# Data Check

1. Oct 11, 2012

### mysearch

Hi,
I am trying to get a better understanding of the mass distribution as described by the LCDM cosmological model and data that might be more anchored in observation. What I mean by this is that the LCDM model appears to operate on the assumption of the large-scale homogeneity of the universe, while observations clearly tell a different story when it comes to the concentration of mass in solar systems and galaxies. By way of a general summary:

There appears to be numerous general sources that estimate the number of particles in the universe in the order 10^80, although most are not explicit as to how this number is determined or what is implied by a particle. However, the following Wikipedia links appear to provide a more considered analysis, which suggest an average density of ~10^6 particles per cubic metre (m^3) linked to the interstellar space within a galaxy, which is then said to fall to a density of ~6 protons per m^3 in the intergalactic space separating the galaxies:

http://en.wikipedia.org/wiki/Outer_space#Interstellar
http://en.wikipedia.org/wiki/Outer_space#Intergalactic
http://en.wikipedia.org/wiki/Interstellar_medium#Interstellar_matter

So using the Wikipedia figures and the volume of the visible universe defined by the Hubble radius [c/H], the total number of particles in the visible universe would appear to be ~6.57*10^79. OK, that seems close enough to the generally quoted figure of 10^80 particles given the potential of error in the estimates, except if you then consider the total mass of the these particles against the LCDM model. If we assume that the particles in Wikipedia are protons with a mass of 1.67*10^(-27)kg, the total particle mass within the visible universe would be 1.10*10^(53)kg. In contrast, the mass density of the LCDM model for 4% matter is 3.82*10^(-28) kg/m^3, which translates to a total mass of 3.50*10^(51)kg. This appears to suggest a significant discrepancy, especially as the LCDM model often appears to be used to suggest that there is not enough normal matter in the universe
.

I realise that the following details are possibly excessive for an OP, but I wanted to try to explain the statement above in the hope that some members of this forum might be able to clarify/correct any of the issues/data raised in the following related bullets:

1. The basic LCDM cosmological model appears to be anchored in the observational evaluation of Hubble’s parameter [H], i.e. ~71km/s/mpc or 2.31*10^(-18)m/s/m.

2. Based on this figure, the Hubble radius [c/H] comes out at ~13.7 lightyears or 1.29*10^(26) metres. This figure is then used to define the visible universe, and its volume, although it is recognised that the physical universe must be much larger than the visible universe with some estimates forwarding a scale factor as large as 10^23.

3. However, as a frame of reference to do calculations, the visible universe is often quoted to have in excess of 100 billion galaxies with each having 100 billion stars. However, if we were use the figure of 10^22 stars of 1 solar mass, i.e. 1.99*10^(30)kg, it would equate to a total mass of 1.99*10^(52)kg, which exceeds the particle mass of the LCDM model by a factor of 10 without apparently factoring any other particle mass associated with interstellar or intergalactic space. Of course, it is accepted that the count of the stars is only meant as a gross estimate, hence the need to reference more detailed models, e.g. LCDM.

4. However, if we use the figures from Wikipedia for the interstellar and intergalactic particle density, i.e. 10^6 and 6 per cubic metre, the total mass excluding any stars seems to lead to the figure quoted above, i.e. 1.10*10^(53)kg, which in itself exceeds the LCDM model by another factor of 100.

5. The critical density of the LCDM model is calculated to be 9.54*10^(-27) kg/m^3, although this is probably best described as the total energy density, i.e. 8.53*10(-10) Joules/m^3, as only 4% of this total is thought to exist in the form of normal matter. As such, the matter density would be 3.8*10^(-28)kg/m^3.

6. Again, using the radius of the visible universe [c/H], we can estimate the volume to be 9.1*10^(78)m^3. If then multiplied by the matter density defined by the LCDM model, i.e. 3.8*10^(-28)kg/m^3, we have the estimate of the LCDM model for the total particle mass of the visible universe, i.e. 3.50*10^(51)kg, which seems at odds with calculations based on the Wikipedia figures.

7. If we divide the total particle mass of the LCDM model by the mass of a proton, the number of total particles/protons falls to 2.09*10^(78) or just 0.23 protons per cubic metre of intergalactic (homogeneous) space instead of the 6 quoted by the Wikipedia reference. So which estimates of particle density does astrophysics currently support and why?

8. As a slightly tangential issue, defining the particles as protons seems reasonable as the universe is said to be made up of 75% hydrogen, i.e. 1 proton and 1 electron, where the electron mass is only ~1/1840 of the proton. So presumably the particle count could include an equal number of electrons without affecting the mass figures in any appreciable way, while making the visible universe essentially charge neutral. However, does astrophysics assume that all solar systems, galaxies and larger structures are always charge neutral?

Sorry to overload this OP with possibly too much detail, but I was interested in the current thinking on these issues and would really appreciate any knowledgeable comments. Thanks

Last edited: Oct 11, 2012
2. Oct 11, 2012

### Chronos

The only realistic way to forge a workable model of the universe is based on fluid dynamics. Relativistic Navier-Stokes equations are the leading approach.

3. Oct 11, 2012

### twofish-quant

Galaxies and solar systems are small scales. One way of thinking about it is to imagine galaxies as being atoms in a gas. If you look at a gas, the mass is in fact highly concentrated in atoms and molecules, but at large scales, you can "average things out" so that this doesn't matter.

One thing that this means is that you can only expect LCDM to give you decent predictions over volumes of space that consists of large numbers of galaxies so that bumpiness is statistically averaged out. If you look at things at the scale of galaxies, then LCDM probably won't work very well as a model.

Also, LCDM works better at the early universe when it appears that everything was a smooth gas. As matter concentrates into galaxies, it's expected that LCDM will work less and less well.

My guess is that somewhere you are mixing the volume of the universe as it was in the past with the volume of the current universe. When you look back in time you are looking at the universe as it was when it was much smaller. The size of the observable universe right now, is much larger than the Hubble distance.

Somewhere the bookkeepping got messed up. The current size of the "observable universe" is 3 or 4 times the Hubble distance, which gives you a difference in volume of about a factor of 100 different, and if you put that into the numbers, I think the bookkeeping works.

One other way of thinking about it is that since you are using the volume of the universe as it was some time in the past, any density that you get will be what the universe was in the past, which is higher than today's density.

Last edited: Oct 11, 2012
4. Oct 11, 2012

### twofish-quant

Also for 3) and 4) there are some explanations for the difference

Most stars are red dwarfs which are much less massive than the sun, and interstellar space is extremely dense compared to most of the universe.

The other thing is that the Wikipedia source cites a press release which might well be wrong. Something that would be a good project would be to go into the standard reference books and academic journals and find a better citation for the Wikipedia numbers. The thing about reference books and journal articles is that they actually show the calculation, so if there is a difference you can quickly figure out why.

Press releases have very, very low value as evidence, since it's quite possible that someone did a quick calculation and just got the numbers wrong.

Reading the press release more closely, what they seem to be saying is that not that universe has 6 protons per cubic meter but rather that the total energy content of the universe added together is 6 protons per cubic meter.

Last edited: Oct 11, 2012
5. Oct 11, 2012

### mysearch

Chronos: I have only had limited time to follow up on your comment regarding the idea of fluid mechanics, but did find an earlier thread ‘Astrophysics and fluid solution’, where you reference a paper by ‘Andersson and Comer’. However, even a cursory scan of this paper suggests that it is not an easy read, which you seem to suggest yourself.
Even if I could understand this stuff, would it contradict the results of the LCDM model in anyway and what energy-mass assumption does this formulation make. As a slightly tangential question, asked in ignorance, does fluid dynamics account for the electromagnetic interaction of plasma? The reason for raising this issue is linked to bullet 8 in the OP. Thanks

twofish-quant: appreciate you addressing some of the issues raised in the OP; especially in your second post, which seems to resolve my problems – see comments below. However, just for the record, I have also raised some general comments on your first response just to check whether I missed the point. Based on the following comment, I think I have a broad understanding of the basic scale limitations of the LCDM model. As far I am aware, the issues/data raised really only related to the large scale defined by the Hubble radius.
I have a slightly different take on the LCDM model regarding the following comment:
As far as I understand the LCDM model, it appears to be anchored in observational evaluation made in the present era, i.e. the Hubble parameter [H] plus the assumptions about the energy-mass density components, i.e. dark energy 73%, dark matter 23% and matter 4% etc. Based on this data and the formulations associated with the Friedmann set of equations, the equation used in most ‘cosmic calculators’ can work out the incremental changes in these densities as a function of time. Personally, I suspect that this model is only as good as its assumption and doubt that they will improve as they are extrapolated back in time away from the present era.
While an error is entirely possible, see your Wikipedia clarification below, the comparative figures relate to the present era. I quantified the definition of the ‘visible universe’ to the Hubble radius [c/H] because it is easy to cross reference to the LCDM model and the measurement of [H] in the current era. I assume what you are referencing by the ‘observable universe’ is the particle horizon, which is around 46 billion lightyears, i.e. 3-4 time bigger than the Hubble radius. However for comparative purpose, I don’t see that it makes any difference what radius is used based on the assumption that the density doesn’t change with radius in any given snapshot in time. Therefore, in this context, the use of larger radii doesn’t have any time connotations as the calculations are determining the mass in a given volume based on a given density in the present era.

Thanks for the second follow-up post, I think its has clarify the discrepancy between the LCDM model and the Wikipedia figure. Again, some quick comments first:
I agree, as stated in bullet 3), using the estimated number of stars averaged out to 1 solar mass is a poor approach, hence the attempt to reference the calculations back to the LCDM model.
Again, I agree, which is why I raised this thread to ask for some confirmation of the Wikipedia numbers or an explanation of the discrepancies with the LCDM model.
Many thanks, I too re-read my own Wikipedia reference, a bit more carefully this time, and you appear to right, as per this extract.
“Present estimates put the average energy density of the Universe at the equivalent of 5.9 protons per cubic meter, including dark energy, dark matter, and ordinary, baryonic matter, or atoms. The atoms account for only 4.6% of the total energy density, or a density of one proton per four cubic meters. “​

Therefore, the density of 1 proton per 4 cubic metres aligns to my calculation given in bullet 7, i.e. 0.23 protons per cubic metre. In terms of the large-scale average implicit in the LCDM model, the follow-on extract below from Wikipedia qualifies even this figure to accommodate the concentration of higher mass densities in stars and galaxies.
“The density of the universe, however, is clearly not uniform; it ranges from relatively high density in galaxies—including very high density in structures within galaxies, such as planets, stars, and black holes—to conditions in vast voids that have much lower density, at least in terms of visible matter.”​

Again, many thanks for resolving the perceived discrepancy, I think I am back on track now, but would still really like to know whether you think all cosmic structures, i.e. solar systems and galaxies, are charge neutral?

6. Oct 13, 2012

### mysearch

If possible, I would like to try to clarify one last aspect of the data underpinning the current model. Thanks to ‘twofish-quant’ I can resolve the density figures of the LCDM model with the Wikipedia references given in the OP. However, the level of observational verification of this data is still not clear to me. Again, to quote from the Wikipedia ‘Intergalactic’ reference:
“Present estimates put the average energy density of the Universe at the equivalent of 5.9 protons per cubic meter, including dark energy, dark matter, and ordinary, baryonic matter, or atoms. The atoms account for only 4.6% of the total energy density, or a density of one proton per four cubic meters. The density of the universe, however, is clearly not uniform; it ranges from relatively high density in galaxies—including very high density in structures within galaxies, such as planets, stars, and black holes—to conditions in vast voids that have much lower density, at least in terms of visible matter.”​

I am assuming that the Wikipedia numbers were probably calculated, as were mine, from the density figures of the LCDM model anchored in a critical energy density of 8.53*10(-10) joules/m^3. If you convert this figure to kg/m^3 then divide by the mass of a proton you end up with the figure ~5.8 protons/m^3, which is misleading as this energy density does not exist as particles within the LCDM model. If you use the actual matter component of the total energy density, e.g. 4.0-4.6%?, then the matter density corresponds to a homogeneous particle density of 1 proton/4m^3 as suggested in the quote. However, as also indicated, the actual particle density of intergalactic space may be even lower when accounting for the concentration of protons in stars and galaxies. Now it is often generally quoted that there are ~100 billion stars in a galaxy and ~100 billion galaxies in the universe, although we presumably need to quantify the size of the universe, e.g. as linked to the Hubble radius [c/H] or the possibly the large particle horizon within some ultimately unknown limit to the physical universe. However, presumably adding to this total is the number of particles associated the range of interstellar particle densities as suggested by the Wikipedia reference. So my question for clarification is:

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

For without some considerable accuracy on these figures, it is unclear to me how the LCDM model can be so precise about the 4.0-4.6% particle mass as a fraction of the critical mass. As I understand it, the critical density is determined from the basic Friedmann equations, which then suggests a basically spatial flat universe, i.e. k=1, but then most references simply suggest that this led to the realisation of the ‘missing’ mass of the universe, which was subsequently filled by dark matter and dark energy. Thanks

Last edited: Oct 13, 2012