Observable Universe mass...

[Orion1]

This is my equation for the observable Universe mass, based upon the Cosmic Energy Inventory (CEI) parameters and the Hubble Space Telescope (HST) parameters in (SI) units.

Universe observable parameters:

Universe total observable radius:
[math]R_u = 4.408 \cdot 10^{26} \; \text{m} \; \; \; (46.6 \cdot 10^{9} \; \text{ly})[/math]

CEI stellar Baryon density:
[math]\Omega_s = 0.00205[/math]

HST observable stellar number:
[math]N_s = 10^{22}[/math]

Solar mass:
[math]M_{\odot} = 1.989 \cdot 10^{30} \; \text{kg}[/math]

Observable Universe mass:
[math]\boxed{M_u = \frac{N_s M_{\odot}}{\Omega_s}}[/math]

[math]\boxed{M_u = 9.705 \cdot 10^{54} \; \text{kg}}[/math]

Any discussions and/or peer reviews about this specific topic thread?

Also, please be sure to vote on the thread to rate this topic.

Reference:
http://en.wikipedia.org/wiki/Lambda-CDM_model
http://en.wikipedia.org/wiki/Universe
http://en.wikipedia.org/wiki/Observable_universe
http://en.wikipedia.org/wiki/Dark_matter
http://arxiv.org/pdf/astro-ph/0406095v2.pdf

Edited November 29, 2014 by Orion1

[Mordred]

You could add up the energy budget to check your numbers

 

http://arxiv.org/pdf/astro-ph/0406095v2.pdf

[Sensei]

You're making assumption that every star has the same mass as Sun and/or that Sun's mass is average star mass across entire observable Universe.

[Strange]

Your figure seems to be about two orders of magnitude larger than other estimates:

http://en.wikipedia.org/wiki/Observable_universe#Mass_of_ordinary_matter

 

(I haven't gone through the "Extrapolation from number of stars" to work out where the difference might come from. Overestimating average star mass, would only seem to account for a factor of 2.)

[Orion1]

The problems with the mass equation model in post #1:
-the model presumes that everything in the Universe is composed of mass.
-the model presumes that the masses of all the stars are equal and that the masses of heavy stars average with the light stars for a main sequence mass.

Universe dark matter composition:
[math]\Omega_{dm} = 0.23[/math]

Universe baryonic matter composition:
[math]\Omega_{b} = 0.045[/math]


A compositional mass fraction is required to compensate for a Universe that is not composed entirely of mass.

The stellar mass fraction is equivalent to the stellar compositional fraction divided by the total compositional mass fractions:
[math]\boxed{\Omega_{sf} = \frac{\Omega_{s}}{\Omega_{dm} + \Omega_{b}}}[/math]

A mass summation formula is required with an extensive stellar survey mass database in order to sum the masses of all the stars:

[math]dM = \sum_{n \mathop = 1}^{N_s} m_n[/math]

The astrophysical volume from which the stellar survey was obtained:
[math]dV \leq V_u[/math]

Observable Universe mass summation integration via substitution:
[math]M_u = \rho_u V_u = \frac{4 \pi}{3 \Omega_{sf}} \left( \frac{dM}{dV} \right) R_u^3 = \frac{4 \pi R_u^3}{3 \Omega_{sf}} \left( \frac{\sum_{n \mathop = 1}^{N_s} m_n}{dV} \right)[/math]

Observable Universe mass summation formula:
[math]\boxed{M_u = \frac{4 \pi R_u^3}{3 \Omega_{sf}} \left( \frac{\sum_{n \mathop = 1}^{N_s} m_n}{dV} \right)}[/math]

However, without an extensive stellar survey mass database, only average approximations are possible to calculate.

HST observable stellar number:
[math]N_s = 10^{22}[/math]

Observable Universe mass:
[math]M_u = \frac{N_s M_{\odot}}{\Omega_{sf}} = 6.597 \cdot 10^{54}[/math]

[math]\boxed{M_u = 6.597 \cdot 10^{54}}[/math]

---

Universe total observable radius:
[math]R_u = 4.408 \cdot 10^{26} \; \text{m} \; \; \; (46.6 \cdot 10^{9} \; \text{ly})[/math]

Radiation constant:
[math]\alpha_{\gamma} = \frac{\pi^2 k_B^4}{15 \hbar^3 c^3}[/math]

CMBR temperature at present time:
[math]T_{\gamma} = 2.72548 \; \text{K}[/math]

CMBR primeval thermal remnant composition:
[math]\Omega_{\gamma} = 10^{-4.3}[/math]

The CMBR primeval thermal remnant fraction is equivalent to the CMBR compositional fraction divided by the total compositional mass fractions:
[math]\boxed{\Omega_{\gamma f} = \frac{\Omega_{\gamma}}{\Omega_{dm} + \Omega_{b}}}[/math]

CMBR energy density:
[math]\epsilon_{\gamma} = \alpha_{\gamma} T_{\gamma}^4[/math]

Observable Universe total mass:
[math]M_u = \frac{\epsilon_{\gamma} V_u}{c^2 \Omega_{\gamma f}} = \frac{4 \pi \epsilon_{\gamma} R_u^3}{3 c^2 \Omega_{\gamma f}} = 9.148 \cdot 10^{53} \; \text{kg}[/math]

[math]\boxed{M_u = \frac{4 \pi \epsilon_{\gamma} R_u^3}{3 c^2 \Omega_{\gamma f}}}[/math]

[math]\boxed{M_u = 9.148 \cdot 10^{53} \; \text{kg}}[/math]

 

Any discussions and/or peer reviews about this specific topic thread?

Also, please be sure to vote on the thread to rate this topic.
Reference:
http://en.wikipedia.org/wiki/Boltzmann_constant
http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_constant
http://en.wikipedia.org/wiki/Cosmic_microwave_background
http://star-www.dur.ac.uk/~csf/homepage/CosmicHistory_lectures/lecture_7-8_notes.pdf
http://arxiv.org/pdf/astro-ph/0406095v2.pdf

 

 

Edited November 30, 2014 by Orion1

[Mordred]

Well I'm glad to see the cosmic inventory included in your links. It's rather extensive and detailed. Judging by your calcs and what I recall its in the right range. For an approximation

Though I am still unclear what you are presenting that is new.

Edited November 30, 2014 by Mordred

[Strange]

Also, please be sure to vote on the thread to rate this topic.

 

OK. I have given it a rating of zero. Happy?

[Orion1]

 

OK. I have given it a rating of zero. Happy?

 

Negative, you would have encountered a rating singularity.

[Strange]

 

Negative, you would have encountered a rating singularity.

 

[Orion1]

Universe total observable radius:
[math]R_u = 4.408 \cdot 10^{26} \; \text{m} \; \; \; (46.6 \cdot 10^{9} \; \text{ly})[/math]

Radiation constant:
[math]\alpha_{\gamma} = \frac{\pi^2 k_B^4}{15 \hbar^3 c^3}[/math]

CMBR temperature at present time:
[math]T_{\gamma} = 2.72548 \; \text{K}[/math]

Cosmic neutrino background radiation temperature at present time:
[math]T_{\nu} = 1.95 \; \text{K}[/math]

Neutrino primeval thermal remnant composition:
[math]\Omega_{\nu} = 10^{-2.9}[/math]

Standard Model neutrino species effective number:
[math]N_{\nu} = 3.046[/math]

The neutrino primeval thermal remnant fraction is equivalent to the neutrino compositional fraction divided by the total compositional mass fractions:
[math]\boxed{\Omega_{\nu f} = \frac{\Omega_{\nu}}{\Omega_{dm} + \Omega_{b}}}[/math]

CMBR energy density:
[math]\epsilon_{\gamma} = \alpha_{\gamma} T_{\gamma}^4[/math]

Relativistic neutrino energy density integration via substitution:
[math]\epsilon_{\nu} = \epsilon_{\gamma} \left[ 1 + \frac{7}{8} \left( \frac{4}{11} \right)^{4/3} N_{\nu} \right] = \alpha_{\gamma} T_{\gamma}^4 \left[ 1 + \frac{7}{8} \left( \frac{4}{11} \right)^{4/3} N_{\nu} \right][/math]

Relativistic neutrino energy density:
[math]\boxed{\epsilon_{\nu} = \alpha_{\gamma} T_{\gamma}^4 \left[ 1 + \frac{7}{8} \left( \frac{4}{11} \right)^{4/3} N_{\nu} \right]}[/math]

Observable Universe total mass:
[math]M_u = \frac{\epsilon_{\nu} V_u}{c^2 \Omega_{\nu f}} = \frac{4 \pi \epsilon_{\nu} R_u^3}{3 c^2 \Omega_{\nu f}} = 6.161 \cdot 10^{52} \; \text{kg}[/math]

[math]\boxed{M_u = \frac{4 \pi \epsilon_{\nu} R_u^3}{3 c^2 \Omega_{\nu f}}}[/math]

[math]\boxed{M_u = 6.161 \cdot 10^{52} \; \text{kg}}[/math]

Any discussions and/or peer reviews about this specific topic thread?

Reference:
http://en.wikipedia.org/wiki/Boltzmann_constant
http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_constant
http://en.wikipedia.org/wiki/Cosmic_neutrino_background
http://star-www.dur.ac.uk/~csf/homepage/CosmicHistory_lectures/lecture_7-8_notes.pdf
http://arxiv.org/pdf/astro-ph/0406095v2.pdf
http://arxiv.org/pdf/hep-ph/0506164.pdf

[Orion1]

A more accurate relativistic neutrino energy density formula...

Universe total observable radius:
[math]R_u = 4.408 \cdot 10^{26} \; \text{m} \; \; \; (46.6 \cdot 10^{9} \; \text{ly})[/math]

Radiation constant:
[math]\alpha_{\gamma} = \frac{\pi^2 k_B^4}{15 \hbar^3 c^3}[/math]

CMBR temperature at present time:
[math]T_{\gamma} = 2.72548 \; \text{K}[/math]

Cosmic neutrino background radiation temperature at present time:
[math]T_{\nu} = 1.95 \; \text{K}[/math]

Neutrino primeval thermal remnant composition:
[math]\Omega_{\nu} = 10^{-2.9}[/math]

Standard Model neutrino species effective number:
[math]N_{\nu} = 3.046[/math]

The neutrino primeval thermal remnant fraction:
[math]\boxed{\Omega_{\nu f} = \frac{\Omega_{\nu}}{\Omega_{dm} + \Omega_{b}}}[/math]

Relativistic neutrino energy density:
[math]\boxed{\epsilon_{\nu} = \alpha_{\gamma} T_{\gamma}^4 \left[ 1 + \frac{7}{8} \left( \frac{T_{\nu}}{T_{\gamma}} \right)^4 N_{\nu} \right]}[/math]

Observable Universe total mass:
[math]\boxed{M_u = \frac{4 \pi \epsilon_{\nu} R_u^3}{3 c^2 \Omega_{\nu f}}}[/math]

[math]\boxed{M_u = 6.185 \cdot 10^{52} \; \text{kg}}[/math]

Any discussions and/or peer reviews about this specific topic thread?

Reference:
http://en.wikipedia.org/wiki/Boltzmann_constant
http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_constant
http://en.wikipedia.org/wiki/Cosmic_neutrino_background
http://star-www.dur.ac.uk/~csf/homepage/CosmicHistory_lectures/lecture_7-8_notes.pdf
http://arxiv.org/pdf/astro-ph/0406095v2.pdf
http://arxiv.org/pdf/hep-ph/0506164.pdf

Edited January 3, 2015 by Orion1

[Mordred]

As neutrinos are fermionic you may get a higher degree of approximation using the Fermi-Dirac statistic equation.

http://en.m.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics

I would also recommend seperating each species of neutrinos, calculating each seperately with the Fermi Dirac then totalling. The number of degrees of freedom of each species is part of the Fermi Dirac

You can group the particle anti particle pairs just make sure you have that reflected in the degrees of freedom

This will account for temperature changes due to neutrino interactions

[Mordred]

http://arxiv.org/abs/1212.6154

 

Neutrino mass from cosmology. Looks like they use the same formula.

Edited January 4, 2015 by Mordred

[Orion1]

Correction to the relativistic neutrino energy density equation on post #11.

The total radiation energy density of the Universe is equivalent to the sum of the Cosmic Microwave Background Radiation energy density plus the Cosmic neutrino Background Radiation energy density.

The total radiation energy density of the Universe:
[math]\epsilon_r = \epsilon_{\gamma} + \epsilon_{\nu} = \epsilon_{\gamma} \left[ 1 + \frac{7}{8} \left( \frac{T_{\nu}}{T_{\gamma}} \right)^4 N_{\nu} \right] = \epsilon_{\gamma} + \epsilon_{\gamma} \left( \frac{7}{8} \right) \left( \frac{T_{\nu}}{T_{\gamma}} \right)^4 N_{\nu}[/math]

Relativistic neutrino energy density integration via substitution:
[math]\epsilon_{\nu} = \epsilon_{\gamma} \left( \frac{7}{8} \right) \left( \frac{T_{\nu}}{T_{\gamma}} \right)^4 N_{\nu} = \alpha_{\gamma} T_{\gamma}^4 \left( \frac{7}{8} \right) \left( \frac{T_{\nu}}{T_{\gamma}} \right)^4 N_{\nu} = \alpha_{\gamma} T_{\nu}^4 \left( \frac{7}{8} \right) N_{\nu}[/math]

Relativistic neutrino energy density:
[math] \boxed{\epsilon_{\nu} = \alpha_{\gamma} T_{\nu}^4 \left( \frac{7}{8} \right) N_{\nu}}[/math]

Observable Universe total mass:
[math]\boxed{M_u = \frac{4 \pi \epsilon_{\nu} R_u^3}{3 c^2 \Omega_{\nu f}}}[/math]

[math]\boxed{M_u = 2.543 \cdot 10^{52} \; \text{kg}}[/math]

Any discussions and/or peer reviews about this specific topic thread?

Reference:
http://en.wikipedia.org/wiki/Cosmic_neutrino_background
http://arxiv.org/pdf/hep-ph/0506164.pdf
http://arxiv.org/abs/1212.6154

Edited January 9, 2015 by Orion1

[Orion1]

Universe total observable radius:
[math] R_u = 4.408 \cdot 10^{26} \; \text{m} \; \; \; (46.6 \cdot 10^{9} \; \text{ly}) [/math]

Radiation constant:
[math] \alpha_{\gamma} = \frac{\pi^2 k_B^4}{15 \hbar^3 c^3} [/math]

Cosmic Microwave Background Radiation temperature at present time:
[math] T_{\gamma} = 2.72548 \; \text{K} [/math]

Cosmic Neutrino Background Radiation temperature at present time:
[math] T_{\nu} = 1.95 \; \text{K} [/math]

Cosmic Microwave Background Radiation primeval thermal remnant composition:
[math] \Omega_{\gamma} = 10^{-4.3} [/math]

Neutrino primeval thermal remnant composition:
[math] \Omega_{\nu} = 10^{-2.9} [/math]

Standard Model neutrino species effective number:
[math] N_{\nu} = 3.046 [/math]

The Universe total relic background radiation primeval remnant fraction is equivalent to the Cosmic Microwave Background Radiation compositional fraction plus the Cosmic Neutrino Background Radiation compositional fraction divided by the total compositional mass fractions.
[math] \boxed{\Omega_{rf} = \frac{\Omega_{\gamma} + \Omega_{\nu}}{\Omega_{dm} + \Omega_{b}}} [/math]

Cosmic Microwave Background Radiation energy density:
[math] \epsilon_{\gamma} = \alpha_{\gamma} T_{\gamma}^4 [/math]

Cosmic Neutrino Background Radiation energy density:
[math] \boxed{\epsilon_{\nu} = \alpha_{\gamma} T_{\nu}^4 \left( \frac{7}{8} \right) N_{\nu}} [/math]

The Universe total radiation energy density is equivalent to the sum of the Cosmic Microwave Background Radiation energy density plus the Cosmic Neutrino Background Radiation energy density.
[math] \epsilon_r = \epsilon_{\gamma} + \epsilon_{\nu} = \epsilon_{\gamma} \left[ 1 + \frac{7}{8} \left( \frac{T_{\nu}}{T_{\gamma}} \right)^4 N_{\nu} \right] [/math]

Observable Universe total mass:
[math] \boxed{M_u = \frac{4 \pi \epsilon_{r} R_u^3}{3 c^2 \Omega_{r f}}} [/math]

[math] \boxed{M_u = 5.948 \cdot 10^{52} \; \text{kg}} [/math]

Any discussions and/or peer reviews about this specific topic thread?

Reference:
http://en.wikipedia.org/wiki/Observable_universe
http://en.wikipedia.org/wiki/Universe
http://en.wikipedia.org/wiki/Cosmic_microwave_background
http://en.wikipedia.org/wiki/Cosmic_neutrino_background
http://arxiv.org/pdf/hep-ph/0506164.pdf
http://arxiv.org/abs/1212.6154
http://star-www.dur.ac.uk/~csf/homepage/CosmicHistory_lectures/lecture_7-8_notes.pdf
http://arxiv.org/pdf/astro-ph/0406095v2.pdf

Edited January 31, 2015 by Orion1

[Mordred]

You might look at the equivalent mass contribution of the cosmological constant. From the critical density formula it derives as roughly

 

[latex] 10^{-29} [/latex] grams/cubic meter

 

The Higgs field energy density should also be considered. I ran across an article at one time with its energy density. I'll try and see if I can track it down.

Edited January 31, 2015 by Mordred

[Orion1]

Hubble constant:
[math] H_0 = 2.3 \cdot 10^{-18} \; \text{s}^{-1} [/math]

Dark Energy compositional density parameter:
[math] \Omega_{\Lambda} = 0.72 [/math]

Cosmological Constant:
[math] \Lambda = \frac{3 \Omega_{\Lambda} H_0^2}{c^2} [/math]

Friedmann equations critical density:
[math] \rho_c = \frac{3 H_0^2}{8 \pi G} [/math]

Dark Energy mass density integration via substitution:
[math]\rho_{\Lambda} = \Omega_{\Lambda} \rho_c = \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} [/math]

Dark Energy mass density:
[math] \boxed{\rho_{\Lambda} = \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G}} [/math]

[math] \boxed{\rho_{\Lambda} = 6.812 \cdot 10^{-27} \; \frac{\text{kg}}{\text{m}^3}} [/math]

Any discussions and/or peer reviews about this specific topic thread?

Reference:
http://relativity.livingreviews.org/Articles/lrr-2001-1/download/lrr-2001-1Color.pdf
http://en.wikipedia.org/wiki/Critical_density_%28cosmology%29#Density_parameter
http://en.wikipedia.org/wiki/Hubble_constant#Hubble_time
http://en.wikipedia.org/wiki/Hubble%27s_law#Matter-dominated_universe_.28with_a_cosmological_constant.29
https://www.physicsforums.com/threads/friedmann-equation.281689/#post-2015381

Edited February 1, 2015 by Orion1

[Mordred]

Hubble constant:

[math] H_0 = 2.3 \cdot 10^{-18} \; \text{s}^{-1} [/math]

 

Dark Energy compositional density parameter:

[math] \Omega_{\Lambda} = 0.72 [/math]

 

Cosmological Constant:

[math] \Lambda = \frac{3 \Omega_{\Lambda} H_0^2}{c^2} [/math]

 

Friedmann equations critical density:

[math] \rho_c = \frac{3 H_0^2}{8 \pi G} [/math]

 

Dark Energy mass density integration via substitution:

[math]\rho_{\Lambda} = \Omega_{\Lambda} \rho_c = \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} [/math]

 

Dark Energy mass density:

[math] \boxed{\rho_{\Lambda} = \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G}} [/math]

 

[math] \boxed{\rho_{\Lambda} = 6.812 \cdot 10^{-27} \; \frac{\text{kg}}{\text{m}^3}} [/math]

 

Any discussions and/or peer reviews about this specific topic thread?

Reference:

http://relativity.livingreviews.org/Articles/lrr-2001-1/download/lrr-2001-1Color.pdf

http://en.wikipedia.org/wiki/Critical_density_%28cosmology%29#Density_parameter

http://en.wikipedia.org/wiki/Hubble_constant#Hubble_time

http://en.wikipedia.org/wiki/Hubble%27s_law#Matter-dominated_universe_.28with_a_cosmological_constant.29

https://www.physicsforums.com/threads/friedmann-equation.281689/#post-2015381

 

 

Looks good bang on the money in this post

[Orion1]

Friedmann equations critical mass integration via substitution:
[math] M_c = \rho_c V_u = \left( \frac{3 H_0^2}{8 \pi G} \right) \left( \frac{4 \pi R_u^3}{3} \right) = \frac{H_0^2 R_u^3}{2 G} [/math]

Friedmann equations critical mass:
[math] \boxed{M_c = \frac{H_0^2 R_u^3}{2 G}} [/math]

[math] \boxed{M_c = 3.396 \cdot 10^{54} \; \text{kg}} [/math]

Observable Universe total mass:
[math] \boxed{M_u = \frac{4 \pi R_u^3}{3} \left( \frac{\epsilon_r}{c^2 \Omega_{rf}} + \rho_{\Lambda} \right)} [/math]

[math] \boxed{M_u = 2.504 \cdot 10^{54} \; \text{kg}} [/math]

Any discussions and/or peer reviews about this specific topic thread?

Reference:
http://relativity.livingreviews.org/Articles/lrr-2001-1/download/lrr-2001-1Color.pdf
http://en.wikipedia.org/wiki/Critical_density_%28cosmology%29#Density_parameter
http://en.wikipedia.org/wiki/Hubble%27s_law#Matter-dominated_universe_.28with_a_cosmological_constant.29

Edited February 2, 2015 by Orion1

[Orion1]

The Higgs field energy density should also be considered. I ran across an article at one time with its energy density. I'll try and see if I can track it down.

 

I am unable to locate either a Standard Model theoretical mathematical prediction value or an astrophysical measured value for the cosmological Higgs field energy density. The closest scientific information that I was able to locate is located in reference 1.

 

Reference:

The New Physics - Paul Davies - page 42

https://books.google.com/books?id=akb2FpZSGnMC&pg=PA42&lpg=PA42#v=onepage&q&f=false

[Mordred]

The paper I had, has the wrong Higgs mass. I'm still looking but you may have already accounted for it, if the Higgs field is responsible for the cosmological constant. Most of the papers I looked at ties the Higgs to the cosmological constant, but I've been unable to find a definite separation of the Higgs field itself from Lambda

[Orion1]

Observable Universe total mass integration via substitution:

[math] M_u = \rho_u V_u = \frac{4 \pi R_u^3}{3} \left( \frac{\epsilon_r}{c^2 \Omega_{rf}} + \rho_{\Lambda} \right) = \frac{4 \pi R_u^3}{3} \left[ \frac{\pi^2 k_B^4}{15 \hbar^3 c^5} \left( T_{\gamma}^4 + T_{\nu}^4 \left( \frac{7}{8} \right) N_{\nu} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right] [/math]

 

Observable Universe total mass:

[math] \boxed{M_u = \frac{4 \pi R_u^3}{3} \left[ \frac{\pi^2 k_B^4}{15 \hbar^3 c^5} \left( T_{\gamma}^4 + T_{\nu}^4 \left( \frac{7}{8} \right) N_{\nu} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right]} [/math]

 

[math] \boxed{M_u = 2.504 \cdot 10^{54} \; \text{kg}} [/math]

 

Any discussions and/or peer reviews about this specific topic thread?

 

Reference:

http://www.scienceforums.net/topic/86694-observable-universe-mass/

Edited April 17, 2015 by Orion1

[Orion1]

Observable Universe average stellar mass: (ref. 1, pg. 20)

[math]M_a = 0.6 \cdot M_{\odot}[/math]

 

CEI stellar Baryon density: (ref. 2, pg. 3)

[math]\Omega_s = (\Omega_{ms} + \Omega_{wd} + \Omega_{ns}) = 0.00246[/math]

 

Observable Universe total mass from average stellar mass: (ref. 3)

[math]M_{u,1} = \frac{N_s M_a}{\Omega_{sf}} = N_s M_a \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{s}} \right)[/math]

 

Observable Universe total mass from cosmic background radiation: (ref. 4)

[math]M_{u,2} = \frac{4 \pi R_u^3}{3} \left( \frac{\epsilon_r}{c^2 \Omega_{rf}} + \rho_{\Lambda} \right) = \frac{4 \pi R_u^3}{3} \left[ \frac{\epsilon_r}{c^2} \left( \frac{\Omega_{dm} + \Omega_b}{\Omega_{\gamma} + \Omega_{\nu}} \right)+ \rho_{\Lambda} \right][/math]

 

Observable Universe total mass from average stellar mass is equivalent to Observable Universe total mass from cosmic background radiation:

[math]\boxed{M_{u,1} = M_{u,2}}[/math]

 

Integration via substitution:

[math]N_s M_a \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{s}} \right) = \frac{4 \pi R_u^3}{3} \left[ \frac{\epsilon_r}{c^2} \left( \frac{\Omega_{dm} + \Omega_b}{\Omega_{\gamma} + \Omega_{\nu}} \right)+ \rho_{\Lambda} \right][/math]

 

Solve for total observable stellar number [math]N_s[/math].

 

Observable Universe total observable stellar number:

[math]\boxed{N_s = \frac{4 \pi R_u^3}{3 \cdot 0.6 \cdot M_{\odot}} \left( \frac{\Omega_{s}}{\Omega_{dm} + \Omega_{b}} \right) \left[ \frac{\epsilon_r}{c^2} \left( \frac{\Omega_{dm} + \Omega_b}{\Omega_{\gamma} + \Omega_{\nu}} \right)+ \rho_{\Lambda} \right]}[/math]

 

[math]\boxed{N_s = 1.877 \cdot 10^{22} \; \; \; \text{stars}}[/math]

 

Hubble Space Telescope (HST) stellar survey Observable Universe total observable stellar number:

[math]\boxed{N_s = 1.000 \cdot 10^{22} \; \; \; \text{stars}}[/math]

 

Any discussions and/or peer reviews about this specific topic thread?

 

Reference:

On The Mass Distribution Of Stars...:

http://www.doiserbia.nb.rs/img/doi/1450-698X/2006/1450-698X0672017N.pdf

The Cosmic Energy Inventory:

http://arxiv.org/pdf/astro-ph/0406095v2.pdf

Observable Universe total mass from stellar mass:

http://www.scienceforums.net/topic/86694-observable-universe-mass/#entry839572

Observable Universe total mass from cosmic background radiation:

http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry864237

Edited June 9, 2015 by Orion1

[Orion1]

Observable Universe total galaxy number: (ref. 4, 5, 6)

[math]N_g = 1.7 \cdot 10^{11} \; \; \; \text{galaxies}[/math]

 

Milky Way galaxy mass: (ref. 1, pg. 1)

[math]M_{mw} = 1.26 \cdot 10^{12} \cdot M_{\odot}[/math]

 

Observable Universe average galaxy mass:

[math]M_a = f_{a} \cdot M_{mw}[/math]

 

Dimensionless average galaxy mass fraction: [math]f_{a}[/math]

 

CEI galaxy baryon density: (ref. 2, pg. 3)

[math]\Omega_b = 0.045[/math]

 

Galaxy compositional fraction is equivalent to baryon rest mass compositional fraction:

[math]\boxed{\Omega_g = \Omega_b}[/math]

 

The total Observable Universe galactic mass fraction is equivalent to the baryon rest mass fraction divided by the total compositional mass fractions.

[math]\boxed{\Omega_{gf} = \left( \frac{\Omega_{b}}{\Omega_{dm} + \Omega_{b}} \right)}[/math]

 

Observable Universe total mass from average galaxy mass:

[math]M_{u,1} = \frac{N_g M_a}{\Omega_{gf}} = N_g M_a \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{b}} \right)[/math]

 

Observable Universe total mass from cosmic background radiation: (ref. 3)

[math]M_{u,2} = \frac{4 \pi R_u^3}{3} \left( \frac{\epsilon_r}{c^2 \Omega_{rf}} + \rho_{\Lambda} \right) = \frac{4 \pi R_u^3}{3} \left[ \frac{\epsilon_r}{c^2} \left( \frac{\Omega_{dm} + \Omega_b}{\Omega_{\gamma} + \Omega_{\nu}} \right)+ \rho_{\Lambda} \right][/math]

 

Observable Universe total mass from average galaxy mass is equivalent to Observable Universe total mass from cosmic background radiation:

[math]\boxed{M_{u,1} = M_{u,2}}[/math]

 

Integration via substitution:

[math]N_g M_a \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{b}} \right) = \frac{4 \pi R_u^3}{3} \left[ \frac{\epsilon_r}{c^2} \left( \frac{\Omega_{dm} + \Omega_b}{\Omega_{\gamma} + \Omega_{\nu}} \right)+ \rho_{\Lambda} \right][/math]

 

Solve for average galaxy mass fraction: [math]f_{a}[/math].

 

Observable Universe average galaxy mass fraction:

[math]\boxed{f_a = \frac{4 \pi R_u^3}{3 N_g M_{mw}} \left( \frac{\Omega_{b}}{\Omega_{dm} + \Omega_{b}} \right) \left[ \frac{\epsilon_r}{c^2} \left( \frac{\Omega_{dm} + \Omega_b}{\Omega_{\gamma} + \Omega_{\nu}} \right)+ \rho_{\Lambda} \right]}[/math]

 

Observable Universe dimensionless average galaxy mass fraction:

[math]\boxed{f_a = 0.962}[/math]

 

Any discussions and/or peer reviews about this specific topic thread?

 

Reference:

Mass models of the Milky Way:
http://arxiv.org/pdf/1102.4340v1

The Cosmic Energy Inventory:
http://arxiv.org/pdf/astro-ph/0406095v2.pdf

 

Observable Universe total mass from cosmic background radiation:
http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry864237

 

A Map of the Universe:

http://arxiv.org/pdf/astro-ph/0310571v2

 

Galaxy:

https://en.wikipedia.org/wiki/Galaxy

 

List of galaxies:

https://en.wikipedia.org/wiki/List_of_galaxies

Edited July 4, 2015 by Orion1

[Orion1]

Photon radiation constant:

[math]\alpha_{\gamma} = \frac{\pi^2 k_B^4}{15 \hbar^3 c^3}[/math]

 

Scalar particle radiation constant is equivalent to one-half the photon radiation constant: (ref. 1, pg. 363)

[math]\alpha_{\phi} = \frac{\alpha_{\gamma}}{2} = \frac{\pi^2 k_B^4}{30 \hbar^3 c^3}[/math]

 

Scalar particle radiation constant: (ref. 1, pg. 363)

[math]\boxed{\alpha_{\phi} = \frac{\pi^2 k_B^4}{30 \hbar^3 c^3}}[/math]

 

Scalar particle radiation temperature is equivalent to cosmic neutrino background radiation temperature: (ref. 1, pg. 363)

[math]\boxed{T_{\phi} = T_{\nu}}[/math]

 

Scalar particle radiation energy density:

[math]\boxed{\epsilon_{\phi} = \alpha_{\phi} T_{\phi}^4}[/math]

 

Average scalar particle energy: (ref. 2, pg. 4)

[math]\boxed{E_{\phi} = \frac{3 k_B T_{\phi}}{2}}[/math]

 

The total average scalar particle radiation number density is equivalent to the scalar particle radiation energy density divided by the average scalar particle energy:

[math]n_{\phi} = \frac{\epsilon_{\phi}}{E_{\phi}} = \frac{2 \epsilon_{\phi}}{3 k_B T_{\phi}} = \frac{2 \alpha_{\phi} T_{\phi}^3}{3 k_B} = \frac{\pi^2}{45} \left( \frac{k_B T_{\phi}}{\hbar c} \right)^3[/math]

 

Total average scalar particle radiation number density:

[math]\boxed{n_{\phi} = \frac{\pi^2}{45} \left( \frac{k_B T_{\phi}}{\hbar c} \right)^3}[/math]

 

The total Observable Universe dark matter fraction is equivalent to the dark matter compositional fraction divided by the total compositional mass fractions:

[math]\boxed{\Omega_{dmf} = \left( \frac{\Omega_{dm}}{\Omega_{dm} + \Omega_{b}} \right)}[/math]

 

Observable Universe total density derived from dark matter scalar particles integration via substitution:

[math]\rho_{u, \phi} = \frac{n_{\phi} m_{\phi}}{\Omega_{dmf}} = n_{\phi} m_{\phi} \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{dm}} \right) = \frac{\pi^2 m_{\phi}}{45} \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{dm}} \right) \left( \frac{k_B T_{\phi}}{\hbar c} \right)^3[/math]

 

Observable Universe total density derived from dark matter scalar particles:

[math]\boxed{\rho_{u, \phi} = \frac{\pi^2 m_{\phi}}{45} \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{dm}} \right) \left( \frac{k_B T_{\phi}}{\hbar c} \right)^3}[/math]

 

Observable Universe total density derived from cosmic background radiation and dark energy:

[math]\boxed{\rho_{u, \gamma , \Lambda} = \left[ \frac{\pi^2 k_B^4}{15 \hbar^3 c^5} \left( T_{\gamma}^4 + T_{\nu}^4 \left( \frac{7}{8} \right) N_{\nu} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right]}[/math]

 

Observable Universe total density derived from dark matter scalar particles is equivalent to the Observable Universe total density derived from cosmic background radiation and dark energy:

[math]\boxed{\rho_{u, \phi} = \rho_{u, \gamma , \Lambda}}[/math]

 

Integration via substitution:

[math]\frac{\pi^2 m_{\phi}}{45} \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{dm}} \right) \left( \frac{k_B T_{\phi}}{\hbar c} \right)^3 = \left[ \frac{\pi^2 k_B^4}{15 \hbar^3 c^5} \left( T_{\gamma}^4 + T_{\nu}^4 \left( \frac{7}{8} \right) N_{\nu} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right][/math]

 

Solve for dark matter scalar particle mass: [math]m_{\phi}[/math]

 

Dark matter scalar particle mass:

[math]\boxed{m_{\phi} = \frac{45}{\pi^2} \left( \frac{\Omega_{dm}}{\Omega_{dm} + \Omega_{b}} \right) \left( \frac{\hbar c}{k_B T_{\phi}} \right)^3 \left[ \frac{\pi^2 k_B^4}{15 \hbar^3 c^5} \left( T_{\gamma}^4 + T_{\nu}^4 \left( \frac{7}{8} \right) N_{\nu} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right]}[/math]

 

Dark matter scalar particle mass:

[math]\boxed{m_{\phi} = 4.309 \cdot 10^{-35} \; \; \text{kg}}[/math]

 

Any discussions and/or peer reviews about this specific topic thread?

 

Reference:

Neutrinos in Particle Physics, Astrophysics and Cosmology
https://books.google.ca/books?id=mRGThuuYHgsC&pg=PA363#v=onepage&q&f=false

 

PHYS 390 Lecture 13 - Simon Fraser University
http://www.sfu.ca/~boal/390lecs/390lec13.pdf

 

The Cosmic Energy Inventory:
http://arxiv.org/pdf/astro-ph/0406095v2.pdf

 

Dark Matter - Wikipedia

https://en.wikipedia.org/wiki/Dark_matter

Edited July 11, 2015 by Orion1