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Red shift distance relationship and dark energy

  1. Aug 1, 2009 #1
    It is my understanding that there is evidence from the red shift/distance relationship that while the rate of universal expansion was once decreasing (from the Big Bang until about 6-7 billion years ago -BYA for short), at about 6-7 BYA it began increasing. This, as I understand it, is the main evidence for "dark energy."

    Assuming I'm correct in the above, my questions are the following:

    1) did Hubble's original linear relationship between red shift and distance take into account gravitational slowing of the rate of expansion? By this I mean, would a plot of red shift on the y-axis and distance on the x-axis be pulled slightly below a straight line (with negative slope) to reflect such slowing? (I should say that in my imagined plot, I've got 14 BYA at the x origin, and present time at the far right, so the Hubble plot starts high at the left, and hits zero on the y-axis at the right.) In other words, was Hubble's "linear" relationship slightly downward bowed? (Not phrased very precisely, but I hope you understand my question.)

    2) At ~ 7BYA, does that plot begin to change from having a gradually decreasing rate of expansion to a gradually increasing rate? (I assume this means the plot around 7 BYA would have an inflection point, and from then on, be bowed upward rather than downward.)

    I assume the plot is never level and always has a negative slope (i.e., there's a monotonically decreasing red shift as objects get nearer the earth).
    Last edited: Aug 1, 2009
  2. jcsd
  3. Aug 3, 2009 #2
    That is an interesting question about the affect of expansion on Hubble's original data analysis. Perhaps the newer analysis consideres this.

    I think the transition from reduced expansion rate to acceleration would be gradual. However, I think the cosmological constant term in the Friedmann equation would be larger than the others at about 7 BYA or so (I once back-of-envolope calculated 8.6 BYA).
  4. Aug 3, 2009 #3
    All interesting -- but in reality the data does not support it. The effects mentioned can all be attributed to the model used -- not to the data.
  5. Aug 3, 2009 #4
    Rymer, do you mean that the data itself is suspect, owing to some systematic error in the Cosmic Distance Ladder? I was simply asking whether the data conform to that type of plot ("reverse sigmoid") or not. I don't really care what the interpretation of the data currently is (i.e., slowing expansion rate followed by increasing rate). I'll post an attachment of the plot soon, to clarify my question.
  6. Aug 3, 2009 #5
    Here's a hand-drawn plot, which according to my understanding represents (qualitatively) the accepted data. The question is, am I correct or not?

    Attached Files:

    Last edited: Aug 3, 2009
  7. Aug 4, 2009 #6
    Not sure what you mean by 'purely linear'.

    The point I was making is that the data at present is not precise enough to choose between many models.

    In fact, it is still possible to have a flat, no gravitation at the cosmological level model that
    fits the current data. With no gravity acting in the time-like coordinate, there would be no acceleration or deceleration.

    Such a model also fits the currently available supernovae data gamma ray burst data, etc.
    And can be produce a linear relation between recession velocity (along the light-path) and a properly geometric transformed distance index in co-moving space.

    Expansion is at a constant rate -- less than the speed of light. After all matter can't have that high of velocity.

    Not saying the model is 'proven' but it does exist and can make predictions others can't.

    Point is the data we have is far to poor to assume we know much about even what kind of model we need. This makes such fanciful thoughts and ideas presented as entertaining,
    but not necessarily useful.

    The idea that someday we might be able to make such calculations with any meaning is encouraging -- but just doing some doesn't mean anything yet.

    Attached Files:

    Last edited: Aug 4, 2009
  8. Aug 4, 2009 #7


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    Those graphs usually show redshift as a funcion of some "distance", like http://www.astro.ucla.edu/~wright/sne_cosmology.html" [Broken].
    What you have in mind apparently is redshift as a function of emission time. The latter cannot be directly measured, but can be derived from cosmological models.
    http://www.astro.ucla.edu/~wright/cosmo_03.htm" [Broken] show the inverse of redshift, the scale factor, as a function of time. The scale factor is zero at the big bang, so redshift would be infinite there, contrary to your plot.
    You can read of acceleration from these graphs intuitively, not from the inverse ones you have in mind.
    Last edited by a moderator: May 4, 2017
  9. Aug 4, 2009 #8
    Rymer, thanks for the plots. I don't understand what's on the X axis, though - fraction of velocity not due to spatial expansion? How can such a fraction be more than 1? Anyway, seeing only that plot (if I understand it correctly), with its seeming pure linearity along the left half, I can't imagine why anyone would propose dark energy.

    Ich, thanks. You're right that I was thinking of recession velocity at the time of the light's emission. And, as you stated, this is not directly measurable, but is based on assumptions of distance, in turn based on observed brightness vs. imputed initial brightness (don't remember the usual terms used). I guess what I'm after is the least derived data I can find. But, assuming c is constant, distance and time should be interchangeable (ignoring the proposed expansion of space itself - possibly a mistake), so is my plot roughly correct?

    Tangential questions for Ich:

    1) the first graph on the first Ned Wright page you linked to (sne_cosmology.html) shows recession rates greater than 300,000 km/s, i.e., greater than c. Is that deemed non-contradictory to special relativity because of spatial expansion?

    2) In the first plot of the second Ned Wright page you linked to (cosmo_03.htm), I gather that for Omega>0 the acceleration slows due to the effect of gravity, when Omega=1 the acceleration slowly asymptotes but never stops increasing, and when >1, a Big Crunch is expected (absent the anti-gravity effect of dark energy or vacuum energy or whatever it's called). Correct?

    3) In that first plot at sne_cosmology.html, is the dotted lavender line - the "closed dark energy model" - the distance (vs. time) counterpart to my graph? It seems to show the initial slowing, then accelerating rate of expansion that I had in mind as the data leading to the dark energy hypothesis (not sure why it's labeled "closed" though, since it doesn't seem to be decelerating).
  10. Aug 4, 2009 #9
    Thanks -- some clarity needed on X. X is fraction in co-moving space -- space moving at the expansion velocity. It is also the space wher Hubble's law is precisely true, so that:

    X = (recession velocity) / expansion velocity) = (co-moving distance / reference distance)

    The distance relation is actually what is used to compute X.

    That is effectively Hubble's Law. The above recession velocity is in co-moving space.
    Actually plotted on the graph is a geometric transform of X to convert it to the light-path coordinate (all that is needed is to do this is the law of cosines).

    On the vertical axis is the apparent recession velocity -- in light-path coordinate. Its found from the redshift z -- Doppler.

    A plot of the two is very linear -- through the entire range of data we currently have.
    Its done this way to calculate the expansion velocity -- which is the slope of the line.

    Using directly the data from Kowaski and Schaefer(corrected for 2008) a value of 0.85 is found for expansion velocity. Using what apparently is a newer calibration of Cepheids from Reiss (May 2009), a value of 0.870 is found. Two different theories suggest values of 0.866 and 0.869.

    In short, yes it is a plot of redshift verses distance.

    In the attached model comparison the SGM curve is the theory-based one -- NO datafitting not even as assumption of Ho. These are based on the 'old' Cepheid calibrations -- same as the ones currently on Ned Wrights page.

    The effect of the new Reiss suggestion would be to move the binned data points and Ned's curves slightly upward. The SGM curve would not move. This would actually bring the SGM curve into closer match.

    Attached Files:

    Last edited by a moderator: May 4, 2017
  11. Aug 4, 2009 #10


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    That'd be the first graph. Both redshift and luminosity distance are directly and independently measured. Independently to the amount that luminosity distance does not contain a redshift correction and so does not correspond to what one would normally call "distance".
    There are two problems with your plot:
    1. As said, you should plot the inverse quantity. Non-accelerating expansion in your plot would look like 1/t, not 1-t as you've shown.
    2. The relationship between distance and time is model-dependent. Further, there are some different definitions of distance. Read Ned Wright's pages, he explains everything.

    They show c times z, which is clearly unbounded. Cosmologists usually use coordinates where c times z corresponds to recession velocity, that's different from SR.
    No. The counterpart to your graph is magenta on "cosmo_03". That's the same as the Flat Dark Energy Model in "sne_...", but as I said, Luminosity Distance lacks some corrections that would make the bending visible. Better try the comparison with the empty model further down. And don't listen to Rymer when he tells you that cosmologists are too dumb to figure out how the data would look like in an empty universe. :wink:
    Last edited: Aug 4, 2009
  12. Aug 4, 2009 #11
    Cute. However, this time I'm not talking about an empty universe, but one with matter.
    And matter can't expand at a relative velocity (relative to the 'inertial reference frame' of the universe's big bang expansion 'point' reference) as great as the speed of light.
  13. Aug 4, 2009 #12
    Ich, thanks for your thoughts. I'm going to have to think about this a while, and re-read Ned Wright's Cosmology pages more carefully. It may be next week before I ask another question, if then.

    Rymer, thanks for your input, though I'm not sure what model you favor, nor the importance of a "geometric transform" for data from stars that are thought to be largely moving straight away from us (due to spatial expansion), and whose peculiar sideways motions make up a vanishingly small fraction of the total relative velocity.
  14. Aug 4, 2009 #13
    Another graph attached. This is my attempt to represent the geometry. The radial is a time-like coordinate -- perpendicular at the interception point of 'now' is the 'co-moving arc'
    (moving at some velocity maybe less than the speed of light). The light path is a straight line (flat). So all that is required to relate 'separation' or apparent recession velocity (scaled as a fraction of the unknown expansion velocity) in the arc to the measured redshift recession velocity on the light-path is a simple law of cosines relation.

    Using Doppler to give a light-path recession velocity and plotting against the geometric corrected apparent recession velocity (which by Hubbles Law should be the same as the the distgance ratio in co-moving space), by the theory should give a straight line whose slope is the actual expansion velocity.

    It was just an exercise to see where the departures were -- and an attempt to see the acceleration of deceleration. That actually failed -- since I did end up with a straight line
    and with a value less than one.

    The value mentioned 0f about 0.869 c is simply the minimum value this model would allow
    for an expansion velocity IF it was desired not to have a maximum redshift cutoff. Meaning that for any velocity below this value there would be a finite maximum redshift.
    This is imposed by the physics assumption of light not 'traveling backward' in time -- another way of saying it is the lowest angle of emission is a tangent to the arc-space and when the arc-length reaches 90 degrees that is the geometric maximum.

    The values on the arc-length can be greater than 1 -- up to pi/2. Remember that this
    arc is scaled in units of the expansion velocity which is less than the speed of light.

    OK the big question: WHY DID THIS WORK? Why did I get a straight line?

    By everything I have read it should not have. Doppler is said 'not to apply' (but it was all I had for a recession velocity in the light path -- so having an engineering physics background I used what I had). So why does the line seem so linear if this is not working?

    Where is the acceleration or deceleration?

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  15. Aug 4, 2009 #14


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    The short answer is Supernova Legacy Study. I fail to see how these 'back of the envelope' arguments are relevant.
  16. Aug 5, 2009 #15
    I fail to see how datafit results can be ignored. They at least have to be checked to see how and why they are working. Lousy 'science' otherwise.

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