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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:

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: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.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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?

- 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

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