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Is vacuum acceleration directly proportional to distance?

  1. Aug 17, 2015 #1
    Do we know if the instantaneous/observed acceleration due to the vacuum is directly proportional to distance or possibly? (ignore any gravitational effects)
    A~D ?
    A~D^2 ?
    A~D^(1/2) ?
    A~D^(Other) ?
    A= constant (edited as I forgot this one)

    If not, is there a best guess/fit or simply not precise enough data?

    Feel free to correct my question if it is simply a bad question. I didn't see this directly address in any thread; if I missed one, a link would be great.
    Last edited: Aug 17, 2015
  2. jcsd
  3. Aug 17, 2015 #2


    Staff: Mentor

    What do you mean by this?
  4. Aug 17, 2015 #3
    The observed acceleration of distant objects from the supernova data or other observation.
  5. Aug 17, 2015 #4


    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    You could look at the Hypersine thread.

    To an excellent approximation, distances are growing and are expected to continue growing as the function
    sinh2/3(1.5 t) where the present is at time t = 0.8

    This looks more and more like exponential growth (at a very low rate of about 1/173 % per million years) as time goes on. Eventually it will be indistinguishable from exponential growth at that rate call it H

    D(t) = eHt

    If you differentiate that you get the expansion speed is proportional to the distance multiplied by H and if you take the derivative again you get the acceleration is proportional to the distance multiplied by the square of H

    The Hypersine thread https://www.physicsforums.com/threads/the-hypersine-cosmic-model.819954/#post-5146660
    has some graphs that show the distance growth curve and the gradual onset of exponential growth at a small constant rate.
    Last edited: Aug 17, 2015
  6. Aug 18, 2015 #5
    The Hypersine thread provided the understanding of the acceleration rate I was looking for.
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