Friday, December 21, 2007

The Cosmological Parameters

[Figure: Supernovae Cosmology Project]

The most puzzling experimental result of the last decade that has inspired hundreds, if not thousands of papers, is the matter composition of our universe. The measurements indicate that the usual matter we are made of is only a small fraction, 4%, of all the matter content of the universe. According to present data, 23% is dark matter, whereas the remaining 73% is dark energy. The matter densities are usually normalized to the so-called critical density ρcrit = 8 π G/3 H2, upon which one obtains the more convenient dimensionless parameters ΩM for the fraction of matter (us + dark), and ΩΛ for the dark energy part.

The plot above shows best fit confidence regions in the ΩΛ versus ΩM plane. It combines data from supernovae redshift, galaxy clustering, and analysis of the Cosmic Microwave Background. The shaded upper left corner indicates a region where there would be no Big Bang (scale factor doesn't go to zero). The diagonal line is a flat universe, and divides the areas of closed and open models. The slightly upward bended line divides region with and without recollapse (derivative of the scale factor can have a zero). If ΩΛ = 0, then a closed universe recollapses eventually. Roughly speaking, more matter requires more dark energy to have continuing expansion, so the line dividing continuing expansion from recollapse bends upwards. (Sean Carroll explains you how to compute these boundaries here.)

The shaded lower right corner would imply the the universe was younger than the oldest observed stars. The supernovae results and the CMB data constrain combinations of both parameters, such that the best fit regions lie on diagonal ellipses, whereas the cluster data is dominantly sensitive to the amount of matter, though the ratio of X-ray gas mass to total mass depends on depends on both parameters, so it yields some weak constraints also on ΩΛ (Allen, Schmidt and Fabian, Mon. Not. Roy. Astron. Soc. 334 (2002) L11 arxiv:astro-ph/0205007).

The present data is compatible with a flat universe. Though one has to be somewhat careful what this analysis actually shows. It shows that the ΛCDM model - a flat cosmology with the above mentioned fractions of dark matter and dark energy - is a parametrization of observed effects that is the best fit to the presently available data. But so far we have no experimental knowledge about the microscopic nature of the unknown constituents of the universe.

Actually, writing this series of posts about today's data and how it is compatible with our theories I am impressed how much the homo sapiens sapiens has learnd about the world around him, ;-).

This post is part of our 2007 advent calendar A Plottl A Day.


  1. The Telegraph a couple of days ago posted a rather radical yet interesting article that time could be slowing down, thus explaining dark energy.

    "The team's proposal, which will be published in the journal Physical Review D, does away altogether with dark energy. Instead, Prof Senovilla says, the appearance of acceleration is caused by time itself gradually slowing down, like a clock that needs winding."

    "... If time is indeed slowing down, so that according to this new suggestion our solitary time dimension is slowly turning into a new space dimension, then the far-distant, ancient stars seen by cosmologists would therefore, from our perspective, look as though they were accelerating."

  2. Hi Kelly,

    sounds interesting, any chances you have a reference? I actually don't even know what it's supposed to mean that 'time slows down'. I mean, do they argue the proper time we're sitting in isn't the 't' the scale factor depends on but a rescaled time? And why would that be? I find it hard to believe that this would work for structure formation etc like a Cosmological constant since it would affect all matter likewise. Best,


  3. Sure B. Here is the link:


    Have a merry Christmas!

  4. Hi Kelly,

    Thanks... Well, I could have expected the article doesn't actually say anything. I will see if I can find the paper. It doesn't even mention anything about structure formation and the CMB, so far it sounds rather weird to me. A Merry Christmas to you too!

    Hi Plato,

    Well, if you allow yourself to temper around with the time coordinates, not even the notion of 'current state' makes much sense.



  5. Random association:

    Our time is running out
    Our time is running out
    You can't push it underground
    You can't stop it screaming out
    How did it come to this?

    ~ Muse, Time is Running out

  6. Here's a thought-experiment of mine (maybe not the first instance, of course) that makes we wonder just what concepts properly apply to gravity and space curvature "as a whole" versus local regions: Suppose space is filled with hard spheres, not yet touching, each with a little test particle P in its center. Let this universe contract until the spheres start touching - what happens?

    In the attempt to model after local Newtonian type concepts, the P in the sphere S_0 at the "true Center" of any collection sits there while the other spheres pile onto it. The Ps in their centers keep moving toward that Center of the group until they hit the in-facing side of the sphere each P is in. (The Ps in the spheres farthest from the Center hit the sides of their enclosing spheres the fastest.)

    This of course contradicts the GR idea of each sphere and its P being equivalent - so what happens? You want to say, the spheres nestle against each other and each of their Ps stays right in the middle (from symmetry) or maybe a bit of shifting, but no preference indicating a "Center" of all that.

    However, what if there's a large (but "accessible") region in such a space, with many such spheres, to define a "center" of the group? Then it should act as in the first description (outer Ps continuing to move in towards the true Center of the aggregation.)

    This brings up the question, of how like the first versus the second way to act, such collections of spheres at various scales would be in a real universe governed by GR and in contraction.

    A bit long-winded, but I wanted to ensure minimal confusion (I hope.)

    (I asked this at Cosmic Variance and got little of use, with a greater tendency there to "self-absorption" and chatting within one's favorite clique etc.)

  7. PS - However, many folks there have patiently put much work into giving me answers, even though I can be aggravating and keep disagreeing with them! Thanks here, to all of them.

  8. Hi Neil,

    Thanks for your interesting comments :-) If you fill space with spheres, i.e. have more than one sphere then you don't have spherical symmetry and the conclusions about the gravitational field in the spheres, Newtonian or GR don't apply. Please note, the Bianchi Theorem in GR works if one has a global spherical symmetry - the local one isn't sufficient. Also, if space is infinitely large then it can be filled with spheres without having a center. You then have some kind of a reduced lattice-like symmetry. In fact, your construction reminds me pretty much of atomic structures etc? Best,


  9. Speaking of Cosmic Matters! ;-)

    Synchronized Global Orgasm for Peace

    (The appointed time grows short, so start looking around ...)

  10. Hi Neil,

    Ah. Or maybe I should say 'Oh'? I am definitely in favor of synchronized orgasms, and I am perfectly sure it will help the world to live in more peace and harmony. Have fun,


  11. ps: I'm much too married to 'look around', and btw my husband gets all comments cc ;-)

  12. Hi, plato, I posted similar to the below at Cosmic Variance and I hope it can explain some terms and things to those who may need it (but I ask a question or two myself):

    First, the Hubble rule means that right now, or any observer in the past or future, is going to find a galaxy twice as far away moving away at twice the “velocity” (I put in quotation marks since it isn’t a simple matter of things just moving in space, but some analogies apply.) (Or, is even that not so simple anymore?)

    That is not to be confused with the basic issue of change in rates of acceleration (”deceleration” if want to refer to inward accel. vector that way) with time. That in turn is not to be confused with the change in rates of acceleration that would occur even if there wasn’t any dark energy (just from a galaxy being subject to a lower density of matter over time - you can “pretend” that the galaxy is being pulled toward us by the mass in the enclosing figural sphere made by a radius between us and it, to get the right rate in the absence of DE, IIRC. So, both the velocity away from us and the acceleration toward us of a given galaxy were higher in the past, but the devil is in the details.

    The important thing to remember is, mass density of the universe changes with time. But if the DE is an intrinsic property of space, it likely stays the same (same value of acceleration/r) which means it will predominate as time goes on. But I hear that Lambda (the factor showing influence of DE) may change, such as increasing with time, which has even more effect in the future. It could literally tear atoms and even particles apart someday by making every point in space like a sort of reverse black hole.

  13. Try this one from The Telegraph:

    Time is running out - literally, says scientist

    By Tom Chivers and Roger Highfield, Science Editor
    Last Updated: 6:01am GMT 18/12/2007


    The idea that time itself could cease to be in billions of years - and everything will grind to a halt - has been set out by Professor José Senovilla, Marc Mars and Raül Vera of the University of the Basque Country, Bilbao, and University of Salamanca, Spain.

    The motivation for this radical end to time itself is to provide an alternative explanation for “dark energy” - the mysterious antigravitational force that has been suggested to explain a cosmic phenomenon that has baffled scientists.

    The problem is that no-one has any idea what dark energy is or where it comes from, and theoreticians around the world have been scrambling to find out what it is, or get rid of it.

    The team’s proposal, which will be published in the journal Physical Review D, does away altogether with dark energy. Instead, Prof Senovilla says, the appearance of acceleration is caused by time itself gradually slowing down, like a clock that needs winding.

    “We do not say that the expansion of the universe itself is an illusion,” he explains. “What we say it may be an illusion is the acceleration of this expansion - that is, the possibility that the expansion is, and has been, increasing its rate.”

    Instead, if time gradually slows “but we naively kept using our equations to derive the changes of the expansion with respect of ‘a standard flow of time’, then the simple models that we have constructed in our paper show that an “effective accelerated rate of the expansion” takes place.”

  14. Hi Neil',

    that's the same article from the Telegraph that Kelly has mentioned before? Anyway, the reference seems to be to this paper: Is the accelerated expansion evidence of a forthcoming change of signature on the brane? by Marc Mars, José M. M. Senovilla, Raül Vera, arXiv:0710.0820v2... no idea what this means and is about..

    Best, Stefan

  15. Yes, Stefan, it is the same Telegraph article (and in general, what an interesting e-zine.) It seems the Telly may, however, have done a bad job popularizing that idea, since the title of the arXiv piece doesn't sound like the "nutty" type physo-babble of the Telegraph article, not that I would really know.


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