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Our past lightcone is pear-shaped

  1. May 29, 2003 #1

    marcus

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    here is a frustrating problem

    http://www.astro.ucla.edu/~wright/cosmo_03.htm

    Scroll down to the "Space-Time Diagrams" section and you
    will see a pear-shape lightcone outlined in red.

    This is the lightcone in the spatially "flat" case which we
    believe applies to our universe-----the Ω = 1 case----
    the critical density case-----whatever.

    But this case drawn here is for zero cosmological constant---zero Lambda----zero vacuum energy density.

    Up to the present this makes hardly any difference because the dark energy has not caused very much acceleration in expansion YET. But in the future that lightcone will no longer look like a pear.

    BTW each of those worldlines is another galaxy, and they have little triangles on them to show their future lightcones.

    The side of the pear always matches the slope of the future lightcone of each galaxy it meets. This determines its shape.

    Suppose the worldlines of the other galaxies started bending out to show accelerated expansion. What new shape would the pear acquire?

    This chapter in Wright, and the preceding one, is suggesting ways to think visually about spacetime.
     
    Last edited: May 30, 2003
  2. jcsd
  3. May 31, 2003 #2

    jeff

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    The tip gradually narrows, collapsing as the expansion overtakes light. This requires the pear inflect into a tear-drop before terminating at the collapse point.

    (Edited for enhanced precision)
     
    Last edited: Jun 1, 2003
  4. May 31, 2003 #3

    marcus

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    Bravo!

    Your verbal description is very like what I have been imagining!
    this time I believe I agree with you, and must give you much
    credit for helping to clarify this!

    By "tip" I understand you to mean the upper, narrower, part of the pear. This is what I have imagined as narrowing and having, at some time, an inflection.

    what is fascinating is the thought that there could actually be two
    parts---the waist could pinch off.

    Do you have a link or web-reference for this-----for further clarification?
     
  5. May 31, 2003 #4

    marcus

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    The conventional picture of what results from an unchanging
    cosm. const./dark energy density is that eventually our observable universe is only 100 or so galaxies.

    this I wish to relate to the forming of the "waist" of the pear.

    I consider that these 100 or so galaxies are, at least for the time being, bound gravitationally to the Milky Way. So the expansion does not carry them off beyond the horizon.

    At least the Local Group of 10 or so galaxies should stay as a cluster.

    But the pinching off of the "waist" of the pear----if this really is what the model predicts---would correspond to everything outside of a few galaxies disappearing! No more Cosmic Microwave Background!

    Am delighted by the extremity of the picture.

    But I can think of no reason to suppose that the dark energy density will remain constant---to date there is nothing but speculation as to its nature, so why should one suppose anything? Or do you disagree?
     
  6. May 31, 2003 #5

    jeff

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    Uh oh. I must be wrong

    Agreed, and at this point it's arguably the single biggest wildcard in theoretical physics.

    I learned about this stuff from Hawking and Ellis's "large scale structure of space-time" which is the standard text on the application of global methods in GR.
     
    Last edited: May 31, 2003
  7. May 31, 2003 #6

    marcus

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    delighted by this witty and helpful post
    thx
    marcus
     
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