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LCDM Densities?

  1. Oct 16, 2012 #1


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    I am interested in how the component densities, as assumed by the LCDM model, have been determined. For example, it seems that the critical density can be determined by rearranging of the Friedmann equation as follows:

    [1] [itex] \rho_C = \frac {3H^2}{8 \pi G} [/itex]

    Therefore, it is assumed that the accuracy in determining the critical density is actually linked to the accuracy of the observational measurements underpinning the value of the Hubble’s parameter [H], i.e.

    [2] [itex] H=71km/s/mpc[/itex] or [itex] 2.31*10^{-18} m/s/m [/itex]

    [3] [itex] \Rightarrow \rho_C= 8.53*10^{-10} Joules/m^3[/itex] or [itex]9.54*10^{-27} kg/m^3[/itex]

    However, the critical density is normally assumed to comprise of a number of distinct components, which all have a different % values in the present era, but which then change at different rates, as a function of time, due to their different ‘equations of state’. However, while the changes in the LCDM model can be examined via one of the many ‘cosmic calculators’ now available, these models all seem to be predicated on some general acceptance of the relative values of the densities components in the present era, e.g.

    [4] [itex] \rho_C (100 \%) =\left[ \rho_M (4 \%) +\rho_{CDM} (23 \%) + \rho_R (0.008 \%) + \rho_k (~0 \%) +\rho_{DE} (73 \%) \right] [/itex]

    In [4], we see the generally accepted % estimates, in the present era, of normal matter [M], cold dark matter [CDM], radiation [R], curvature [k] and dark energy [DE]. However, the requirement for CDM and DE appears to be based on the assumption that there is not enough normal matter in the universe, e.g. protons and electrons. So my basic question is:

    How is/was the particle mass or density of the universe determined so accurately?

    Would appreciate any insights. Thanks
  2. jcsd
  3. Oct 16, 2012 #2
    There are multiple measurements where the accurate values come from, but let's consider only supernovae, as they are the simplest. In FRW, you have the formula for luminosity distance as a function of redshift,
    [tex] d_L(z) = \frac{1+z}{\sqrt{-K}} \sinh \left(\sqrt{-K} \int^z_0 \frac{dz'}{H(z')} \right) [/tex]

    Now, you see that the whole thing is directly proportional to Hubble parameter today if you write [itex] H(z) = H_0 (\Omega_m(1+z)^3 + ... ) [/itex]. Unfortunately, we cannot measure luminosity distances; we don't have a clue how bright the exploding supernovae actually are. All we can do is to measure the relative brightnesses (so, say, a supernova with z=0.1 is four times brighter as the one at z=0.2).

    But since every supernova's luminosity distance is proportional to H0, there is no way of determining the value of this parameter from supernova data. It just isn't sensitive to it at all. What the data is sensitive to are the relative densities today, [itex]*\Omega_m, \Omega_\Lambda, \Omega_K [/itex], and those ones we can measure with some accuracy.

    To determine H0, you need to actually measure it locally. So you look at a large number of nearby galaxies and measure how fast they appear to move away from us.

    And then there's of course a bunch of other measurements you can make, like the cosmic microwave background, baryon acoustic oscillations, weak gravitational lensing and so on. All of these depend on the parameters slightly differently, so when you combine the measurements, you end up with a pretty accurate estimate for them.
  4. Oct 17, 2012 #3


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    Thanks for the useful outline of some of the methods used, although it seems that the saying ‘the devil is in the detail’ very much applies in this case. As such, it is difficult to assess the accuracy implied or all the assumptions on which any of these measurements are being anchored. The equation you present suggests that luminosity might be determined as a function of redshift [z] and the Hubble [H], which I presume can be measured relatively accurately. However, it is unclear that any accurate assessment of the mass density can be determined by luminosity measurements alone, if much of this density simply ‘floats’ around intergalactic space as isolated protons and electrons – see Ned Wright reference below. However, based on some of the other measurement sources you reference, I quickly reviewed a number of links as outlined below as a staring point to improve my understanding. Any links to other sources would be much appreciated.

    • How do Astronomer's Measure the Density of the Universe?: While this is an informative article, it doesn’t seem to necessarily support the required accuracy assumed by the next reference.

    • What is the Universe Made Of?: This NASA source seems very confident that WMAP provides the ‘accuracy of better than a few percent of the overall density’ and seems confident enough to specify the matter content to one decimal place, i.e. 4.6%. However, the rest of the article then appears to throw some doubt on this certainty.

    • Mass density of the universe: This reference also gives another overview, but no real explanation of how the mass density might be estimated with the required accuracy.

    • Cosmic Microwave Background: This reference might be seen as a primer for the next reference. However, it is not clear how CMB might be used to determine mass density other than via some assumptions about the photon to baryon ratio?

    • CMB Anisotropy: This reference appears highly technical, but suggests quite a spread of ideas dependent on which underlying premise is assumed.

    • Baryon acoustic oscillations: While this Wikipedia article provides good insight to the scope of the astrophysics going into this subject, it is not clear that it can explain the accuracy of the matter density.

    As a somewhat tangential issue, do all cosmological models assume that all the large scale structures of the universe, e.g. solar systems and galaxies, are charge neutral? It seems that most cosmological models are essentially gravitational models, where electromagnetic charge is generally neutralised at the atomic level. The reason for asking is to understand whether the energy-mass of the universe ever accounts for this energy source, which is much, much stronger than gravity. Thanks
    Last edited: Oct 17, 2012
  5. Oct 17, 2012 #4
    It depends. In the Friedmann-Robertson-Walker-model, knowing H(z) means you also know the relative densities exactly. Measuring Hubble parameter at earlier times directly is possible, but so far the measurements have been very very inaccurate. The luminosity distance is sensitive to integral of H(z), so there's no one to one mapping from all possible physical fluid configurations to possible H(z) curves. That means the integral of H(z) can be compatible with multiple different parameter values.

    So measuring dL does not directly give you the energy densities of different particle species, but under some assumptions (homogeneous model, only certain kinds of matter fields) it does. If you decrease your assumptions, then the mapping becomes more and more poorly defined, and making inferences becomes harder. For example, one can show that the expansion of universe is accelerating, if one assumes a FRW cosmology with matter, radiation, curvature and some fourth species of energy with negative energy. Without the assumptions for these species, the data isn't good enough to tell whether acceleration is actually happening or not.

    Yes. As you know, electric effects have a tendency of regulating themselves; there are no runaway collapses. If I pile protons at one pile and electrons in another, the piles scatter and mix due to electric effects, leading to a nearly uniform charge distribution. In the case of gravity, it only pulls. So the piles would collapse further, creating two compact objects and a lot of empty space. If the universe started from a nearly smooth initial state, then there's no way you could have significant fluctuations in charge density like you have in matter density. There's just no mechanism for creating it.

    There are some smaller effects which are being looked at, like cosmic magnetic fields, which could be interesting. I however don't know much about that.
  6. Oct 18, 2012 #5


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    Again, appreciate the feedback. I only have a general interest in cosmology, so I am not pretending to be talking with any authority. However, I recently came across a couple of papers that triggered my interest regarding galactic rotation curves and the role of plasma physics within the universe. While I not sure whether these ideas would be considered ‘mainstream’, they seem to be authored by people with some academic status. The paper related to galactic rotation suggests an alternative model that does not require dark matter and goes on to question the stability of any rotating system that is not orientated around a gravitational centre, i.e. the dark matter halo approach. The second paper starts with the statement that “99% of the luminous matter in the universe is in a plasma state”. As such, it was these papers that led to my question about the measurement of the component densities and the assumptions that underpin the interpretation of these measurements; especially if some astrophysicists still question the existence of dark matter or appear to be highlighting a potential underestimation of the role of plasma physics in cosmological structures. However, it is difficult for a person simply interested in this subject to weigh all the evidence being forwarded, hence the reason for raising questions in this forum.
    My understanding of the FRW model only extends to the basic metric, which if reduced to its simplest form, i.e. a fixed point in the equatorial plane where k=1, it becomes:

    [itex]ds^2=c^2dt^2 – a(t)^2 dr^2[/itex]

    Here a(t) appears to represent the spatial expansion of the universe as a function of time (t), but gives no hint as to how this metric would allow the component densities to be determined ‘exactly
    This statement seems to qualify the practical difficult of exact calculation.
    Again, there is a suggestion that the validity of any model, and subsequent calculations, can be entirely dependent on underlying assumptions. However, I am not trying to challenge every statement, but simply highlighting the questions that come to mind as I try to understand the more detailed arguments.
    I don’t know much about any of this stuff either, but a number of sources appear to be considering the implications of electric and magnetic fields within the formation of large scale structures of the universe. Again, I would really appreciate any links to sources that might substantially refute these ideas and save me wasting too much time looking into ideas that have already been invalidated. However, at this stage, I remain somewhat unconvinced about the accuracy of the component densities being quoted within the LCDM model. Thanks again.
    Last edited: Oct 18, 2012
  7. Oct 18, 2012 #6

    You can do a quick calculation and ask "how far will this electric field go before the gases rearrange to cancel themselves out"


    For intergalactic gas, it turns out to be 100 km. That's much smaller than any astronomy length scale, so for astrophysics a standard assumption is zero electric field. Now you can get large magnetic fields, but that's something different.

    For intergalactic gas, 100 km is more than atomic, but it's still pretty small considering we are talking about things that are millions of light years across.

    The other thing is that this is something you can test. Take a gas, charge it, see how far the charge goes.

    No, since you can't create charges so the net potential energy assuming that the total charge of the universe is zero is zero.
  8. Oct 18, 2012 #7
    Probably a MOND paper. There are some papers trying to explain dark matter with modified gravity models. They were more popular a few years ago, but the coffin is having more and more nails in it. It's not 100% shut, but modified gravity models aren't terribly popular right now, for several reasons which you can find on wikipedia.

    The other point is that there are other reasons to think that there is dark matter other than halos. Even if it turns out that dark matter isn't causing galaxy rotations, you still have baryon acoustic oscillation.

    Wikipedia is pretty good for this sort of thing. Also one problem with asking questions is that you might be 1000th person asking the same question, which means that people might be less friendly than they should be.

    One problem is that there is so much evidence that you can't summarize it all in one forum post.

    Right. And one thing about FRW is that it works just as well with non-big bang calculations. so to get something out of FRW, you have to put in an equation for a(t). You get this by putting in those things, a pressure model and a gravity model. The pressure model tells you how the pressure changes assuming the density. The gravity model models gravity.

    Then you put in one more piece. FRW assumes that the universe is homogenous. What you then to is to add perturbations from perfect homogenity and that gets you how "wiggles" in the universe behave.

    So the historical line was FRW (1930) -> BB (1960) -> CDM (1990) -> LCDM (2000)

    Right so you list the assumptions and try to figure out how that effects the result.

    Magnetic fields *might* have some impact. It's pretty hard to create something with electric fields. I fill a room with cool hydrogen. It's hard to get an electric field extend beyond 10 meters much less 1 million light years.

    Keep in might that people use LCDM as a "reference model." If you want, you can view LCDM is a curve fitting exercise in which people fit the data to some curve. One way this is useful is that it lets you do comparisons.

    For example, suppose I have a NOT-LCDM model. To describe my model, I plot out how the numbers end up different from LCDM. Also LCDM is useful to "bolt on" new physics. Suppose I think that positron-annihilation was important in early fusion. LCDM is useful as a "baseline" which I can use to make comparisons.
  9. Oct 18, 2012 #8
    The two big ones are baryon acoustic oscillations and big bang nucleosynthesis. You can figure out what's in a melon by thumping it. The big bang as a big thump that produced a lot of noise and that produces a certain sound, which you can see in the CMB.

    One thing analogy is that you see a dog house, and want to know the size of the dog. You hit the dog house and based on the sound of the bark, you can figure out what the dog is. The nice thing about this is that there is a sanity check. If you hear anything that sounds like a dog, then you can be pretty sure that it's a dog or a wolf or something like a dog. If you hit the dog house and you hear a "meow" then you have to step back and try to reconsider everything that made you think there was a dog.

    At a conceptual level. Normal matter is loud, and dark matter is quiet. If I toss two bricks at each other, it makes a lot of noise. If I toss two pieces of dark matter at each other, it won't make a sound. You can look at what the universe "sounds" like by looking at galaxies distributions and the microwave background that "freezes" the sound at a moment in time. You can tell (and there are some cool graphs) that there is something in universe that is absorbing sound waves, since the universe is less "loud" than it would be if it was all regular matter. It's not very much different than thumping a melon to see if it's ripe. A unripe melon is dense and will transmit sound easily. A ripe melon has a lot of water that absorbs sound.

    BB nucleosynthesis is another. The fact that the universe is 25% helium makes us think that we are on the right track, and it turns out that the amount of matter in the universe will change the deuterium content a lot. If you have a lot of matter, then all the deuterium will burn up. The fact that we see any deuterium at all, means limits the maximum density at early periods in the universe.

    An analogy. I know there was a fire in my garage. I have good reason to think that it didn't burn for ten hours. I know this because there is a can of gasoline there, and if there was a fire that didn't get put out quickly, that can of gasoline wouldn't be there. Once I know that the first didn't burn up the can of gasoline, I can work backward to figure out what happened.

    Astrophysicists do the same thing.

    One point that I'm making this that none of this is particularly mysterious. We figure out what the universe is made of by pretty much the exact way we tell if a melon is ripe or not.
    Last edited: Oct 18, 2012
  10. Oct 18, 2012 #9
    That is correct. Now, the way you find the link between geometry of spacetime and the matter content is through the Einstein field equations. Writing them out for an FRW spacetime, you get
    [tex] \frac{\dot{a}^2}{a^2} = H^2 = \frac{k}{a^2} + \frac{8 \pi G}{3} \rho [/tex]
    [tex]\frac{\ddot{a}}{a} = -\frac{4\pi G}{3} (\rho + 3p) [/tex]
    The first one can be used to determine [itex]\rho [/itex] if H is known.
  11. Oct 18, 2012 #10


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    Thank you for all the information and clarifications in posts 6,7,8,9. While it will take me some time to review this information in full, I just want to post some initial comments.
    I had never heard of the ‘Debye length’ and the Wikipedia reference probably needs some more careful reading. There is also a link on this page to material from a Caltech Physic course, which other PF members might find to be a useful source of reference. While I don’t really want to comment on the detailed information being raised, I did notice the Wikipedia reference also mention Hannes Alfvén, who I believe had some fairly controversial views on the scope of plasma physics in cosmology. However, I will review this material first and try to find the other papers discussing plasma phenomena in astrophysics before raising any specific issues.
    No, it wasn’t MOND, but an idea forwarded by two mathematicians from Warwick University. It seems to be predicated on a rotating black hole causing frame dragging, but they argue that the Kerr metric is inappropriate because it is incompatible with Mach’s principle. However, I am not sure this is the right forum to discuss speculative ideas. Clamtrox also raise the issue of baryon acoustic oscillation, which I have only started to review, but now recognise to be an important source of data.
    I hope my threads do not conflict with the list in this posting ‘Physics Forums Global Guidelines’ but I understand your point in that endless replication of questions must be tiresome for many of the mentors and advisors who give up their time to help. Although the PF is not always the best source of indexed material, its value to people outside formal education is invaluable in that you can ask questions, even if a bit dumb to the knowledgeable. In addition, the PF seems to have a fairly effective feedback mechanism in that if nobody is interested in a topic it will quick die, a process which I sure many mentors and advisors support as much as anybody.:eek:
    I think you are both pointing out the same common link back to what I think of as the Friedmann set of equations. So by way of cross check:
    1. Friedmann: as derived from the conservation of energy
    2. Fluid: as derived from the 1st law of thermodynamics
    3. Acceleration: as derived from the Friedmann & Fluid equations
    What I mean is that the Friedman equation has its roots in kinetic and potential energy, the latter being primarily gravitation. The fluid equation introduces pressure via thermodynamics of an expanding system, which concludes that [H] is proportional to [itex][d \rho/dt][/itex]. Finally, the acceleration equation seems to be mathematical exercise based on differentiating the Friedmann equation with respect to time. If so, it would seem that a lot different assumptions could go into defining the components of densities and pressure?
    I think this is a very good way to summarise the LCDM model. The problem I sense, rightly or wrongly, is that some people seem to want to present this model as the last word on the subject, when in reality astrophysicists know that they are only really beginning to understand the full complexity of the processes in play.
    Yes, I will attempt to review these idea in more detail. Thanks
    :tongue: Can I quote you on this?

    Seriously, thanks for all the information. As indicated, I now need to do some more reading into some of the background issues that I wasn’t aware of. However, I would like to come back to clarify a few issues regarding charged plasma in astrophysics.
    Last edited: Oct 18, 2012
  12. Oct 20, 2012 #11


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    While I initially thought that I might quickly get a basic insight into some of supplementary issues raised in this thread, it seems that there are a raft of issues, which are subject to debate. Therefore, I am not sure that this thread, or even this sub-forum, is the most appropriate to raise questions on some of these issues, especially in ignorance without some further reading into the lists below:

    Mainstream topics to follow-up:
    • Big-Bang Nucleosynthesis
    • Baryon Acoustic Oscillations
    • Debye length
    More contentious topics in plasma astrophysics?:
    • Double Layers
    • Frozen-in magnetic field
    • Birkeland currents
    • Open Magnetic Fields
    • Magnetic Reconnection
    • Z-Pinch
    However, my immediate reaction, as somebody simply interested in the overall general consensus, is why so many different ‘scientists’ contest so many different and seemingly opposing views? Is it simply that some are stupid or that the evidence to support the accepted consensus is not yet conclusive? Maybe the ‘melon’ just sounds different to different people!

    P.S. While I have already found possibly too much information on all the topics above, would still appreciate any links to other PF threads or references. Thanks
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