  17. Aug 24, 2004 #16
    If one wants to understand what has happened in the early universe, and the dynamical changes that this universe has gone through, what would have been appropriately considered as I said in the temperatures values?

    What and how can we geometrically realize the process unfolding, is given by example currently in how we percieve the information in Gamma ray detection of these bursts?

    Question then would be raised as to what shape the universe was in the begining, and what have we realized today? This transformative change is very simplistic in its consideration. :smile:
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