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Orion1

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  1. [math]\begin{tabular}{l*{6}{c}r} & identity & state & spin & ns & Ns & Nn \\ b & scalar & 0 & 0 & 1 & 1 & 1 \\ f & neutrino & +,- & 1/2 & 2 & 3 & 3 \\ f & sterile neutrino & +,- & 1/2 & 2 & 3 & 3 \\ f & neutralino & +,- & 1/2 & 2 & 4 & 4 \\ b & photon & +,- & 1 & 2 & 1 & 2 \\ b & graviton & +,- & 2 & 2 & 1 & 2 \\ \end{tabular}[/math] Observable Universe Dark Matter scalar particle interaction rate at scalar particle decoupling time: (ref. 1) [math]\boxed{\Gamma_{\phi,t} = 39.232 \; \frac{\phi \; \text{particles}}{\text{s}}}[/math] Observable Universe cosmic neutrino background radiation neutrino interaction rate at neutrino decoupling time: (ref. 2) [math]\boxed{\Gamma_{\nu,t} = 6.749 \; \frac{\nu \; \text{particles}}{\text{s}}}[/math] Observable Universe Dark Matter sterile neutrino interaction rate at sterile neutrino decoupling time: (ref. 1) [math]\boxed{\Gamma_{\nu,t} = 2.689 \; \frac{\nu \; \text{particles}}{\text{s}}}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Observable Universe Dark Matter scalar particle interaction rate at scalar particle decoupling time: (ref. 1) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-3#entry999725 Observable Universe Dark Matter sterile neutrino interaction rate at sterile neutrino decoupling time: (ref. 2) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-3#entry999725
  2. [math]\begin{tabular}{l*{6}{c}r} & identity & state & spin & ns & Ns & Nn \\ b & scalar & 0 & 0 & 1 & 1 & 1 \\ f & neutrino & +,- & 1/2 & 2 & 3 & 3 \\ f & sterile neutrino & +,- & 1/2 & 2 & 3 & 3 \\ f & neutralino & +,- & 1/2 & 2 & 4 & 4 \\ b & photon & +,- & 1 & 2 & 1 & 2 \\ b & graviton & +,- & 2 & 2 & 1 & 2 \\ \end{tabular}[/math] Observable Universe Dark Matter scalar particle decoupling time: (ref. 1) [math]\boxed{T_{u, \phi} = 0.0255 \; \text{s}} \; \; \; m_{\phi} \neq 0[/math] Observable Universe cosmic neutrino background radiation neutrino decoupling time: (ref. 2) [math]\boxed{T_{u , \nu} = 0.148 \; \text{s}}\; \; \; m_{\nu} \neq 0[/math] Observable Universe Dark Matter sterile neutrino decoupling time: (ref. 3) [math]\boxed{T_{u, \nu} = 0.372 \; \text{s}} \; \; \; m_{\nu} \neq 0[/math] Observable Universe cosmic neutrino background radiation massless neutrino decoupling time: (ref. 4) [math]\boxed{T_{u , \nu} = 0.893 \; \text{s}} \; \; \; m_{\nu} = 0[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Orion1 - Observable Universe Dark Matter scalar particle decoupling time: (ref. 1) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-3#entry999388 Orion1 - Observable Universe neutrino background radiation neutrino decoupling time: (ref. 2) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-3#entry999033 Orion1 - Observable Universe Dark Matter sterile neutrino decoupling time: (ref. 3) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-3#entry999725 Orion1 - Observable Universe neutrino background radiation massless neutrino decoupling time: (ref. 4) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry882631
  3. WMAP satellite cosmological parameters at photon decoupling time: (ref. 1) [math]\Omega_{\nu , t} = 0.10[/math] [math]\Omega_{\Lambda , t} \neq 0[/math] Observable Universe cosmic neutrino background radiation neutrino decoupling temperature: (ref. 2) [math]T_{\nu , t} = 1 \cdot 10^{10} \; \text{K}[/math] Solve for Observable Universe cosmic neutrino background radiation neutrino interaction rate [math]\Gamma_{\nu,t}[/math] at neutrino decoupling time: (ref. 3) [math]\Gamma_{\nu,t} = \sqrt{\frac{4 G N_{\nu} \pi^3 (k_B T_{\nu,t})^4}{3 C_{\nu} \Omega_{\nu,t} \hbar^3 c^5}} = 2 (k_B T_{\nu,t})^2 \sqrt{\frac{G N_{\nu} \pi^3}{3 C_{\nu} \Omega_{\nu,t} \hbar^3 c^5}} = 6.749 \; \frac{ \nu \; \text{particles}}{\text{s}}[/math] Observable Universe cosmic neutrino background radiation neutrino interaction rate at neutrino decoupling time: [math]\boxed{\Gamma_{\nu,t} = 2 (k_B T_{\nu,t})^2 \sqrt{\frac{G N_{\nu} \pi^3}{3 C_{\nu} \Omega_{\nu,t} \hbar^3 c^5}}}[/math] Observable Universe cosmic neutrino background radiation neutrino interaction rate at neutrino decoupling time: [math]\boxed{\Gamma_{\nu,t} = 6.749 \; \frac{\nu \; \text{particles}}{\text{s}}}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: WMAP satellite cosmological parameters at photon decoupling time: (ref. 1) https://map.gsfc.nasa.gov/media/080998/index.html Wikipedia - neutrino decoupling: (ref. 2) https://en.wikipedia.org/wiki/Neutrino_decoupling Fermi-Dirac total neutrino distribution constant: (ref. 3) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry886860
  4. WMAP satellite cosmological parameters at photon decoupling time: (ref. 1) [math]\Omega_{dm , t} = 0.63[/math] [math]\Omega_{\gamma , t} = 0.15[/math] [math]\Omega_{\Lambda , t} \neq 0[/math] Observable Universe Dark Matter sterile neutrino composition is equivalent to Dark Matter composition at photon decoupling time: [math]\boxed{\Omega_{\nu , t} = \Omega_{dm , t}}[/math] Observable Universe Dark Matter sterile neutrino mass: [math]\boxed{m_{\nu} \neq 0}[/math] Observable Universe Dark Matter sterile neutrino decoupling temperature is equivalent to cosmic neutrino background radiation neutrino decoupling temperature: (ref. 2) [math]\boxed{T_{\nu, t} = T_{\nu , t}} = 1 \cdot 10^{10} \; \text{K}[/math] Observable Universe Fermi-Dirac Dark Matter sterile neutrino composition: (ref. 3) [math]\boxed{\Omega_{\nu} = \frac{4 G N_{\nu} \pi^3 (k_B T_{\nu})^4}{3 C_{\nu} H_0^2 \hbar^3 c^5}}[/math] Observable Universe Dark Matter sterile neutrino decoupling time: (ref. 4) [math]\boxed{T_{u , \nu} = \frac{1}{H_{\nu , t}}}[/math] Solve for Observable Universe Dark Matter sterile neutrino decoupling time [math]T_{u , \nu}[/math]: [math]T_{u , \nu} = \frac{1}{H_{\nu, t}} = \sqrt{\frac{3 \Omega_{\nu,t} C_{\nu} \hbar^3 c^5}{4 G N_{\nu} \pi^3 (k_B T_{\nu,t})^4}} = \frac{}{2 (k_B T_{\nu,t})^2} \sqrt{\frac{3 \Omega_{\nu,t} C_{\nu} \hbar^3 c^5}{G N_{\nu} \pi^3}} = 0.372 \; \text{s}[/math] Observable Universe Dark Matter sterile neutrino decoupling time: [math]\boxed{T_{u , \nu} = \frac{}{2 (k_B T_{\nu,t})^2} \sqrt{\frac{3 \Omega_{\nu,t} C_{\nu} \hbar^3 c^5}{G N_{\nu} \pi^3}}}[/math] Observable Universe Dark Matter sterile neutrino decoupling time: [math]\boxed{T_{u, \nu} = 0.372 \; \text{s}} \; \; \; m_{\nu} \neq 0[/math] --- Particle interaction rate is equivalent to Hubble Parameter at particle decoupling time: (ref. 5), (ref .6) [math]\boxed{\Gamma_{t} = n \langle \sigma v \rangle = H_{t}}[/math] Solve for Observable Universe photon interaction rate [math]\Gamma_{\gamma,t}[/math] at photon decoupling time: [math]\Gamma_{\gamma,t} = \sqrt{\frac{4 G N_{\gamma} \pi^3 (k_B T_{\gamma,t})^4}{45 \Omega_{\gamma,t} \hbar^3 c^5}} = \frac{2 (k_B T_{\gamma,t})^2}{3} \sqrt{\frac{G N_{\gamma} \pi^3}{5 \Omega_{\gamma,t} \hbar^3 c^5}} = 4.957 \cdot 10^{-14} \; \frac{ \gamma \; \text{particles}}{\text{s}}[/math] Observable Universe photon interaction rate at photon decoupling time: [math]\boxed{\Gamma_{\gamma,t} = \frac{2 (k_B T_{\gamma,t})^2}{3} \sqrt{\frac{G N_{\gamma} \pi^3}{5 \Omega_{\gamma,t} \hbar^3 c^5}}}[/math] Observable Universe photon interaction rate at photon decoupling time: [math]\boxed{\Gamma_{\gamma,t} = 4.957 \cdot 10^{-14} \; \frac{ \gamma \; \text{particles}}{\text{s}}}[/math] Solve for Observable Universe Dark Matter scalar particle interaction rate [math]\Gamma_{\phi,t}[/math] at scalar particle decoupling time: [math]\Gamma_{\phi,t} = \sqrt{\frac{4 G N_{\phi} \pi^3 (k_B T_{\phi,t})^4}{3 C_{\phi} \Omega_{\phi,t} \hbar^3 c^5}} = 2 (k_B T_{\phi,t})^2 \sqrt{\frac{G N_{\phi} \pi^3}{3 C_{\phi} \Omega_{\phi,t} \hbar^3 c^5}} = 39.232 \; \frac{ \phi \; \text{particles}}{\text{s}}[/math] Observable Universe Dark Matter scalar particle interaction rate at scalar particle decoupling time: [math]\boxed{\Gamma_{\phi,t} = 2 (k_B T_{\phi,t})^2 \sqrt{\frac{G N_{\phi} \pi^3}{3 C_{\phi} \Omega_{\phi,t} \hbar^3 c^5}}}[/math] Observable Universe Dark Matter scalar particle interaction rate at scalar particle decoupling time: [math]\boxed{\Gamma_{\phi,t} = 39.232 \; \frac{\phi \; \text{particles}}{\text{s}}}[/math] Solve for Observable Universe Dark Matter sterile neutrino interaction rate [math]\Gamma_{\nu,t}[/math] at sterile neutrino decoupling time: [math]\Gamma_{\nu,t} = \sqrt{\frac{4 G N_{\nu} \pi^3 (k_B T_{\nu,t})^4}{3 C_{\nu} \Omega_{\nu,t} \hbar^3 c^5}} = 2 (k_B T_{\nu,t})^2 \sqrt{\frac{G N_{\nu} \pi^3}{3 C_{\nu} \Omega_{\nu,t} \hbar^3 c^5}} = 2.689 \; \frac{ \nu \; \text{particles}}{\text{s}}[/math] Observable Universe Dark Matter sterile neutrino interaction rate at sterile neutrino decoupling time: [math]\boxed{\Gamma_{\nu,t} = 2 (k_B T_{\nu,t})^2 \sqrt{\frac{G N_{\nu} \pi^3}{3 C_{\nu} \Omega_{\nu,t} \hbar^3 c^5}}}[/math] Observable Universe Dark Matter sterile neutrino interaction rate at sterile neutrino decoupling time: [math]\boxed{\Gamma_{\nu,t} = 2.689 \; \frac{\nu \; \text{particles}}{\text{s}}}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: WMAP satellite cosmological parameters at photon decoupling time: (ref. 1) https://map.gsfc.nasa.gov/media/080998/index.html Wikipedia - neutrino decoupling: (ref. 2) https://en.wikipedia.org/wiki/Neutrino_decoupling Orion1 - Cosmic neutrino background radiation electron neutrino composition: (ref. 3) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry884367 Orion1 - Observable Universe neutrino background radiation massless neutrino decoupling time: (ref. 4) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry882631 Wikipedia - Derivation of decoupling time: (ref. 5) https://en.wikipedia.org/wiki/Neutrino_decoupling#Derivation_of_decoupling_time Wikipedia - Cross section (physics): (ref. 6) https://en.wikipedia.org/wiki/Cross_section_(physics)
  5. WMAP satellite cosmological parameters at photon decoupling time: (ref. 1) [math]\Omega_{dm , t} = 0.63[/math] [math]\Omega_{\Lambda , t} \neq 0[/math] Observable Universe Dark Matter scalar particle composition is equivalent to Dark Matter composition at photon decoupling time: [math]\boxed{\Omega_{\phi , t} = \Omega_{dm , t}}[/math] Observable Universe Dark Matter scalar particle mass: [math]\boxed{m_{\phi} \neq 0}[/math] Observable Universe Dark Matter scalar particle decoupling temperature is equivalent to cosmic neutrino background radiation neutrino decoupling temperature: (ref. 2) [math]\boxed{T_{\phi , t} = T_{\nu , t}} = 1 \cdot 10^{10} \; \text{K}[/math] Observable Universe Bose-Einstein Dark Matter scalar particle composition: (ref. 3) [math]\boxed{\Omega_{\phi} = \frac{4 G N_{\phi} \pi^3 (k_B T_{\phi})^4}{3 C_{\phi} H_0^2 \hbar^3 c^5}}[/math] Observable Universe Dark Matter scalar particle decoupling time: (ref. 4) [math]\boxed{T_{u , \phi} = \frac{1}{H_{\phi , t}}}[/math] Solve for Observable Universe Dark Matter scalar particle decoupling time [math]T_{u , \phi}[/math]: [math]T_{u , \phi} = \frac{1}{H_{\phi, t}} = \sqrt{\frac{3 \Omega_{\phi,t} C_{\phi} \hbar^3 c^5}{4 G N_{\phi} \pi^3 (k_B T_{\phi,t})^4}} = \frac{}{2 (k_B T_{\phi,t})^2} \sqrt{\frac{3 \Omega_{\phi,t} C_{\phi} \hbar^3 c^5}{G N_{\phi} \pi^3}} = 0.0255 \; \text{s}[/math] Observable Universe Dark Matter scalar particle decoupling time: [math]\boxed{T_{u , \phi} = \frac{}{2 (k_B T_{\phi,t})^2} \sqrt{\frac{3 \Omega_{\phi,t} C_{\phi} \hbar^3 c^5}{G N_{\phi} \pi^3}}}[/math] Observable Universe Dark Matter scalar particle decoupling time: [math]\boxed{T_{u, \phi} = 0.0255 \; \text{s}} \; \; \; m_{\phi} \neq 0[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: WMAP satellite cosmological parameters at photon decoupling time: (ref. 1) https://map.gsfc.nasa.gov/media/080998/index.html Wikipedia - neutrino decoupling: (ref. 2) https://en.wikipedia.org/wiki/Neutrino_decoupling Orion1 - Dark Matter scalar particle composition: (ref. 3) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry909539 Orion1 - Observable Universe neutrino background radiation massless neutrino decoupling time: (ref. 4) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry882631
  6. WMAP satellite cosmological parameters at photon decoupling time: (ref. 1) [math]\Omega_{\nu , t} = 0.10[/math] [math]\Omega_{\Lambda , t} \neq 0[/math] Neutrino mass: [math]\boxed{m_{\nu} \neq 0}[/math] Observable Universe cosmic neutrino background radiation neutrino decoupling temperature: (ref. 2) [math]T_{\nu , t} = 1 \cdot 10^{10} \; \text{K}[/math] Observable Universe Fermi-Dirac neutrino composition: (ref. 3),(ref. 4) [math]\boxed{\Omega_{\nu} = \frac{4 G N_{\nu} \pi^3 (k_B T_{\nu})^4}{3 C_{\nu} H_0^2 \hbar^3 c^5}}[/math] Observable Universe neutrino background radiation neutrino decoupling time: (ref. 5) [math]\boxed{T_{u , \nu} = \frac{1}{H_{\nu , t}}}[/math] Solve for Observable Universe neutrino decoupling time [math]T_{u , \nu}[/math]: [math]T_{u , \nu} = \frac{1}{H_{\nu , t}} = \sqrt{\frac{3 \Omega_{\nu,t} C_{\nu} \hbar^3 c^5}{4 G N_{\nu} \pi^3 (k_B T_{\nu,t})^4}} = \frac{}{2 (k_B T_{\nu,t})^2} \sqrt{\frac{3 \Omega_{\nu,t} C_{\nu} \hbar^3 c^5}{G N_{\nu} \pi^3}} = 0.148 \; \text{s}[/math] Observable Universe neutrino background radiation neutrino decoupling time: [math]\boxed{T_{u , \nu} = \frac{}{2 (k_B T_{\nu,t})^2} \sqrt{\frac{3 \Omega_{\nu,t} C_{\nu} \hbar^3 c^5}{G N_{\nu} \pi^3}}}[/math] Observable Universe neutrino background radiation neutrino decoupling time: [math]\boxed{T_{u , \nu} = 0.148 \; \text{s}}\; \; \; m_{\nu} \neq 0[/math] Observable Universe neutrino background radiation massless neutrino decoupling time: (ref. 5) [math]\boxed{T_{u , \nu} = 0.893 \; \text{s}} \; \; \; m_{\nu} = 0[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Orion1 - WMAP satellite cosmological parameters at photon decoupling time: (ref. 1) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry882631 Wikipedia - neutrino decoupling: (ref. 2) https://en.wikipedia.org/wiki/Neutrino_decoupling Orion1 - Cosmic neutrino background radiation electron neutrino composition: (ref. 3) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry884367 Orion1 - Fermi-Dirac and Bose-Einstein total neutrino distribution constant: (ref. 4) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry886860 Orion1 - Observable Universe neutrino background radiation massless neutrino decoupling time: (ref. 5) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry882631
  7. Observable Universe Cosmological Constant: (ref. 1), (ref. 2) [math]\Lambda_s = \frac{3 \Omega_{\Lambda} H_0^2}{c^2} = 1.180 \cdot 10^{-52} \; \text{m}^{-2}[/math] Observable Universe Bose-Einstein scalar particle Dark Energy composition: (ref. 3) [math]\boxed{\Omega_{\Lambda} = \frac{4 G N_{\Lambda} \pi^3 (k_B T_{\Lambda})^4}{45 H_0^2 \hbar^3 c^5}}[/math] Observable Universe scalar particle Dark Energy Cosmological Constant integration via substitution: [math]\Lambda_s = \frac{3 H_0^2}{c^2} \left( \frac{4 G N_{\Lambda} \pi^3 (k_B T_{\Lambda})^4}{45 H_0^2 \hbar^3 c^5} \right) = \frac{4 G N_{\Lambda} \pi^3 (k_B T_{\Lambda})^4}{15 \hbar^3 c^7} = 1.180 \cdot 10^{-52} \; \text{m}^{-2}[/math] Observable Universe scalar particle Dark Energy Cosmological Constant: [math]\boxed{\Lambda_s = \frac{4 G N_{\Lambda} \pi^3 (k_B T_{\Lambda})^4}{15 \hbar^3 c^7}}[/math] Observable Universe scalar particle Dark Energy Cosmological Constant: [math]\boxed{\Lambda_s = 1.180 \cdot 10^{-52} \; \text{m}^{-2}}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Wikipedia - Cosmological Constant: (ref. 1) http://en.wikipedia.org/wiki/Hubble%27s_law#Matter-dominated_universe_.28with_a_cosmological_constant.29 Orion1 - Cosmological Constant: (ref. 2) http://www.scienceforums.net/topic/86694-observable-universe-mass/#entry850783 Orion1 - Dark Energy: (ref. 3) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-3#entry931225
  8. [math]\begin{tabular}{l*{6}{c}r} & identity & state & spin & ns & Ns & Nn \\ b & scalar & 0 & 0 & 1 & 1 & 1 \\ f & neutrino & +,- & 1/2 & 2 & 3 & 3 \\ f & sterile neutrino & +,- & 1/2 & 2 & 3 & 3 \\ f & neutralino & +,- & 1/2 & 2 & 4 & 4 \\ b & photon & +,- & 1 & 2 & 1 & 2 \\ b & graviton & +,- & 2 & 2 & 1 & 2 \\ \end{tabular}[/math] Observable Universe composition Equation of State: [math]\Omega_{dm} + \Omega_{b} + \Omega_{\Lambda} = 1[/math] Observable Universe photon and neutrino and scalar particle Dark Energy composition Equation of State: [math]\boxed{\frac{4 G \pi^3 k_B^4}{3 H_0^2 \hbar^3 c^5} \left[ \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\nu}} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \frac{N_{\Lambda} T_{\Lambda}^4}{15} \right] = 1}[/math] Observable Universe scalar particle Dark Matter and scalar particle Dark Energy composition Equation of State: [math]\boxed{\frac{4 G \pi^3 k_B^4}{3 H_0^2 \hbar^3 c^5} \left[ \left( \frac{N_{\phi} T_{\phi}^4}{C_{\phi}} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\phi}} \right) + \frac{N_{\Lambda} T_{\Lambda}^4}{15} \right] = 1}[/math] Observable Universe sterile neutrino Dark Matter and scalar particle Dark Energy composition Equation of State: [math]\boxed{\frac{4 G \pi^3 k_B^4}{3 H_0^2 \hbar^3 c^5} \left[ \left( \frac{N_{\nu} T_{\nu}^4}{C_{\nu}} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\nu}} \right) + \frac{N_{\Lambda} T_{\Lambda}^4}{15} \right] = 1}[/math] Observable Universe total energy integration via substitution: [math]E_u = M_u c^2 = \frac{\pi^3 k_B^4}{12 (\hbar H_0)^3} \left[ \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\nu}} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \frac{N_{\Lambda} T_{\Lambda}^4}{15} \right] \left( \ln (1 + z) \right)^3 = 3.410 \cdot 10^{71} \; \text{j}[/math] Observable Universe total energy: [math]\boxed{E_u = \frac{\pi^3 k_B^4}{12 (\hbar H_0)^3} \left[ \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\nu}} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \frac{N_{\Lambda} T_{\Lambda}^4}{15} \right] \left( \ln (1 + z) \right)^3}[/math] Observable Universe total energy: [math]\boxed{E_u = 3.410 \cdot 10^{71} \; \text{j}}[/math] Any discussions and/or peer reviews about this specific topic thread?
  9. Photon particle mass: [math]\boxed{m_{\gamma} = 0}[/math] Neutrino particle mass: [math]\boxed{m_{\nu} \neq 0}[/math] Dark Energy scalar particle mass: [math]\boxed{m_{\Lambda} = 0}[/math] Dark Matter scalar particle mass: [math]\boxed{m_{\phi} \neq 0}[/math] Observable Universe Bose-Einstein photon composition: (ref. 1) [math]\boxed{\Omega_{\gamma} = \frac{4 G N_{\gamma} \pi^3 (k_B T_{\gamma})^4}{45 H_0^2 \hbar^3 c^5}}[/math] Observable Universe Fermi-Dirac neutrino composition: (ref. 2) [math]\boxed{\Omega_{\nu} = \frac{4 G N_{\nu} \pi^3 (k_B T_{\nu})^4}{3 C_{\nu} H_0^2 \hbar^3 c^5}}[/math] Observable Universe Bose-Einstein Dark Energy composition: (ref. 3) [math]\boxed{\Omega_{\Lambda} = \frac{4 G N_{\Lambda} \pi^3 (k_B T_{\Lambda})^4}{45 H_0^2 \hbar^3 c^5}}[/math] Observable Universe Bose-Einstein Dark Matter composition: (ref. 4) [math]\boxed{\Omega_{\phi} = \frac{4 G N_{\phi} \pi^3 (k_B T_{\phi})^4}{3 C_{\phi} H_0^2 \hbar^3 c^5}}[/math] Observable Universe compositional Equation of State: [math]\Omega_{dm} + \Omega_{b} + \Omega_{\Lambda} = 1[/math] Observable Universe compositional Equation of State: (ref. 5) [math]\boxed{\frac{4 G \pi^3 k_B^4}{3 H_0^2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\nu}} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \Omega_{\Lambda} = 1}[/math] Observable Universe compositional Equation of State integration via substitution: [math]\frac{4 G \pi^3 k_B^4}{3 H_0^2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\nu}} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \frac{4 G N_{\Lambda} \pi^3 (k_B T_{\Lambda})^4}{45 H_0^2 \hbar^3 c^5} = \frac{4 G \pi^3 k_B^4}{3 H_0^2 \hbar^3 c^5} \left[ \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\nu}} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \frac{N_{\Lambda} T_{\Lambda}^4}{15} \right] = 1[/math] Observable Universe compositional Equation of State: [math]\boxed{\frac{4 G \pi^3 k_B^4}{3 H_0^2 \hbar^3 c^5} \left[ \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\nu}} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \frac{N_{\Lambda} T_{\Lambda}^4}{15} \right] = 1}[/math] Observable Universe compositional Equation of State: (ref. 4) [math]\boxed{\frac{4 G \pi^3 k_B^4}{3 H_0^2 \hbar^3 c^5} \left[ \left( \frac{N_{\phi} T_{\phi}^4}{C_{\phi}} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\phi}} \right) + \frac{N_{\Lambda} T_{\Lambda}^4}{15} \right] = 1}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Orion1 - Cosmic Microwave Background Radiation photon composition: (ref. 1) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry882069 Orion1 - Cosmic neutrino background radiation electron neutrino composition: (ref. 2) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry884367 Orion1 - Dark Energy: (ref. 3) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-3#entry931225 Orion1 - Dark Matter scalar particle composition: (ref. 4) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry909539 Orion1 - Observable Universe compositional Equation of State: (ref. 5) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-3#entry980016
  10. Observable Universe Friedmann equations critical mass: (ref. 1) [math]M_c = \frac{H_0^2 R_u^3}{2 G} = \frac{H_0^2}{2 G} \left[ \left( \frac{c}{H_0} \right) \frac{\ln (1 + z)}{2} \right]^3 = \frac{[c \ln (1 + z)]^3}{16 G H_0} = 3.794 \cdot 10^{54} \; \text{kg}[/math] [math]\boxed{M_c = \frac{[c \ln (1 + z)]^3}{16 G H_0}}[/math] [math]\boxed{M_c = 3.794 \cdot 10^{54} \; \text{kg}}[/math] Observable Universe total mass: (ref. 2) [math]M_u = \rho_u V_u = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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 = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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 = 3.794 \cdot 10^{54} \; \text{kg}}[/math] Observable Universe Friedmann equations critical mass is equivalent to Observable Universe total mass: [math]\boxed{M_c = M_u}[/math] Observable Universe Friedmann equations critical mass is equivalent to Observable Universe total mass integration via substitution: [math]\frac{[c \ln (1 + z)]^3}{16 G H_0} = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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]\frac{8 \pi G}{3 H_0^2} \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\nu}} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right] = 1[/math] Observable Universe compositional Equation of State: [math]\boxed{\frac{4 G \pi^3 k_B^4}{3 H_0^2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\nu}} \right) \left( \frac{\Omega_{dm} + \Omega_{b}}{\Omega_{\gamma} + \Omega_{\nu}} \right) + \Omega_{\Lambda} = 1}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Orion1 - Friedmann equations critical mass: (ref. 1) http://www.scienceforums.net/topic/86694-observable-universe-mass/#entry850915 Orion1 - Observable Universe total mass: (ref. 2) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry909462
  11. A scalar particle is a boson with spin 0. A flavor of neutrinos such as neutralinos and sterile neutrinos are fermions with spin 1/2. However, the resulting mathematical modelling of physical radiation properties due to the differences in quantum spin properties are intrinsically built into this model as total effective degeneracy number . (ref. 1), (ref. 2) [math]\begin{tabular}{l*{6}{c}r} & identity & state & spin & ns & Ns & Nn \\ b & scalar & 0 & 0 & 1 & 1 & 1 \\ f & neutrino & +,- & 1/2 & 2 & 3 & 3 \\ f & sterile neutrino & +,- & 1/2 & 2 & 3 & 3 \\ f & neutralino & +,- & 1/2 & 2 & 4 & 4 \\ b & photon & +,- & 1 & 2 & 1 & 2 \\ b & graviton & +,- & 2 & 2 & 1 & 2 \\ \end{tabular}[/math] Symbolic identity key: [math]n_s[/math] - spin states total number [math]N_s[/math] - species total number [math]N_n[/math] - total effective degeneracy number If [math]n_s \geq N_s[/math] Then [math]N_n = n_s[/math] If [math]n_s \leq N_s[/math] Then [math]N_n = N_s[/math] Dark Energy scalar particle mass: [math]\boxed{m_{\Lambda} = 0}[/math] Dark Energy scalar particle mass total effective degeneracy number: [math]\boxed{N_{\Lambda} = 1}[/math] Planck satellite cosmological parameters: (ref. 3, pg. 11) [math]\Omega_{\Lambda} = 0.6825[/math] Planck satellite redshift parameter at photon decoupling time: (ref. 3, pg. 11) [math]z = 1090.43[/math] Dark Energy scalar particle radiation energy density Bose-Einstein distribution integration via substitution: [math]\epsilon_{\Lambda , 1} = \alpha_{\Lambda} T_{\Lambda}^4 = \frac{4 \pi N_{\Lambda} (k_B T_{\Lambda})^4}{( 2 \pi \hbar c )^3} \int_{0}^\infty \frac{E_t (\omega)^3}{e^{\frac{E_t (\omega)}{E_1 (T_{\Lambda})}} - 1} d \omega = \frac{4 \pi N_{\Lambda} (k_B T_{\Lambda})^4}{( 2 \pi \hbar c )^3} \left( \frac{\pi^4}{15} \right) = \frac{\pi^2 N_{\Lambda} (k_B T_{\Lambda})^4}{30 ( \hbar c )^3}[/math] Dark Energy scalar particle radiation energy density: [math]\boxed{\epsilon_{\Lambda , 1} = \frac{\pi^2 N_{\Lambda} (k_B T_{\Lambda})^4}{30 ( \hbar c )^3}}[/math] Dark Energy scalar particle radiation constant: [math]\boxed{\alpha_{\Lambda} = \frac{\pi^2 k_B^4 N_{\Lambda}}{30 ( \hbar c )^3}}[/math] Dark Energy scalar particle radiation composition energy density: (ref. 7) [math]\epsilon_{\Lambda , 2} = \rho_{\Lambda} c^2 = \frac{3 \Omega_{\Lambda} \left(c H_{0} \right)^2}{8 \pi G} = 5.685 \cdot 10^{-10} \; \frac{\text{j}}{\text{m}^3}[/math] Dark Energy scalar particle radiation composition energy density: [math]\boxed{\epsilon_{\Lambda , 2} = \frac{3 \Omega_{\Lambda} \left(c H_{0} \right)^2}{8 \pi G}}[/math] Dark Energy scalar particle radiation composition energy density: [math]\boxed{\epsilon_{\Lambda , 2} = 5.685 \cdot 10^{-10} \; \frac{\text{j}}{\text{m}^3}}[/math] Dark Energy scalar particle radiation energy density is equivalent to Dark Energy scalar radiation composition energy density: [math]\boxed{\epsilon_{\Lambda , 1} = \epsilon_{\Lambda , 2}}[/math] Dark Energy scalar particle radiation energy density is equivalent to Dark Energy scalar particle radiation composition energy density integration via substitution: [math]\frac{\pi^2 N_{\Lambda} (k_B T_{\Lambda})^4}{30 ( \hbar c )^3} = \frac{3 \Omega_{\Lambda} \left(c H_0 \right)^2}{8 \pi G}[/math] Solve for Dark Energy scalar particle radiation temperature: [math]T_{\Lambda}[/math] [math]T_{\Lambda}^4 = \frac{30 ( \hbar c )^3}{\pi^2 N_{\Lambda} k_B^4} \left( \frac{3 \Omega_{\Lambda} \left(c H_0 \right)^2}{8 \pi G} \right) = \frac{45 \Omega_{\Lambda} H_0^2 \hbar^3 c^5}{4 G N_{\Lambda} \pi^3 k_{B}^4}[/math] [math]T_{\Lambda}^4 = \frac{45 \Omega_{\Lambda} H_0^2 \hbar^3 c^5}{4 G N_{\Lambda} \pi^3 k_{B}^4}[/math] Dark Energy scalar particle radiation temperature: [math]\boxed{T_{\Lambda} = \left( \frac{45 \Omega_{\Lambda} H_0^2 \hbar^3 c^5}{4 G N_{\Lambda} \pi^3 k_{B}^4} \right)^{1/4}}[/math] Dark Energy scalar particle radiation temperature: [math]\boxed{T_{\Lambda} = 35.013 \; \text{K}}[/math] Observable Universe total Dark Energy scalar particle number: (ref. 5, eq. 7) [math]\boxed{N_{\Lambda t} = \frac{\zeta (3) N_{\Lambda}}{6 \pi} \left( \frac{k_B T_{\Lambda} \ln (1 + z)}{\hbar H_0} \right)^3}[/math] Observable Universe total Dark Energy scalar particle number: (ref. 5, eq. 7) [math]\boxed{N_{\Lambda t} = 1.782 \cdot 10^{92} \; \Lambda \; \text{particles}}[/math] Dark Energy scalar particle peak energy: [math]E_{\Lambda} = k_B T_{\Lambda}[/math] Dark Energy scalar particle peak frequency: [math]E_{\Lambda} = 2 \pi \hbar f_{\Lambda} = k_B T_{\Lambda}[/math] Dark Energy scalar particle peak frequency integration via substitution: [math]f_{\Lambda} = \frac{k_B T_{\Lambda}}{2 \pi \hbar} = \frac{k_B}{2 \pi \hbar} \left( \frac{45 \Omega_{\Lambda} H_0^2 \hbar^3 c^5}{4 G N_{\Lambda} \pi^3 k_B^4} \right)^{1/4} = \left( \frac{45 \Omega_{\Lambda} c^5}{64 \hbar G N_{\Lambda} \pi^7} \right)^{1/4}[/math] Dark Energy scalar particle peak T-ray frequency: (ref. 6) [math]\boxed{f_{\Lambda} = \left( \frac{45 \Omega_{\Lambda} c^5}{64 \hbar G N_{\Lambda} \pi^7} \right)^{1/4}}[/math] Dark Energy scalar particle peak terahertz radiation T-ray frequency: (ref. 6) [math]\boxed{f_{\Lambda} = 7.295 \cdot 10^{11} \; \text{Hz}}[/math] [math]f_{\Lambda} = 7.295 \cdot 10^{11} \; \text{Hz} = 0.729 \; \text{THz}[/math] Dark Energy scalar particle peak terahertz radiation T-ray frequency: (ref. 6) [math]\boxed{f_{\Lambda} = 0.729 \; \text{THz}}[/math] Dark Energy scalar particle peak energy: [math]\boxed{E_{\Lambda} = 4.834 \cdot 10^{-22} \; \text{j}}[/math] Dark Energy scalar particle peak energy: [math]\boxed{E_{\Lambda} = 3.018 \; \frac{\text{mV}}{c^2}}[/math] What are the possibilities for a terahertz antenna or a terahertz receiver tuned to the Dark Energy scalar particle peak terahertz frequency of being capable of detecting Dark Energy scalar particle terahertz T-ray radiation? What are the possibilities of terahertz radiation T-ray astronomy? Any discussions and/or peer reviews about this specific topic thread? Reference: Wikipedia - Scalar boson (ref. 1) https://en.wikipedia...ki/Scalar_boson Wikipedia - Fermion (ref. 2) https://en.wikipedia.org/wiki/Fermion Planck 2013 results. XVI. Cosmological parameters: (ref. 3) http://planck.caltech.edu/pub/2013results/Planck_2013_results_16.pdf Wikipedia - Dark energy: (ref. 4) https://en.wikipedia.org/wiki/Dark_energy Introduction to Cosmology: Lecture 6 - Thermal history of the Universe - Joao G. Rosa (ref. 5) http://gravitation.web.ua.pt/sites/gravitation.web.ua.pt/files/Lecture_6.pdf Wikipedia - Terahertz radiation: (ref. 6) https://en.wikipedia.org/wiki/Terahertz_radiation Orion1 - Dark Energy mass density: (ref. 7) http://www.scienceforums.net/topic/86694-observable-universe-mass/#entry850783
  12. Observable Universe electron neutrino mass: [math]m_{\nu_e} = \frac{\Omega_{\nu} M_u}{N_{\nu t}} = 6.839 \cdot 10^{-38} \; \text{kg}[/math] [math]\boxed{m_{\nu_e} = \frac{\Omega_{\nu} M_u}{N_{\nu t}}}[/math] [math]\boxed{m_{\nu_e} = 6.839 \cdot 10^{-38} \; \text{kg}}[/math] Observable Universe dark matter scalar particle mass: [math]m_{\phi} = \frac{\Omega_{\phi} M_u}{N_{\phi t}} = 3.326 \cdot 10^{-35} \; \text{kg}[/math] [math]\boxed{m_{\phi} = \frac{\Omega_{\phi} M_u}{N_{\phi t}}}[/math] [math]\boxed{m_{\phi} = 3.326 \cdot 10^{-35} \; \text{kg}}[/math] Observable Universe dark matter sterile neutrino mass: [math]m_{\nu} = \frac{\Omega_{dm} M_u}{N_{\nu t}} = 1.456 \cdot 10^{-35} \; \text{kg}[/math] [math]\boxed{m_{\nu} = \frac{\Omega_{dm} M_u}{N_{\nu t}}}[/math] [math]\boxed{m_{\nu} = 1.456 \cdot 10^{-35} \; \text{kg}}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Wikipedia - Cosmic neutrino background radiation: (ref. 1) https://en.wikipedia.org/wiki/Cosmic_neutrino_background Wikipedia - Scalar field dark matter: (ref. 2) https://en.wikipedia.org/wiki/Scalar_field_dark_matter Wikipedia - Sterile neutrino: (ref. 3) https://en.wikipedia.org/wiki/Sterile_neutrino
  13. A scalar particle is a boson with spin 0. A flavor of neutrinos such as neutralinos and sterile neutrinos are fermions with spin 1/2. However, the resulting mathematical modelling of physical radiation properties due to the differences in quantum spin properties are intrinsically built into this model as total effective degeneracy number [math]N_n[/math]. (ref. 1), (ref. 2) [math]\begin{tabular}{l*{6}{c}r} bosons (b) = integer spin & Bose-Einstein statistics \\ fermions (f) = half-integer spin & Fermi-Dirac statistics \\ \end{tabular}[/math] [math]\begin{tabular}{l*{6}{c}r} & identity & state & spin & ns & Ns & Nn \\ b & scalar & 0 & 0 & 1 & 1 & 1 \\ f & neutrino & +,- & 1/2 & 2 & 3 & 3 \\ f & sterile neutrino & +,- & 1/2 & 2 & 3 & 3 \\ f & neutralino & +,- & 1/2 & 2 & 4 & 4 \\ b & photon & +,- & 1 & 2 & 1 & 2 \\ b & graviton & +,- & 2 & 2 & 1 & 2 \\ \end{tabular}[/math] Symbolic identity key: [math]n_s[/math] - spin states total number [math]N_s[/math] - species total number [math]N_n[/math] - total effective degeneracy number If [math]n_s \geq N_s[/math] Then [math]N_n = n_s[/math] If [math]n_s \leq N_s[/math] Then [math]N_n = N_s[/math] Note that if each neutrino species has a corresponding supersymmetric sterile neutrino species, then [math]\boxed{N_n = N_s = 3}[/math]. Neutralinos and sterile neutrinos are hypothetical particles. (ref. 3), (ref. 4) The mass spectrum range for neutralinos is 10 GeV to 1 TeV. (ref. 3) The mass spectrum range for sterile neutrinos is 1 eV to 10^15 GeV. (ref. 4) These particles are theoretically embedded into SO(10) MSSM models. (ref. 5), (ref. 6), (ref. 11) Observable Universe baryonic Hydrogen composition: [math]\Omega_{\text{H}} = 0.75[/math] Observable Universe baryonic Helium composition: [math]\Omega_{\text{He}} = 0.25[/math] Observable Universe total Hydrogen particle number: [math]N_{\text{H}} = \Omega_b \Omega_{\text{H}} \left( \frac{M_u}{m_{\text{H}}} \right) = 8.417 \cdot 10^{79} \; \text{H particles}[/math] [math]\boxed{N_{\text{H}} = \Omega_b \Omega_{\text{H}} \left( \frac{M_u}{m_{\text{H}}} \right)}[/math] [math]\boxed{N_{\text{H}} = 8.417 \cdot 10^{79} \; \text{H particles}}[/math] Observable Universe total Helium particle number: [math]N_{\text{He}} = \Omega_b \Omega_{\text{He}} \left( \frac{M_u}{m_{\text{He}}} \right) = 7.065 \cdot 10^{78} \; \text{He particles}[/math] [math]\boxed{N_{\text{He}} = \Omega_b \Omega_{\text{He}} \left( \frac{M_u}{m_{\text{He}}} \right)}[/math] [math]\boxed{N_{\text{He}} = 7.065 \cdot 10^{78} \; \text{He particles}}[/math] Observable Universe total proton particle number: [math]N_{pt} = N_{\text{H}} + 2N_{\text{He}} = 9.830 \cdot 10^{79} \; \text{p particles}[/math] [math]\boxed{N_{pt} = N_{\text{H}} + 2N_{\text{He}}}[/math] [math]\boxed{N_{pt} = 9.830 \cdot 10^{79} \; \text{p particles}}[/math] Observable Universe total neutron particle number: [math]N_{nt} = 2N_{\text{He}} = 1.413 \cdot 10^{79} \; \text{n particles}[/math] [math]\boxed{N_{nt} = 1.413 \cdot 10^{79} \; \text{n particles}}[/math] Observable Universe total electron particle number: [math]N_{\beta} = N_{\text{H}} + 2 N_{\text{He}} = 9.830 \cdot 10^{79} \; \beta \; \text{particles}[/math] [math]\boxed{N_{\beta t} = N_{\text{H}} + 2 N_{\text{He}}}[/math] [math]\boxed{N_{\beta t} = 9.830 \cdot 10^{79} \; \beta \; \text{particles}}[/math] Observable Universe total up quark particle number: [math]N_{u t} = 2 N_{\text{H}} + 6 N_{\text{He}} = 2.107 \cdot 10^{80} \; \text{u quark particles}[/math] [math]\boxed{N_{u t} = 2.107 \cdot 10^{80} \; \text{u quark particles}}[/math] Observable Universe total down quark particle number: [math]N_{d t} = N_{\text{H}} + 6 N_{\text{He}} = 1.266 \cdot 10^{80} \; \text{d quark particles}[/math] [math]\boxed{N_{d t} = 1.266 \cdot 10^{80} \; \text{d quark particles}}[/math] Observable Universe total photon particle number: (ref. 13, eq. 7) [math]N_{\gamma t} = n_{\gamma} V_u = \left( \frac{\zeta (3) N_{\gamma} (k_{B} T_{\gamma} )^3}{\pi^2 (\hbar c)^3} \right) \left[ \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_{0}} \right)^3 \right] = \frac{\zeta (3) N_{\gamma}}{6 \pi} \left( \frac{k_B T_{\gamma} \ln (1 + z)}{\hbar H_0} \right)^3 = 1.682 \cdot 10^{89} \; \gamma \; \text{particles}[/math] [math]\boxed{N_{\gamma t} = \frac{\zeta (3) N_{\gamma}}{6 \pi} \left( \frac{k_B T_{\gamma} \ln (1 + z)}{\hbar H_0} \right)^3}[/math] [math]\boxed{N_{\gamma t} = 1.682 \cdot 10^{89} \; \gamma \; \text{particles}}[/math] Observable Universe total neutrino particle number: (ref. 13, eq. 8) [math]N_{\nu t} = n_{\nu} V_u = \left( \frac{3 \zeta (3) N_{\nu} (k_{B} T_{\nu} )^3}{4 \pi^2 (\hbar c)^3} \right) \left[ \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_{0}} \right)^3 \right] = \frac{\zeta (3) N_{\nu}}{8 \pi} \left( \frac{k_B T_{\nu} \ln (1 + z)}{\hbar H_0} \right)^3 = 6.984 \cdot 10^{88} \; \nu \; \text{particles}[/math] [math]\boxed{N_{\nu t} = \frac{\zeta (3) N_{\nu}}{8 \pi} \left( \frac{k_B T_{\nu} \ln (1 + z)}{\hbar H_0} \right)^3}[/math] [math]\boxed{N_{\nu t} = 6.984 \cdot 10^{88} \; \nu \; \text{particles}}[/math] Observable Universe total dark matter scalar particle number: (ref. 13, eq. 7) [math]N_{\phi t} = n_{\phi} V_u = \left( \frac{\zeta (3) N_{\phi} (k_{B} T_{\phi} )^3}{\pi^2 (\hbar c)^3} \right) \left[ \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_{0}} \right)^3 \right] = \frac{\zeta (3) N_{\phi}}{6 \pi} \left( \frac{k_B T_{\phi} \ln (1 + z)}{\hbar H_0} \right)^3 = 3.057 \cdot 10^{88} \; \phi \; \text{particles}[/math] [math]\boxed{N_{\phi t} = \frac{\zeta (3) N_{\phi}}{6 \pi} \left( \frac{k_B T_{\phi} \ln (1 + z)}{\hbar H_0} \right)^3}[/math] [math]\boxed{N_{\phi t} = 3.057 \cdot 10^{88} \; \phi \; \text{particles}}[/math] Observable Universe total dark matter sterile neutrino particle number: (ref. 13, eq. 8) [math]N_{\nu t} = n_{\nu} V_u = \left( \frac{3 \zeta (3) N_{\nu} (k_{B} T_{\nu} )^3}{4 \pi^2 (\hbar c)^3} \right) \left[ \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_{0}} \right)^3 \right] = \frac{\zeta (3) N_{\nu}}{8 \pi} \left( \frac{k_B T_{\nu} \ln (1 + z)}{\hbar H_0} \right)^3 = 6.984 \cdot 10^{88} \; \nu \; \text{particles}[/math] [math]\boxed{N_{\nu t} = \frac{\zeta (3) N_{\nu}}{8 \pi} \left( \frac{k_B T_{\nu} \ln (1 + z)}{\hbar H_0} \right)^3}[/math] [math]\boxed{N_{\nu t} = 6.984 \cdot 10^{88} \; \nu \; \text{particles}}[/math] Observable Universe dark matter scalar particle total fundamental particle number: [math]N_t = (N_{ut} + N_{dt} + N_{\beta t} + N_{\gamma t} + N_{\nu t} + N_{\phi t}) = 2.686 \cdot 10^{89} \; \text{particles}[/math] [math]\boxed{N_t = (N_{ut} + N_{dt} + N_{\beta t} + N_{\gamma t} + N_{\nu t} + N_{\phi t})}[/math] [math]\boxed{N_t = 2.686 \cdot 10^{89} \; \text{particles}}[/math] Observable Universe dark matter sterile neutrino particle total fundamental particle number: [math]N_t = (N_{ut} + N_{dt} + N_{\beta t} + N_{\gamma t} + N_{\nu t} + N_{\nu t}) = 3.078 \cdot 10^{89} \; \text{particles}[/math] [math]\boxed{N_t = (N_{ut} + N_{dt} + N_{\beta t} + N_{\gamma t} + N_{\nu t} + N_{\nu t})}[/math] [math]\boxed{N_t = 3.078 \cdot 10^{89} \; \text{particles}}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Wikipedia - Scalar boson (ref. 1) https://en.wikipedia.org/wiki/Scalar_boson Wikipedia - Fermion (ref. 2) https://en.wikipedia.org/wiki/Fermion Wikipedia - Neutralino - Origins in supersymmetric theories (ref. 3) https://en.wikipedia.org/wiki/Neutralino#Origins_in_supersymmetric_theories Wikipedia - Sterile neutrinos (ref. 4) https://en.wikipedia.org/wiki/Sterile_neutrino Wikipedia - Standard Model - Total particle count (ref. 5) https://en.wikipedia.org/wiki/Standard_Model#Total_particle_count Wikipedia - SO[10] (ref. 6) https://en.wikipedia.org/wiki/SO%2810%29 CERN - Next decade of sterile neutrino studies (ref. 7) http://arxiv.org/pdf/1306.4954v1.pdf Wikipedia - Dark matter (ref. 8) https://en.wikipedia.org/wiki/Dark_matter PHYS: 652 Cosmic Inventory I: Radiation (ref. 9) http://www.nicadd.niu.edu/~bterzic/PHYS652/Lecture_09.pdf Formaggio - Relic Neutrinos - Institute for Nuclear Theory (ref. 10) http://www.int.washington.edu/talks/WorkShops/int_10_44W/People/Formaggio_J/Formaggio.pdf WIkipedia - Minimal supersymmetric standard model - dark matter (ref. 11) https://en.wikipedia.org/wiki/Minimal_Supersymmetric_Standard_Model#Dark_matter Orion1 - Dark matter scalar particle radiation energy density Bose-Einstein distribution (ref. 12) http://www.scienceforums.net/topic/90189-neutrino-mass-from-fermi-dirac-statistics/?p=887017 Introduction to Cosmology: Lecture 6 - Thermal history of the Universe - Joao G. Rosa (ref. 13) http://gravitation.web.ua.pt/sites/gravitation.web.ua.pt/files/Lecture_6.pdf
  14. WMAP satellite cosmological parameters at photon decoupling time: (ref. 1) [math]\Omega_{dm} = 0.63[/math] [math]\Omega_{b} = 0.12[/math] [math]\Omega_{\gamma} = 0.15[/math] [math]\Omega_{\nu} = 0.10[/math] [math]\Omega_{\Lambda} \neq 0[/math] Planck satellite redshift parameter at photon decoupling time: (ref. 2, pg. 11) [math]z = 1090.43[/math] Cosmology scale factor: [math]\boxed{\frac{R_u(t_0)}{R_u(t)} = \frac{a(t_0)}{a(t)} = \frac{T_t}{T_0} = 1 + z}[/math] Symbolic definition key: [math]R_u(t_0)[/math] - Observable Universe total radius at present time. [math]R_u(t)[/math] - Observable Universe total radius at past time. [math]a(t_0)[/math] - scale factor at present time. [math]a(t)[/math] - scale factor at past time. [math]T_t[/math] - cosmic background radiation temperature at past time. [math]T_0[/math] - cosmic background radiation temperature at present time. [math]z[/math] - redshift at photon decoupling time. Observable Universe total co-moving radius at present time: (ref. 3) [math]\boxed{R_u(t_0) = \frac{c \ln (1 + z)}{2 H_0}}[/math] Observable Universe total radius at photon decoupling time: [math]R_u(t) = \frac{R_u(t_0)}{1 + z} = \frac{c \ln (1 + z)}{2 H_0 (1 + z)} = 4.220 \cdot 10^{23} \; \text{m}[/math] [math]\boxed{R_u(t) = \frac{c \ln (1 + z)}{2 H_0 (1 + z)}}[/math] [math]\boxed{R_u(t) = 4.220 \cdot 10^{23} \; \text{m}} \; \; \; 4.461 \cdot 10^{7} \; \text{ly}[/math] Observable Universe photon cosmic background radiation temperature at photon decoupling time: [math]T_{\gamma , t} = T_{\gamma} (1 + z) = 2974.67 \; \text{K}[/math] [math]\boxed{T_{\gamma , t} = 2974.67 \; \text{K}}[/math] Observable Universe neutrino cosmic background radiation temperature at photon decoupling time: [math]T_{\nu , t} = T_{\nu} (1 + z) = 2123.22 \; \text{K}[/math] [math]\boxed{T_{\nu , t} = 2123.22 \; \text{K}}[/math] Observable Universe total mass at photon decoupling time: [math]\boxed{M_u = \frac{4 \pi}{3} \left( \frac{c \ln (1 + z)}{2 H_0 (1 + z)} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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 at photon decoupling time: [math]\boxed{M_u = 1.245 \cdot 10^{54} \; \text{kg}}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: WMAP satellite content of the Universe: (ref. 1) http://map.gsfc.nasa.gov/media/080998/index.html Planck 2013 results. XVI. Cosmological parameters: (ref. 2) http://planck.caltech.edu/pub/2013results/Planck_2013_results_16.pdf UCLA Division of Astronomy and Astrophysics - Homogeneity and Isotropy: (ref. 3) http://www.astro.ucla.edu/~wright/cosmo_02.htm#DL Orion1 - Friedmann equations critical mass: (ref. 4) http://www.scienceforums.net/topic/86694-observable-universe-mass/#entry850915
  15. Sterile neutrinos and neutralinos are potential dark matter candidates. However, scalar particles are also dark matter candidates. (ref. 1) Scalar particles are only the first particles on that quantum spin list to model as dark matter. Reference: Wikipedia - Scalar field dark matter (ref. 1) https://en.wikipedia.org/wiki/Scalar_field_dark_matter
  16. Negative, a scalar particle is a boson with spin 0. A flavor of neutrinos such as neutralinos and sterile neutrinos are fermions with spin 1/2. However, the resulting mathematical modelling of physical radiation properties due to the differences in quantum spin properties are intrinsically built into this model as total effective degeneracy number [math]N_n[/math]. (ref. 1), (ref. 2) [math]\begin{tabular}{l*{6}{c}r} bosons (b) = integer spin & Bose-Einstein statistics \\ fermions (f) = half-integer spin & Fermi-Dirac statistics \\ \end{tabular}[/math] [math]\begin{tabular}{l*{6}{c}r} & identity & state & spin & ns & Ns & Nn \\ b & scalar & 0 & 0 & 1 & 1 & 1 \\ f & neutrino & +,- & 1/2 & 2 & 3 & 3 \\ f & sterile neutrino & +,- & 1/2 & 2 & 3 & 3 \\ f & neutralino & +,- & 1/2 & 2 & 4 & 4 \\ b & photon & +,- & 1 & 2 & 1 & 2 \\ b & graviton & +,- & 2 & 2 & 1 & 2 \\ \end{tabular}[/math] Symbolic identity key: [math]n_s[/math] - spin states total number [math]N_s[/math] - species total number [math]N_n[/math] - total effective degeneracy number If [math]n_s \geq N_s[/math] Then [math]N_n = n_s[/math] If [math]n_s \leq N_s[/math] Then [math]N_n = N_s[/math] Note that if each neutrino species has a corresponding supersymmetric sterile neutrino species, then [math]\boxed{N_n = N_s = 3}[/math]. Neutralinos and sterile neutrinos are hypothetical particles. (ref. 3), (ref. 4) The mass spectrum range for neutralinos is 10 GeV to 1 TeV. (ref. 3) The mass spectrum range for sterile neutrinos is 1 eV to 10^15 GeV. (ref. 4) Affirmative, theses particles are theoretically embedded into SO(10) MSSM models. (ref. 5), (ref. 6), (ref. 11) See PHYS: 652 Cosmic Inventory I: Radiation (ref. 9) and Formaggio - Relic Neutrinos - Institute for Nuclear Theory (ref. 10) and Orion1 - Dark matter scalar particle radiation energy density Bose-Einstein distribution (ref. 12) and Orion1 - Photon radiation energy density Bose-Einstein distribution (ref. 13) in Reference. Do you have a citation reference link for the equation derivation for that number? Reference: Wikipedia - Scalar boson (ref. 1) https://en.wikipedia.org/wiki/Scalar_boson Wikipedia - Fermion (ref. 2) https://en.wikipedia.org/wiki/Fermion Wikipedia - Neutralino - Origins in supersymmetric theories (ref. 3) https://en.wikipedia.org/wiki/Neutralino#Origins_in_supersymmetric_theories Wikipedia - Sterile neutrinos (ref. 4) https://en.wikipedia.org/wiki/Sterile_neutrino Wikipedia - Standard Model - Total particle count (ref. 5) https://en.wikipedia.org/wiki/Standard_Model#Total_particle_count Wikipedia - SO[10] (ref. 6) https://en.wikipedia.org/wiki/SO%2810%29 CERN - Next decade of sterile neutrino studies (ref. 7) http://arxiv.org/pdf/1306.4954v1.pdf Wikipedia - Dark matter (ref. 8) https://en.wikipedia.org/wiki/Dark_matter PHYS: 652 Cosmic Inventory I: Radiation (ref. 9) http://www.nicadd.niu.edu/~bterzic/PHYS652/Lecture_09.pdf Formaggio - Relic Neutrinos - Institute for Nuclear Theory (ref. 10) http://www.int.washington.edu/talks/WorkShops/int_10_44W/People/Formaggio_J/Formaggio.pdf WIkipedia - Minimal supersymmetric standard model - dark matter (ref. 11) https://en.wikipedia.org/wiki/Minimal_Supersymmetric_Standard_Model#Dark_matter Orion1 - Dark matter scalar particle radiation energy density Bose-Einstein distribution (ref. 12) http://www.scienceforums.net/topic/90189-neutrino-mass-from-fermi-dirac-statistics/?p=887017 Orion1 - Photon radiation energy density Bose-Einstein distribution (ref. 13) http://www.scienceforums.net/topic/86694-observable-universe-mass/?p=884367
  17. Planck satellite cosmological parameters: (ref. 1, pg. 11) [math]\Omega_{dm} = 0.268[/math] Dark matter scalar particle composition is equivalent to dark matter composition: [math]\boxed{\Omega_{\phi} = \Omega_{dm}}[/math] Dark matter scalar particle species total effective degeneracy number: (ref. 2) [math]\boxed{N_{\phi} = 1}[/math] Dark matter scalar particle radiation temperature is equivalent to neutrino cosmic background radiation temperature: [math]\boxed{T_{\phi} = T_{\nu}}[/math] Bose-Einstein total dark matter scalar particle distribution constant: (ref. 3) [math]C_{\phi} = \frac{4 \pi^3 G N_{\phi} (k_B T_{\phi})^4}{3 \Omega_{\phi} H_0^2 \hbar^3 c^5} = 3.640 \cdot 10^{-4}[/math] [math]\boxed{C_{\phi} = \frac{4 \pi^3 G N_{\phi} (k_B T_{\phi})^4}{3 \Omega_{\phi} H_0^2 \hbar^3 c^5}}[/math] [math]\boxed{C_{\phi} = 3.640 \cdot 10^{-4}}[/math] Observable Universe total mass: [math]M_u = \rho_u V_u = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\phi} T_{\phi}^4}{C_{\phi}} \right) \left( \frac{\Omega_{\phi} + \Omega_{b}}{\Omega_{\phi}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right][/math] [math]\boxed{M_u = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\phi} T_{\phi}^4}{C_{\phi}} \right) \left( \frac{\Omega_{\phi} + \Omega_{b}}{\Omega_{\phi}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right]}[/math] [math]\boxed{M_u = 3.794 \cdot 10^{54} \; \text{kg}}[/math] Solve for dark matter scalar particle rest mass with highest relative maximum at critical mass number: (ref. 3) [math]\frac{d}{dm} I_{\phi} (m_{\phi}) = 0[/math] Dark matter scalar particle rest mass: [math]\boxed{m_{\phi} = 6.586 \cdot 10^{-40} \; \text{kg}} \; \; \; T_{\phi} = T_{\nu}[/math] Observable Universe total dark matter scalar particle number: [math]N_{\phi} = \Omega_{\phi} \left( \frac{M_u}{m_{\phi}} \right) = \frac{\pi \Omega_{\phi}}{6 m_{\phi}} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\phi} T_{\phi}^4}{C_{\phi}} \right) \left( \frac{\Omega_{\phi} + \Omega_{b}}{\Omega_{\phi}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right][/math] [math]\boxed{N_{\phi} = \frac{\pi \Omega_{\phi}}{6 m_{\phi}} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\phi} T_{\phi}^4}{C_{\phi}} \right) \left( \frac{\Omega_{\phi} + \Omega_{b}}{\Omega_{\phi}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right]}[/math] [math]\boxed{N_{\phi} = 1.544 \cdot 10^{93} \; \phi \; \text{particles}}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Planck 2013 results. XVI. Cosmological parameters: (ref. 1) http://planck.caltech.edu/pub/2013results/Planck_2013_results_16.pdf Orion 1 - total effective degeneracy number: (ref. 2) http://www.scienceforums.net/topic/90189-neutrino-mass-from-fermi-dirac-statistics/#entry879233 Orion1 - dark matter scalar particle composition: (ref. 3) http://www.scienceforums.net/topic/90189-neutrino-mass-from-fermi-dirac-statistics/#entry887017 Dark matter - Wikipedia https://en.wikipedia.org/wiki/Dark_matter
  18. Planck satellite cosmological parameters: (ref. 1, pg. 11) [math]\Omega_{\Lambda} = 0.6825[/math] [math]\Omega_{dm} = 0.268[/math] [math]\Omega_{b} = 0.0495[/math] [math]\Omega_s = 2.460 \cdot 10^{-3}[/math] (ref. 2, pg. 3) [math]\Omega_{\nu} = 1.258 \cdot 10^{-3}[/math] (ref. 2, pg. 3) [math]\Omega_{\gamma} = 5.012 \cdot 10^{-5}[/math] (ref. 2, pg. 3) Neutrino particle mass: [math]\boxed{m_{\nu} \neq 0}[/math] Photon particle mass: [math]\boxed{m_{\gamma} = 0}[/math] Hubble radius: (ref. 3) [math]R_h = \frac{c}{H_0}[/math] Planck satellite redshift parameter at photon decoupling time: (ref. 4, pg. 11) [math]z = \left( \frac{T_{\gamma , t}}{T_{\gamma}} \right) - 1 = 1090.43[/math] Observable Universe total co-moving radius: (ref. 5) [math]R_u = R_h \left( \frac{\ln{(1 + z)}}{2} \right) = \left( \frac{c}{H_0} \right) \frac{\ln (1 + z)}{2} = \frac{c \ln (1 + z)}{2 H_0} = 4.606 \cdot 10^{26} \; \text{m}[/math] [math]\boxed{R_u = \frac{c \ln (1 + z)}{2 H_0}}[/math] [math]\boxed{R_u = 4.606 \cdot 10^{26} \; \text{m}} \; \; \; (48.689 \cdot 10^{9} \; \text{ly})[/math] Friedmann equations critical mass: (ref. 6) [math]M_c = \frac{H_0^2 R_u^3}{2 G} = \frac{H_0^2}{2 G} \left[ \left( \frac{c}{H_0} \right) \frac{\ln (1 + z)}{2} \right]^3 = \left( \frac{c^3}{16 G H_0} \right) [\ln (1 + z)]^3 = 3.794 \cdot 10^{54} \; \text{kg}[/math] [math]\boxed{M_c = \left( \frac{c^3}{16 G H_0} \right) [\ln (1 + z)]^3}[/math] [math]\boxed{M_c = 3.794 \cdot 10^{54} \; \text{kg}}[/math] Fermi-Dirac and Bose-Einstein total neutrino distribution constant: (ref. 7) [math]C_{\nu} = \frac{4 \pi^3 G N_{\nu} (k_B T_{\nu})^4}{3 \Omega_{\nu} H_0^2 \hbar^3 c^5} = 0.236[/math] [math]\boxed{C_{\nu} = \frac{4 \pi^3 G N_{\nu} (k_B T_{\nu})^4}{3 \Omega_{\nu} H_0^2 \hbar^3 c^5}}[/math] [math]\boxed{C_{\nu} = 0.236}[/math] Observable Universe total co-moving volume: [math]V_u = \frac{4 \pi R_u^3}{3} = \frac{4 \pi}{3} \left( \frac{c \ln (1 + z)}{2 H_0} \right)^3 = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 = 4.094 \cdot 10^{80} \; \text{m}^3[/math] [math]\boxed{V_u = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3}[/math] [math]\boxed{V_u = 4.094 \cdot 10^{80} \; \text{m}^3} \; \; \; (1.154 \cdot 10^{32} \; \text{ly}^3)[/math] Observable Universe total mass: [math]M_u = \rho_u V_u = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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 = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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 = 3.794 \cdot 10^{54} \; \text{kg}}[/math] Milky Way galaxy mass: (ref. 8, pg. 1) [math]M_{mw} = 1.26 \cdot 10^{12} \cdot M_{\odot} = 2.506 \cdot 10^{42} \; \text{kg}[/math] [math]\boxed{M_{mw} = 2.506 \cdot 10^{42} \; \text{kg}}[/math] Observable Universe total galaxy number: (ref. 9) [math]N_g = \Omega_{b} \left( \frac{M_u}{M_{mw}} \right) = \frac{\pi \Omega_{b}}{6 M_{mw}} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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{N_g = \frac{\pi \Omega_{b}}{6 M_{mw}} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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{N_g = 7.496 \cdot 10^{10} \; \text{galaxies}}[/math] Stellar class number parameters: (ref. 12) [math]n_c = 1 \rightarrow 7[/math] key:1 O, 2 B, 3 A, 4 F, 5 G, 6 K, 7 M [math]\Omega_n[/math] - main sequence stars stellar class fraction [math]N_s[/math] - total observable stellar number [math]M_n[/math] - Main-sequence mass Observable Universe average stellar mass: [math]M_a = \frac{1}{N_s} \sum_{n_c = 1}^{7} (\Omega_n N_s M_n) = \sum_{n_c = 1}^{7} \Omega_n M_n = 0.595 \cdot M_{\odot} \rightarrow 0.769 \cdot M_{\odot}[/math] [math]\boxed{M_a = \sum_{n_c = 1}^{7} \Omega_n M_n}[/math] [math]\boxed{M_a = (0.595 \rightarrow 0.769) \cdot M_{\odot}}[/math] [math]\boxed{M_a = 1.183 \cdot 10^{30} \; \text{kg}}[/math] Observable Universe average stellar mass: (ref. 10, pg. 20) [math]M_a = 0.6 \cdot M_{\odot} = 1.193 \cdot 10^{30} \; \text{kg}[/math] Stellar baryon density: (ref. 2, pg. 3) [math]\Omega_s = (\Omega_{ms} + \Omega_{wd} + \Omega_{ns}) = 2.460 \cdot 10^{-3}[/math] [math]\Omega_s = 2.460 \cdot 10^{-3}[/math] Observable Universe total observable stellar number: (ref. 11) [math]N_s = \Omega_{s} \left( \frac{M_u}{M_{a}} \right) = \frac{\pi \Omega_{s}}{6 M_{a}} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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{N_s = \frac{\pi \Omega_{s}}{6 M_{a}} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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{N_s = 7.889 \cdot 10^{21} \; \text{stars}}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Planck 2013 results. XVI. Cosmological parameters: (ref. 1) http://planck.caltech.edu/pub/2013results/Planck_2013_results_16.pdf The Cosmic Energy Inventory: (ref. 2) http://arxiv.org/pdf/astro-ph/0406095v2.pdf Wikipedia - Hubble radius: (ref. 3) https://en.wikipedia.org/wiki/Hubble_volume Planck 2013 results. XVI. Cosmological parameters: (ref. 4) http://planck.caltech.edu/pub/2013results/Planck_2013_results_16.pdf UCLA Division of Astronomy and Astrophysics - Homogeneity and Isotropy: (ref. 5) http://www.astro.ucla.edu/~wright/cosmo_02.htm#DL Orion1 - Friedmann equations critical mass: (ref. 6) http://www.scienceforums.net/topic/86694-observable-universe-mass/#entry850915 Orion1 - Cosmic neutrino background radiation electron neutrino composition: (ref. 7) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry884367 Mass models of the Milky Way: (ref. 8) http://arxiv.org/pdf/1102.4340v1 Orion1 - Observable Universe total galaxy number: (ref. 9) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry874489 On The Mass Distribution Of Stars...: (ref. 10) http://www.doiserbia.nb.rs/img/doi/1450-698X/2006/1450-698X0672017N.pdf Orion1 - Observable Universe total observable stellar number: (ref. 11) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry871244 Wikipedia - Stellar classification - Harvard spectral classification: (ref. 12) https://en.wikipedia.org/wiki/Stellar_classification#Harvard_spectral_classification
  19. The calculation would not become 'irrelevant', the transitional epoch times would remain relatively the same, however the calculation would require an update to the latest data. For example, transitioning the calculation from RNA to DNA or the discovery of life fossils on other solar planets that are older than those on Earth. The Drake equation was not considered when the equation on post #1 was derived, however I am intrigued by the similarities. Extrapolating relevant variables from the Drake equation and using current data results from Wikipedia and setting the duration of the RNA world epoch between biogenic carbon in zircon at 4.1 Gy and microbial mat fossils found in 3.48 billion-year-old sandstone: [math]L_{RNA} = (4.1 \; \text{Gy} - 3.48 \; \text{Gy}) = 620 \; \text{My}[/math] Total number of planets currently experiencing the RNA world epoch: (ref. 5) [math]N_{RNA} = R_{\ast} \cdot f_p \cdot n_e \cdot f_{\ell} \cdot L_{RNA} = 1.736 \cdot 10^{9} \; \text{planets}[/math] [math]\boxed{N_{RNA} = 1.736 \cdot 10^{9} \; \text{planets}}[/math] Reference: Wikipedia - The earliest biological evidence for life on Earth (ref. 1) https://en.wikipedia.org/wiki/Abiogenesis#The_earliest_biological_evidence_for_life_on_Earth Bell, Elizabeth A.; Boehnike, Patrick; Harrison, T. Mark; et al. - Potentially biogenic carbon preserved in a 4.1 billion-year-old zircon: (ref. 2) http://www.pnas.org/content/early/2015/10/14/1517557112.full.pdf Wikipedia - Abiogenesis - support_and_difficulties: (ref. 3) https://en.wikipedia.org/wiki/RNA_world#Support_and_difficulties Wikipedia - RNA world - Support and difficulties: (ref. 4) https://en.wikipedia.org/wiki/RNA_world#Support_and_difficulties Wikipedia - Drake equation: (ref. 5) https://en.wikipedia.org/wiki/Drake_equation#Equation
  20. According to stellar data, first generation (Population III) stars lasted less than 21.5 million years. (ref. 2) However, the first generation stellar epoch itself could have lasted up to 800 million years after the Big Bang (ref. 3), and placing the formation of the oldest second generation (Population II) star (SMSS J0313-6708) in the Milky Way galaxy within the first generation stellar epoch at 199 million years: [math]\boxed{dt_1 = (t_u - t_s) = 1.99 \cdot 10^{8} \; \text{y}}[/math] And what a spectacular stellar display that epoch would have been. Affirmative, very dynamic factors are involved, however nature's efficiency is intrinsically built into the chronological equation on post #1. Reference: Wikipedia - First Generation stars (Population III stars) (ref. 1) https://en.wikipedia.org/wiki/Stellar_population#Population_III_stars Wikipedia - Stellar evolution (ref. 2) https://en.wikipedia.org/wiki/Stellar_evolution Wikipedia - Cosmos Redshift 7: (ref. 3) https://en.wikipedia.org/wiki/Cosmos_Redshift_7
  21. [math]t_u = 13.799 \cdot 10^{9} \; \text{y}[/math] - Universe age (ref. 1) [math]t_s = 13.6 \cdot 10^{9} \; \text{y}[/math] - oldest second generation star age in Milky Way galaxy (ref. 2) [math]t_{\odot} = 4.57 \cdot 10^{9} \; \text{y}[/math] - solar age (ref. 3) [math]t_E = 4.54 \cdot 10^{9} \; \text{y}[/math] - Earth age (ref. 4) [math]t_z = 4.4 \cdot 10^{9} \; \text{y}[/math] - oldest Zircon age (ref. 5) [math]t_l = 4.0 \cdot 10^{9} \; \text{y}[/math] - oldest fossilized RNA life age (ref. 6) key: [math]dt_1[/math] - minimum time required for second generation stars to form. [math]dt_2[/math] - minimum time required for inner planets to form. [math]dt_3[/math] - minimum time required for liquid water to form. [math]dt_4[/math] - minimum time required for RNA life to form. According to this basic equation, the amount of universal evolutionary time required to generate self-replicating RNA: [math]t_{RNA} = dt_1 + dt_2 + dt_3 + dt_4 = (t_u - t_s) + (t_{\odot} - t_E) + (t_E - t_z) + (t_z - t_l)[/math] [math]\boxed{t_{RNA} = (t_u - t_s) + (t_{\odot} - t_E) + (t_E - t_z) + (t_z - t_l)}[/math] [math]\boxed{t_{RNA} = 7.69 \cdot 10^{8} \; \text{y}}[/math] The first self-replicating RNA life could have been generated 769 million years after the Big Bang on the inner planets around second generation and third generation stars, which formed together at the same time. Any discussions and/or peer reviews about this specific topic thread? Reference: Wikipedia - Universe: (ref. 1) https://en.wikipedia.org/wiki/Universe Wikipedia - SMSS J0313-6708: (ref. 2) https://en.wikipedia.org/wiki/SM0313 Wikipedia - Sun: (ref. 3) https://en.wikipedia.org/wiki/Sun Wikipedia - Earth: (ref. 4) https://en.wikipedia.org/wiki/Earth Wikipedia - Cryptic era: (ref. 5) https://en.wikipedia.org/wiki/Cryptic_era Wikipedia - Basin Groups: (ref. 6) https://en.wikipedia.org/wiki/Basin_Groups
  22. Radial decrease rate between two bodies versus time: (ref. 1, pg. 20), (ref. 2) [math]\frac{dr}{dt} = - \frac{64 G^3 (m_1 m_2)(m_1 + m_2)}{5 c^5 r^3}[/math] Time decrease rate between two bodies versus radius: (ref. 1, pg. 20), (ref. 2) [math]\boxed{\frac{dt}{dr} = - \frac{5 c^5 r^3}{64 G^3 (m_1 m_2)(m_1 + m_2)}}[/math] Integration for total inspiral time from total radius [math]R[/math] to zero. [math]\tau = - \frac{5 c^5}{64 G^3 (m_1 m_2)(m_1 + m_2)} \int_R^0 r^3 dr = \frac{5 c^5 R^4}{256 G^3 (m_1 m_2)(m_1 + m_2)}[/math] Two-body total orbit inspiral lifetime: (ref. 3) [math]\boxed{\tau = \frac{5 c^5 R^4}{256 G^3 (m_1 m_2)(m_1 + m_2)}}[/math] Milky Way galaxy mass: (ref. 4, pg. 1) [math]M_{g} = 1.26 \cdot 10^{12} \cdot M_{\odot} = 2.506 \cdot 10^{42} \; \text{kg}[/math] [math]\boxed{M_{g} = 2.506 \cdot 10^{42} \; \text{kg}}[/math] Milky Way galaxy radius: (ref. 5), (ref. 6) [math]R_g = 8.515 \cdot 10^{20} \; \text{m} \; \; \; (90 \; \text{kly})[/math] Milky Way galaxy total orbit inspiral lifetime: [math]\boxed{\tau_g = \frac{5 c^5 R_g^4}{256 G^3 (M_g M_{\odot})(M_g + M_{\odot})}}[/math] [math]\boxed{\tau_g = 6.697 \cdot 10^{39} \; \text{s}} \; \; \; (2.122 \cdot 10^{32} \; \text{y})[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Orbital decay from gravitational radiation: (ref. 1) http://www.eftaylor.com/exploringblackholes/GravWaves150909v1.pdf Wikipedia - Orbital decay from gravitational radiation: (ref. 2) https://en.wikipedia.org/wiki/Gravitational_wave#Orbital_decay_from_gravitational_radiation Wikipedia - Orbital lifetime limits from gravitational radiation: (ref. 3) https://en.wikipedia.org/wiki/Gravitational_wave#Orbital_lifetime_limits_from_gravitational_radiation Mass models of the Milky Way: (ref. 4) http://arxiv.org/pdf/1102.4340v1 Space.com - Milky Way galaxy size: (ref. 5) http://www.space.com/29270-milky-way-size-larger-than-thought.html Wikipedia - Milky Way galaxy: (ref. 6) https://en.wikipedia.org/wiki/Milky_Way
  23. Planck satellite cosmological parameters: (ref. 1, pg. 11) [math]\Omega_{dm} = 0.268[/math] Dark matter scalar particle composition is equivalent to dark matter composition: [math]\boxed{\Omega_{\phi} = \Omega_{dm}}[/math] Dark matter scalar particle species total effective degeneracy number: (ref. 2) [math]\boxed{N_{\phi} = 1}[/math] Dark matter scalar particle radiation temperature is equivalent to neutrino cosmic background radiation temperature: [math]\boxed{T_{\phi} = T_{\nu}}[/math] Bose-Einstein total dark matter scalar particle distribution constant: (ref. 3) [math]C_{\phi} = \frac{4 \pi^3 G N_{\phi} (k_B T_{\phi})^4}{3 \Omega_{\phi} H_0^2 \hbar^3 c^5} = 3.640 \cdot 10^{-4}[/math] [math]\boxed{C_{\phi} = \frac{4 \pi^3 G N_{\phi} (k_B T_{\phi})^4}{3 \Omega_{\phi} H_0^2 \hbar^3 c^5}}[/math] [math]\boxed{C_{\phi} = 3.640 \cdot 10^{-4}}[/math] Observable Universe total mass: [math]M_u = \rho_u V_u = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\phi} T_{\phi}^4}{C_{\phi}} \right) \left( \frac{\Omega_{\phi} + \Omega_{b}}{\Omega_{\phi}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right][/math] [math]\boxed{M_u = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\phi} T_{\phi}^4}{C_{\phi}} \right) \left( \frac{\Omega_{\phi} + \Omega_{b}}{\Omega_{\phi}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right]}[/math] [math]\boxed{M_u = 5.485 \cdot 10^{54} \; \text{kg}}[/math] Solve for dark matter scalar particle rest mass with highest relative maximum at critical mass number: (ref. 3) [math]\frac{d}{dm} I_{\phi} (m_{\phi}) = 0[/math] Dark matter scalar particle rest mass: [math]\boxed{m_{\phi} = 6.586 \cdot 10^{-40} \; \text{kg}} \; \; \; T_{\phi} = T_{\nu}[/math] Observable Universe total dark matter scalar particle number: [math]N_{\phi t} = \Omega_{\phi} \left( \frac{M_u}{m_{\phi}} \right) = \frac{\pi \Omega_{\phi}}{6 m_{\phi}} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\phi} T_{\phi}^4}{C_{\phi}} \right) \left( \frac{\Omega_{\phi} + \Omega_{b}}{\Omega_{\phi}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right][/math] [math]\boxed{N_{\phi t} = \frac{\pi \Omega_{\phi}}{6 m_{\phi}} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\phi} T_{\phi}^4}{C_{\phi}} \right) \left( \frac{\Omega_{\phi} + \Omega_{b}}{\Omega_{\phi}} \right) + \frac{3 \Omega_{\Lambda} H_0^2}{8 \pi G} \right]}[/math] [math]\boxed{N_{\phi t} = 2.232 \cdot 10^{93} \; \phi \; \text{particles}}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Planck 2013 results. XVI. Cosmological parameters: (ref. 1) http://planck.caltech.edu/pub/2013results/Planck_2013_results_16.pdf Orion 1 - total effective degeneracy number: (ref. 2) http://www.scienceforums.net/topic/90189-neutrino-mass-from-fermi-dirac-statistics/#entry879233 Orion1 - dark matter scalar particle composition: (ref. 3) http://www.scienceforums.net/topic/90189-neutrino-mass-from-fermi-dirac-statistics/#entry887017 Dark matter - Wikipedia https://en.wikipedia.org/wiki/Dark_matter
  24. Planck satellite cosmological parameters: (ref. 1, pg. 11) [math]\Omega_{\Lambda} = 0.6825[/math] [math]\Omega_{dm} = 0.268[/math] [math]\Omega_{b} = 0.0495[/math] [math]\Omega_s = 2.460 \cdot 10^{-3}[/math] (ref. 2, pg. 3) [math]\Omega_{\nu} = 1.258 \cdot 10^{-3}[/math] (ref. 2, pg. 3) [math]\Omega_{\gamma} = 5.012 \cdot 10^{-5}[/math] (ref. 2, pg. 3) Neutrino particle mass: [math]\boxed{m_{\nu} \neq 0}[/math] Photon particle mass: [math]\boxed{m_{\gamma} = 0}[/math] Hubble radius: (ref. 3) [math]R_h = \frac{c}{H_0}[/math] Planck satellite redshift parameter at photon decoupling time: (ref. 4, pg. 11) [math]z = \left( \frac{T_{\gamma , t}}{T_{\gamma}} \right) - 1 = 1090.43[/math] Observable Universe total co-moving radius: (ref. 5) [math]R_u = R_h \left( \frac{\ln{(1 + z)}}{2} \right) = \left( \frac{c}{H_0} \right) \frac{\ln (1 + z)}{2} = \frac{c \ln (1 + z)}{2 H_0} = 4.606 \cdot 10^{26} \; \text{m}[/math] [math]\boxed{R_u = \frac{c \ln (1 + z)}{2 H_0}}[/math] [math]\boxed{R_u = 4.606 \cdot 10^{26} \; \text{m}} \; \; \; (48.689 \cdot 10^{9} \; \text{ly})[/math] Friedmann equations critical mass: (ref. 6) [math]M_c = \frac{H_0^2 R_u^3}{2 G} = \frac{H_0^2}{2 G} \left[ \left( \frac{c}{H_0} \right) \frac{\ln (1 + z)}{2} \right]^3 = \left( \frac{c^3}{16 G H_0} \right) [\ln (1 + z)]^3 = 3.794 \cdot 10^{54} \; \text{kg}[/math] [math]\boxed{M_c = \left( \frac{c^3}{16 G H_0} \right) [\ln (1 + z)]^3}[/math] [math]\boxed{M_c = 3.794 \cdot 10^{54} \; \text{kg}}[/math] Fermi-Dirac and Bose-Einstein total neutrino distribution constant: (ref. 7) [math]C_{\nu} = \frac{4 \pi^3 G N_{\nu} (k_B T_{\nu})^4}{3 \Omega_{\nu} H_0^2 \hbar^3 c^5} = 0.236[/math] [math]\boxed{C_{\nu} = \frac{4 \pi^3 G N_{\nu} (k_B T_{\nu})^4}{3 \Omega_{\nu} H_0^2 \hbar^3 c^5}}[/math] [math]\boxed{C_{\nu} = 0.236}[/math] Observable Universe total co-moving volume: [math]V_u = \frac{4 \pi R_u^3}{3} = \frac{4 \pi}{3} \left( \frac{c \ln (1 + z)}{2 H_0} \right)^3 = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 = 4.094 \cdot 10^{80} \; \text{m}^3[/math] [math]\boxed{V_u = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3}[/math] [math]\boxed{V_u = 4.094 \cdot 10^{80} \; \text{m}^3} \; \; \; (1.154 \cdot 10^{32} \; \text{ly}^3)[/math] Observable Universe total mass: [math]M_u = \rho_u V_u = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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 = \frac{\pi}{6} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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 = 5.485 \cdot 10^{54} \; \text{kg}}[/math] Milky Way galaxy mass: (ref. 8, pg. 1) [math]M_{mw} = 1.26 \cdot 10^{12} \cdot M_{\odot} = 2.506 \cdot 10^{42} \; \text{kg}[/math] [math]\boxed{M_{mw} = 2.506 \cdot 10^{42} \; \text{kg}}[/math] Observable Universe total galaxy number: (ref. 9) [math]N_g = \Omega_{b} \left( \frac{M_u}{M_{mw}} \right) = \frac{\pi \Omega_{b}}{6 M_{mw}} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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{N_g = \frac{\pi \Omega_{b}}{6 M_{mw}} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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{N_g = 1.084 \cdot 10^{12} \; \text{galaxies}}[/math] Observable Universe average stellar mass: (ref. 10, pg. 20) [math]M_a = 0.6 \cdot M_{\odot} = 1.193 \cdot 10^{30} \; \text{kg}[/math] [math]\boxed{M_a = 1.193 \cdot 10^{30} \; \text{kg}}[/math] Stellar baryon density: (ref. 2, pg. 3) [math]\Omega_s = (\Omega_{ms} + \Omega_{wd} + \Omega_{ns}) = 2.460 \cdot 10^{-3}[/math] [math]\Omega_s = 2.460 \cdot 10^{-3}[/math] Observable Universe total observable stellar number: (ref. 11) [math]N_s = \Omega_{s} \left( \frac{M_u}{M_{a}} \right) = \frac{\pi \Omega_{s}}{6 M_{a}} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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{N_s = \frac{\pi \Omega_{s}}{6 M_{a}} \left( \frac{c \ln (1 + z)}{H_0} \right)^3 \left[ \frac{\pi^2 k_B^4}{2 \hbar^3 c^5} \left( \frac{N_{\gamma} T_{\gamma}^4}{15} + \frac{N_{\nu} T_{\nu}^4}{C_{\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{N_s = 1.131 \cdot 10^{22} \; \text{stars}}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Planck 2013 results. XVI. Cosmological parameters: (ref. 1) http://planck.caltech.edu/pub/2013results/Planck_2013_results_16.pdf The Cosmic Energy Inventory: (ref. 2) http://arxiv.org/pdf/astro-ph/0406095v2.pdf Wikipedia - Hubble radius: (ref. 3) https://en.wikipedia.org/wiki/Hubble_volume Planck 2013 results. XVI. Cosmological parameters: (ref. 4) http://planck.caltech.edu/pub/2013results/Planck_2013_results_16.pdf UCLA Division of Astronomy and Astrophysics - Homogeneity and Isotropy: (ref. 5) http://www.astro.ucla.edu/~wright/cosmo_02.htm#DL Orion1 - Friedmann equations critical mass: (ref. 6) http://www.scienceforums.net/topic/86694-observable-universe-mass/#entry850915 Orion1 - Cosmic neutrino background radiation electron neutrino composition: (ref. 7) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry884367 Mass models of the Milky Way: (ref. 8) http://arxiv.org/pdf/1102.4340v1 Orion1 - Observable Universe total galaxy number: (ref. 9) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry874489 On The Mass Distribution Of Stars...: (ref. 10) http://www.doiserbia.nb.rs/img/doi/1450-698X/2006/1450-698X0672017N.pdf Orion1 - Observable Universe total observable stellar number: (ref. 11) http://www.scienceforums.net/topic/86694-observable-universe-mass/page-2#entry871244
  25. Planck satellite cosmological parameters: (ref. 1, pg. 11) [math]\Omega_{dm} = 0.268[/math] Dark matter scalar particle composition is equivalent to dark matter composition: [math]\boxed{\Omega_{\phi} = \Omega_{dm}}[/math] Dark matter scalar particle species total effective degeneracy number: (ref. 2) [math]\boxed{N_{\phi} = 1}[/math] Dark matter scalar particle radiation temperature is equivalent to neutrino cosmic background radiation temperature: [math]\boxed{T_{\phi} = T_{\nu}}[/math] Dark matter scalar particle radiation energy density Bose-Einstein distribution: [math]\epsilon_{\phi} = \frac{4 \pi k_B^4 N_{\phi} T_{\phi}^4}{( 2 \pi \hbar c )^3} \int_{0}^c \frac{E_t (v)^3}{e^{\frac{E_t (v)}{E_1 (T_{\phi})}} - 1} dv[/math] Dark matter quantum scalar particle Bose-Einstein distribution integral: [math]I_{\phi} = \int_{0}^c \frac{E_t (v)^3}{e^{\frac{E_t (v)}{E_1 (T_{\phi})}} - 1} dv[/math] Solve for dark matter scalar particle rest mass with highest relative maximum at critical mass number: [math]\frac{d}{dm} I_{\phi} (m_{\phi}) = 0[/math] Dark matter scalar particle rest mass: [math]\boxed{m_{\phi} = 6.586 \cdot 10^{-40} \; \text{kg}} \; \; \; T_{\phi} = T_{\nu}[/math] Dark matter scalar particle cosmic background radiation energy density Bose-Einstein distribution integration via substitution: [math]\epsilon_{\phi} = \alpha_{\phi} T_{\phi}^4 = \frac{4 \pi N_{\phi} (k_B T_{\phi})^4}{( 2 \pi \hbar c )^3} \int_{0}^c \frac{E_t (v)^3}{e^{\frac{E_t (v)}{E_1 (T_{\phi})}} - 1} dv = \frac{4 \pi N_{\phi} (k_B T_{\phi})^4}{( 2 \pi \hbar c )^3} \left( \frac{\pi^4}{C_{\phi}} \right) = \frac{\pi^2 N_{\phi} (k_B T_{\phi})^4}{2 C_{\phi} ( \hbar c )^3}[/math] Dark matter scalar particle cosmic background radiation energy density: [math]\boxed{\epsilon_{\phi} = \frac{\pi^2 N_{\phi} (k_B T_{\phi})^4}{2 C_{\phi} ( \hbar c )^3}}[/math] Dark matter scalar particle cosmic background radiation constant: [math]\boxed{\alpha_{\phi} = \frac{\pi^2 N_{\phi} k_B^4}{2 C_{\phi} ( \hbar c )^3}}[/math] Dark matter scalar particle cosmic background radiation composition integration via substitution: [math]\Omega_{\phi} = \frac{\epsilon_{\phi}}{\epsilon_c} = \frac{\alpha_{\phi} T_{\phi}^4}{\rho_c c^2} = \left( \frac{\pi^2 N_{\phi} (k_B T_{\phi})^4}{2 C_{\phi} ( \hbar c )^3} \right) \left( \frac{8 \pi G}{3 (c H_0)^2} \right) = \frac{4 \pi^3 G N_{\phi} (k_B T_{\phi})^4}{3 C_{\phi} H_0^2 \hbar^3 c^5}[/math] Dark matter scalar particle cosmic background radiation composition: [math]\boxed{\Omega_{\phi} = \frac{4 \pi^3 G N_{\phi} (k_B T_{\phi})^4}{3 C_{\phi} H_0^2 \hbar^3 c^5}}[/math] Bose-Einstein total dark matter scalar particle distribution constant: [math]C_{\phi} = \frac{4 \pi^3 G N_{\phi} (k_B T_{\phi})^4}{3 \Omega_{\phi} H_0^2 \hbar^3 c^5} = 3.640 \cdot 10^{-4}[/math] [math]\boxed{C_{\phi} = \frac{4 \pi^3 G N_{\phi} (k_B T_{\phi})^4}{3 \Omega_{\phi} H_0^2 \hbar^3 c^5}}[/math] [math]\boxed{C_{\phi} = 3.640 \cdot 10^{-4}}[/math] Any discussions and/or peer reviews about this specific topic thread? Reference: Planck 2013 results. XVI. Cosmological parameters: (ref. 1) http://planck.caltech.edu/pub/2013results/Planck_2013_results_16.pdf Orion 1 - total effective degeneracy number: (ref. 2) http://www.scienceforums.net/topic/90189-neutrino-mass-from-fermi-dirac-statistics/#entry879233 Dark matter - Wikipedia https://en.wikipedia.org/wiki/Dark_matter
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