Observable Universe mass...

[Mordred]

NoNo SUSY or SM particle can break any of the conservation laws. I don't think you can connect quintessence with the higgsino if memory serves me correct it is the fermionic superpartner to the Higgs boson and thus will have fractional spin. While quintessence is spin 0 (bosonic).

I will of course check that 

Edit confirmed each SM boson will have a fermionic superpartner under SUSY.

Edited July 13, 2019 by Mordred

[Orion1]

On 7/1/2017 at 1:18 AM, Mordred said:

the treatments I am familiar with usually has DM freezing out before neutrinos.

Toy model particle chart:
[math]\begin{array}{l*{7}{c}r} & \text{identity} & \text{state} & \text{spin} & n_{s} & N_{s} & N_{n} & \text{mass} & \text{type} \\ b & \text{scalar} & 0 & 0 & 1 & 1 & 1 & 0 & \Lambda \\ b & \text{scalar} & 0 & 0 & 1 & 1 & 1 & \neq 0 & \phi \\ f & \text{neutrino} & +,- & 1/2 & 2 & 3 & 3 & \neq 0 & \nu \\ b & \text{photon} & +,- & 1 & 2 & 1 & 2 & 0 & \gamma \\ b & \text{graviton} & +,- & 2 & 2 & 1 & 2 & 0 & \text{G} \\ \end{array}[/math]
[math]\;[/math]
Supersymmetry particle and sparticle chart:
[math]\begin{array}{l*{7}{c}r} & \text{identity} & \text{state} & \text{spin} & n_{s} & N_{s} & N_{n} & \text{mass} & \text{type} \\ sf & \text{sneutrino} & 0 & 0 & 1 & 3 & 3 & \neq 0 & \tilde{\nu} \\ b & \text{Higgs} & 0 & 0 & 1 & 1 & 1 & 125.18 \; \text{GeV} & H^{0} \\ sf & \text{higgsino} & +,- & 1/2 & 2 & 1 & 2 & 1.1 \; \text{TeV} & \ddot{H} \\ f & \text{sterile neutrino} & +,- & 1/2 & 2 & 3 & 3 & <1 \; \text{eV} - 10^{15} \; \text{GeV} & \nu \\ sf & \text{neutralino} & +,- & 1/2 & 2 & 4 & 4 & 100 \; \text{GeV} - 1 \; \text{TeV} & \ddot{N}^{0} \\ sf & \text{gravitino} & +,- & 3/2 & 2 & 1 & 2 & 1 \; \text{TeV} & \ddot{G} \\ \end{array}[/math]
[math]\;[/math]
Bose-Einstein scalar particle dark matter density:
[math]\boxed{\rho_{\phi} = \frac{N_{\phi} \pi^2 \left(k_B T_{\phi} \right)^4}{2 C_{\phi} \hbar^3 c^5}}[/math]
[math]\;[/math]
Bose-Einstein scalar particle dark matter number density: (ref. 1, eq. 7)
[math]n_{\phi} = \left(\frac{\zeta \left(3 \right) N_{\phi} \left(k_{B} T_{\phi} \right)^3}{\pi^2 \left(\hbar c \right)^3} \right)[/math]
[math]\;[/math]
Bose-Einstein scalar particle dark matter mass:
[math]m_{\phi} = \frac{\rho_{\phi}}{n_{\phi}} = \left(\frac{N_{\phi} \pi^2 \left(k_B T_{\phi} \right)^4}{2 C_{\phi} \hbar^3 c^5} \right)\left(\frac{\pi^2 \left(\hbar c \right)^3}{\zeta \left(3 \right) N_{\phi} \left(k_{B} T_{\phi} \right)^3} \right) = \frac{\pi^{4} k_B T_{\phi}}{2 C_{\phi} c^{2} \zeta \left(3 \right)} = 3.326 \cdot 10^{-35} \; \text{kg}[/math]
[math]\;[/math]
Bose-Einstein scalar particle dark matter mass:
[math]\boxed{m_{\phi} = \frac{\pi^{4} k_B T_{\phi}}{2 C_{\phi} c^{2} \zeta \left(3 \right)}}[/math]
[math]\;[/math]
[math]\boxed{m_{\phi} = 3.326 \cdot 10^{-35} \; \text{kg}}[/math]
[math]\boxed{m_{\phi} = 18.658 \; \frac{\text{eV}}{c^2}}[/math]
[math]\;[/math]
Fermi-Dirac neutrino density:
[math]\boxed{\rho_{\nu} = \frac{N_{\nu} \pi^2 \left(k_B T_{\nu} \right)^4}{2 C_{\nu} \hbar^3 c^5}}[/math]
[math]\;[/math]
Fermi-Dirac neutrino number density: (ref. 1, eq. 8)
[math]n_{\nu} = \left(\frac{3 \zeta \left(3 \right) N_{\nu} \left(k_{B} T_{\nu} \right)^3}{4 \pi^2 \left(\hbar c \right)^3} \right)[/math]
[math]\;[/math]
Fermi-Dirac neutrino mass:
[math]m_{\nu} = \frac{\rho_{\nu}}{n_{\nu}} = \left(\frac{N_{\nu} \pi^2 \left(k_B T_{\nu} \right)^4}{2 C_{\nu} \hbar^3 c^5} \right)\left(\frac{4 \pi^2 \left(\hbar c \right)^3}{3 \zeta \left(3 \right) N_{\nu} \left(k_{B} T_{\nu} \right)^3} \right) = \frac{2 \pi^{4} k_B T_{\nu}}{3 C_{\nu} c^{2} \zeta \left(3 \right)} = 6.839 \cdot 10^{-38} \; \text{kg}[/math]
[math]\;[/math]
Fermi-Dirac neutrino mass:
[math]\boxed{m_{\nu} = \frac{2 \pi^{4} k_B T_{\nu}}{3 C_{\nu} c^{2} \zeta \left(3 \right)}}[/math]
[math]\;[/math]
[math]\boxed{m_{\nu} = 6.839 \cdot 10^{-38} \; \text{kg}}[/math]
[math]\boxed{m_{\nu} = 0.038 \; \frac{\text{eV}}{c^2}}[/math]
[math]\;[/math]
Disqualifying dark matter particle candidates for this toy model based upon the predicted mass range, results in the remaining candidates chart.
[math]\;[/math]
Toy model dark matter particle remaining candidates chart:
[math]\begin{array}{l*{7}{c}r} & \text{identity} & \text{state} & \text{spin} & n_{s} & N_{s} & N_{n} & \text{mass} & \text{type} \\ b & \text{scalar} & 0 & 0 & 1 & 1 & 1 & 18.658 \; \text{eV} & \phi \\ f & \text{sterile neutrino} & +,- & 1/2 & 2 & 3 & 3 & <1 \; \text{eV} - 10^{15} \; \text{GeV} & \nu \\ sf & \text{sneutrino} & 0 & 0 & 1 & 3 & 3 & \neq 0 & \tilde{\nu} \\ \end{array}[/math]
[math]\;[/math]
Would dark matter particle candidates that quantum mechanically decouple before/after neutrinos be a candidate qualifier/disqualifier?
[math]\;[/math]
Any discussions and/or peer reviews about this specific topic thread?
[math]\;[/math]
Reference:
Introduction to Cosmology: Lecture 6 - Thermal history of the Universe: (ref. 1)
http://gravitation.web.ua.pt/sites/default/files/migrated2016/Lecture_6.pdf
Wikipedia - Scalar boson: (ref. 2)
https://en.wikipedia.org/wiki/Scalar_boson
Wikipedia - Sterile neutrinos: (ref. 3)
https://en.wikipedia.org/wiki/Sterile_neutrino
Wikipedia - Dark matter: (ref. 4)
https://en.wikipedia.org/wiki/Dark_matter

Edited July 14, 2019 by Orion1
sour

[Orion1]

On 3/6/2016 at 8:38 AM, Mordred said:

you should be using the Fermi-Dirac statistics for dark matter

Affirmative, in this toy model, sterile neutrinos have equivalent dark matter candidacy as scalar particles.
[math]\;[/math]
Planck satellite cosmological parameters at present time: (ref. 1, pg. 11)
[math]\Omega_{dm} = 0.268[/math]
[math]\;[/math]
sterile neutrino composition is equivalent to dark matter composition at present time.
[math]\boxed{\Omega_{s \nu} = \Omega_{dm}}[/math]
[math]\;[/math]
Fermi-Dirac total dark matter sterile neutrino distribution constant:
[math]\boxed{C_{s \nu} = \frac{4 G N_{s \nu} \pi^3 \left(k_B T_{s \nu} \right)^4}{3 \Omega_{s \nu} H_0^2 \hbar^3 c^5}}[/math]
[math]\;[/math]
[math]\boxed{C_{s \nu} = 1.109 \cdot 10^{-3}}[/math]
[math]\;[/math]
Fermi-Dirac sterile neutrino density:
[math]\boxed{\rho_{s \nu} = \frac{N_{s \nu} \pi^2 \left(k_B T_{s \nu} \right)^4}{2 C_{s \nu} \hbar^3 c^5}}[/math]
[math]\;[/math]
Fermi-Dirac sterile neutrino number density: (ref. 3, eq. 8)
[math]n_{s \nu} = \left(\frac{3 \zeta \left(3 \right) N_{s \nu} \left(k_{B} T_{s \nu} \right)^3}{4 \pi^2 \left(\hbar c \right)^3} \right)[/math]
[math]\;[/math]
Fermi-Dirac dark matter sterile neutrino mass integration via substitution:
[math]m_{s \nu} = \frac{\rho_{s \nu}}{n_{s \nu}} = \left(\frac{N_{s \nu} \pi^2 \left(k_B T_{s \nu} \right)^4}{2 C_{s \nu} \hbar^3 c^5} \right)\left(\frac{4 \pi^2 \left(\hbar c \right)^3}{3 \zeta \left(3 \right) N_{s \nu} \left(k_{B} T_{s \nu} \right)^3} \right) = \frac{2 \pi^{4} k_B T_{s \nu}}{3 C_{s \nu} c^{2} \zeta \left(3 \right)} = 1.456 \cdot 10^{-35} \; \text{kg}[/math]
[math]\;[/math]
Fermi-Dirac dark matter sterile neutrino mass:
[math]\boxed{m_{s \nu} = \frac{2 \pi^{4} k_B T_{s \nu}}{3 C_{s \nu} c^{2} \zeta \left(3 \right)}}[/math]
[math]\;[/math]
[math]\boxed{m_{s \nu} = 1.456 \cdot 10^{-35} \; \text{kg}}[/math]
[math]\boxed{m_{s \nu} = 8.167 \; \frac{\text{eV}}{c^2}}[/math]
[math]\;[/math]
WMAP satellite cosmological parameters at photon decoupling time: (ref. 2)
[math]\Omega_{dm,t} = 0.63[/math]
[math]\;[/math]
Sterile neutrino composition is equivalent to dark matter composition at photon decoupling time.
[math]\boxed{\Omega_{s \nu,t} = \Omega_{dm,t}}[/math]
[math]\;[/math]
Fermi-Dirac dark matter sterile neutrino decoupling time:
[math]\boxed{T_{u,s \nu} = \frac{}{2\left(k_B T_{s \nu,t} \right)^2} \sqrt{\frac{3 \Omega_{s \nu,t} C_{s \nu} \hbar^3 c^5}{G N_{s \nu} \pi^3}}} \; \; \; m_{s \nu} \neq 0[/math]
[math]\;[/math]
[math]\boxed{T_{u,s \nu} = 0.0255 \; \text{s}} \; \; \; m_{s \nu} \neq 0[/math]
[math]\;[/math]
Toy model dark matter particle candidates chart:
[math]\begin{array}{l*{8}{c}r} & \text{identity} & \text{state} & \text{spin} & n_{s} & N_{s} & N_{n} & \text{mass} & \text{type} & \text{decoupling time} \\ b & \text{scalar} & 0 & 0 & 1 & 1 & 1 & 18.658 \; \text{eV} & \phi & 0.0255 \; \text{s} \\ f & \text{sterile neutrino} & +,- & 1/2 & 2 & 3 & 3 & 8.167 \; \text{eV} & \nu_{s} & 0.0255 \; \text{s} \\ \end{array}[/math]
[math]\;[/math]
Any discussions and/or peer reviews about this specific topic thread?
[math]\;[/math]
Reference:
Planck 2013 results. XVI. Cosmological parameters: (ref. 1)
http://planck.caltech.edu/pub/2013results/Planck_2013_results_16.pdf
WMAP satellite cosmological parameters at photon decoupling time: (ref. 2)
https://map.gsfc.nasa.gov/media/080998/index.html
Introduction to Cosmology: Lecture 6 - Thermal history of the Universe: (ref. 3)
http://gravitation.web.ua.pt/sites/default/files/migrated2016/Lecture_6.pdf
Wikipedia - Scalar boson: (ref. 4)
https://en.wikipedia.org/wiki/Scalar_boson
Wikipedia - Sterile neutrinos: (ref. 5)
https://en.wikipedia.org/wiki/Sterile_neutrino
Wikipedia - Dark matter: (ref. 6)
https://en.wikipedia.org/wiki/Dark_matter

Edited July 20, 2019 by Orion1

[Orion1]

Toy model calculation versus observation comparison summary:
[math]\begin{array}{l*{3}{c}r} \text{symbol} & \text{quantity} & \text{percent} \\ N_{g} & 2.330 \cdot 10^{12} \; \text{galaxies} & 116.5 \\ N_{g} & 2.000 \cdot 10^{12} \; \text{galaxies} & \\ N_{s} & 2.453 \cdot 10^{23} \; \text{stars} & 81.767 \\ N_{s} & 3.000 \cdot 10^{23} \; \text{stars} \\ N_p & 3.536 \cdot 10^{23} \; \text{planets} & 110.5 \\ N_p & 3.200 \cdot 10^{23} \; \text{planets} \\ \frac{N_s}{N_g} & 1.053 \cdot 10^{11} \; \frac{\text{stars}}{\text{galaxy}} & 70.2 \\ \frac{N_s}{N_g} & 1.500 \cdot 10^{11} \; \frac{\text{stars}}{\text{galaxy}} \\ \frac{N_p}{N_g} & 1.518 \cdot 10^{11} \; \frac{\text{planets}}{\text{galaxy}} & 94.875 \\ \frac{N_p}{N_g} & 1.600 \cdot 10^{11} \; \frac{\text{planets}}{\text{galaxy}} \\ \frac{N_p}{N_s} & 1.443 \; \frac{\text{planets}}{\text{star}} & 135.24 \\ \frac{N_p}{N_s} & 1.067 \; \frac{\text{planets}}{\text{star}} \\ \end{array}[/math]
[math]\;[/math]
Toy model particle properties chart:
[math]\begin{array}{l*{9}{c}r} & \text{identity} & \text{state} & \text{spin} & n_{s} & N_{s} & N_{n} & \text{mass} & \text{type} & \text{decoupling time} \\ b & \text{scalar} & 0 & 0 & 1 & 1 & 1 & 0 & \Lambda & >0 \; \text{s} \\ b & \text{scalar} & 0 & 0 & 1 & 1 & 1 & 18.658 \; \text{eV} & \phi & 0.0255 \; \text{s} \\ f & \text{sterile neutrino} & +,- & 1/2 & 2 & 3 & 3 & 8.167 \; \text{eV} & \nu_{s} & 0.0255 \; \text{s} \\ f & \text{neutrino} & +,- & 1/2 & 2 & 3 & 3 & 0.038 \; \text{eV} & \nu & 0.148 \; \text{s} \\ b & \text{photon} & +,- & 1 & 2 & 1 & 2 & 0 & \gamma & 1.009 \cdot 10^{13} \; \text{s} & \left(3.197 \cdot 10^{5} \; \text{years} \right) \\ b & \text{graviton} & +,- & 2 & 2 & 1 & 2 & 0 & \text{G} & >0 \; \text{s} \\ \end{array}[/math]
[math][/math]
[math]\;[/math]
Any discussions and/or peer reviews about this specific topic thread?
[math]\;[/math]
Reference:
Scienceforums - Orion1 - toy model revision:
https://www.scienceforums.net/topic/86694-observable-universe-mass/?do=findComment&comment=1089828
https://www.scienceforums.net/topic/86694-observable-universe-mass/?do=findComment&comment=1091408