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Article with good analysis of different models?

  1. Jun 1, 2015 #1


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    I reading article "The Cosmological Constant and Dark Energy" P. J. E. Peebles, Bharat Ratra http://arxiv.org/abs/astro-ph/0207347
    They use following sources of density:
    ## \Omega_{M0}+\Omega_{R0}+\Omega_{\Lambda0}+\Omega_{K0}=1##
    Next I see "
    The measurements agree with the
    relativistic cosmological model with
    ##\Omega_{K0}=0##, meaning no space curvature, and
    ##\Omega_{\Lambda0} ∼ 0.7##, meaning nonzero ##\Lambda##. A model with
    ##\Omega_{\Lambda0} = 0## is two or three standard deviations off the best fit, depending on the data set and analysis
    Looked at referenced articles, not found where comes "two or three standard deviations off the best fit".
    Is any paper with good analysis of different models and with calculations of deviations for best fit?
  2. jcsd
  3. Jun 1, 2015 #2


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    Gold Member

  4. Jun 1, 2015 #3


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    Dearly Missed

    I won't try to directly address your question. Wabbit gave links to sources. I want to just start out with a little intuition about how redshift-distance data determines the estimate of Λ
    View attachment 84151
    View attachment 84153
    Each choice of Λ corresponds to a different asymptotic (long-term) distance growth rate H$$H_\infty = \sqrt{\Lambda/3}$$Each of the color-coded choices for H generates a different curve (green, black, blue, purple, orange)
    For a given redshift z, the predicted distance to a supernova with redshift z is the area under the curve out to z+1 on the x-axis.
    The orange curve, is essentially for ZERO COSMOLOGICAL CONSTANT. It is for an asymptotic growth rate of 1/1000 ppb per year, which is negligible compared with the others. It is the lowest curve, and so it gives the smallest distance predictions for any given redshift.

    I have plotted 5 possibilities:
    green 1/16.3 ppb per year
    black 1/17.3 ppb per year
    blue 1/18.3 ppb per year
    purple 1/40 ppb per year
    orange 1/1000 ppb per year

    When you get down to 1/50, 1/60, etc the curves all tend to pile up. They coincide visually with the 1/1000 curve. For practical purposes that can represent the limit of zero Λ.

    The best fit is 1/17.3 , the black curve. You can see what it predicts for example for redshift 0.8.
    That would be the area under the curve from 1 to 1.8 as it slopes down from 14.4 to 9.
    That is easy to estimate: .8*23.4/2 = 9.36 lightyears now to a supernova we are seeing at z=0.8.
    The green curve slopes down from 14.4 to 10, so it predicts .8*24.4/2 = 9.76 lightyears now to that same supernova.

    Between the green and blue curves (1/16.3 and 1/18.6) seems like a reasonable uncertainty and by comparison the zero cosmological curvature constant, or the 1/1000 option seems way off. It would give distance predictions that are way too low. Less than .8*(14.4+6)/2 = .8*20.4/2 = 8.16 light years in the example.
    Last edited: Jun 1, 2015
  5. Jun 1, 2015 #4


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    That's a very old paper, more than a decade old.

    One more recent results can be found on NASA's Lambda archive. This table combines data from four different experiments (WMAP, SPT, ACT, and SNLS3):

    It reports ##\Omega_\Lambda = 0.749 \pm 0.024##, which is about 30 standard deviations from zero.

    The Planck results are more accurate, but they don't have as nice of a website for formatting the data, so it's not quite as easy to find the constraints on ##\Omega_\Lambda## if we don't assume flat space (with flat space assumed, the result is about 50 standard deviations from zero).
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