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The new Riess numbers (*FAPP*)

  1. Jun 10, 2009 #1


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    Sylas supplied the link to the Riess et al 2009 paper with a new Hubble rate, and tighter bounds generally.

    To do standard model cosmology (LCDM assumes w = -1) it usually suffices to have handy the matter fraction, dark energy fraction, and the Hubble rate. For some years we have been using .27, .73, and 71 for these. For example in Ned Wright's calculator those values are the default. If you want anything else you have to type it in.

    *FAPP* means "for all practical purposes". I am not bothering with error bounds and extra accuracy. i round off numbers. I don't want to have to remember 74.2 because for all practical purposes 74 is good enough.

    The thing is, suppose we take Riess et al seriously, which I definitely do. What are some of the other numbers? It will turn out that the Age is now 13.4 billion years, for example. So we have to stop saying 13.7, or 14.
    What about the particle horizon---the radius of the observable? It will turn out to be about 46.0, so we have to stop saying 46.5.

    These are minor niggling matters but they still need a bit of discussion.

    The point is that the critical density goes as the square of H, so whatever it was before it is now (74/71)^2 times that. Keeping the same actual matter density means that the matter fraction is now smaller. The denominator is bigger so instead of 0.27 the matter fraction is now 0.27*(71/74)^2 = 0.25.

    Near flatness then makes the dark energy fraction 0.75.

    So to avoid unnecessary noise in the numberchannels, we need to stop saying
    (.27, .73, 71) and start saying (.25, .75, 74)

    OK so what is the particle horizon now? That means google "wright calculator" and put in the new threesome in place of the default threesome, and try z = 10000. You could also use z = 100000. It won't make any appreciable difference. You will get that the particle horizon is about 46.0 (call it 46) billion lightyears from here. Actual now distance.

    That is how far the galaxies are where the people could now be receiving signals from our matter at the very earliest times, before our material condensed to form any structures. I don't know what of signals those could be. Ordinary light from before year 380,000 gets wiped by the glare. It's just the theoretical max. And it slowly increases as the universe gets older. The same distance limit applies to us getting signals or particles from their matter. The material that eventually became galaxies and stuff. It's the present day distance to the farthest stuff we can see.

    AND at the same time the calculator will give you the age of the universe is 13.39 billion years. Call it 13.4 billion.
    We should not say 13.7 any more. The new age of 13.4 reflects the new parameters (.25, .75, 74).

    Now what about the distance to last scattering? The distance to the material that sent us the microwave background light that we are now receiving with the WMAP spacecraft and will soon be receiving with the new Planck spacecraft.

    Well, you prime the calculator with the new threesome and try z = 1090. And you get 45.2 billion lightyears. It says the usual thing: the age of expansion is 13.4 billion years, the light was released in year 380,000. Which is nothing compared with 13.4 billion, so the CMB light travel time was 13.4 billion years.

    And it also tells you the distance to the CMB material was when it released the light, that is the angular size distance which the calculator says is 41.4 million lightyears. Again that is an actual or proper distance (the kind astronomers typically use) but referred to back when the light was emitted. The material was much closer then. 41.4 million and 45.2 billion should be about in the ratio 1090, the factor by which actual distances expanded while the light was in transit.

    Those are about all the essential numbers I can think of at the moment. Maybe someone else will want to add some. Or I will think of more later.

    Oh, there is the Hubble distance c/H. This is the actual presentday distance which is currently increasing at exactly rate c. You calculate it by putting "c/(74 km/s per megaparsec) in lightyears" into google. Google immediately tells you it is 13.2 billion lightyears.
    What redshift does that correspond to?
    Wright calculator tells you z = 1.4. Try putting that 1.4 into the calculator, primed with the new threesome, and you will get 13.2.
    So the galaxies that come in with redshift 1.4 are the ones where the distance to them is increasing at rate c.
    Last edited: Jun 10, 2009
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  3. Jun 11, 2009 #2


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  4. Jul 1, 2009 #3


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    Ranku was just now expressing dissatisfaction over not having a clear unique authoritative figure for when acceleration started.

    All these numbers depend on the model and on the parameters. Let's assume flat LCDM model. Even then we have the new Riess value of H = 74.2 plus/minus. This is different from the 71 that most of us have been using. A lot of things depend on the square of H, so there are going to be noticeable percentage changes.

    Anyway let's get a few handy numbers using the new Hubble rate of 74.

    I get that the critical energy density rho_crit = 0.93 nPa.
    (for convenience, writing nanopascal for nanojoule per cubic meter)

    And matter, expressed as energy density is today 25% of that so rho_M = 0.23 nPa.
    And dark energy density is 75% so rho_Lambda = 0.70 nPa

    The changeover from decel to accel must happen at a redshift z when twice the dark energy density is equal to the matter density. That is just the Friedman accel eqn.

    Twice rho_Lambda = 1.4 nPa and that has to equal 0.23*(1+z)^3 nPa which was the matter energy density back at that redshift.

    So 1+z = cuberoot(1.4/.23) = 1.83
    and therefore changeover occurred at z = 0.83.

    The redshift is usually more convenient to work with than the expansion age in billions of years, but if someone wants we can always find the expansion age using one of the calculators. Like google "wright calculator" and correct the parameters to say .25, .75, and 74 instead of the old numbers .27, .73, 71. And put in z = .83.
    The new age of expansion is no longer 13.7, it is 13.4 with the new Riess numbers, but that is a small difference. We are only doing rough approximate calculations.
    I put in z = 0.826 just to avoid a little roundoff error. I got that changeover happened at expansion age 6.65 billion year and that this was 6.74 billion years ago.
    Last edited: Jul 1, 2009
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