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LQC Lambda-CDM model bounce radius

  1. Feb 22, 2012 #1

    These are my equations for the total Universe_mass-energy equivalence based upon the Lambda-CDM model parameters and the Hubble Space Telescope (HST) and WMAP observational parameters and the observable Universe radius in Systeme International units.

    I attempted to collapse the Lambda-CDM model parameter dimensions using the maximum LQC bounce density to determine the bounce radius.

    Observable Universe radius:
    [tex]R_u = 4.399 \cdot 10^{26} \; \text{m}[/tex]
    Lambda-CDM stellar Baryon density parameter:
    [tex]\Omega_s = 0.005[/tex]
    Hubble Space Telescope observable stellar number:
    [tex]dN_s = 10^{22}[/tex]
    Hubble Space Telescope observable stellar volume:
    [tex]dV_s = 3.3871 \cdot 10^{78} \; \text{m}^3 \; \; \; (4 \cdot 10^{30} \; \text{ly}^3)[/tex]
    Solar mass:
    [tex]M_{\odot} = 1.9891 \cdot 10^{30} \; \text{kg}[/tex]

    Planck energy density:
    [tex]\boxed{\rho_p = \frac{E_p}{V_p} = \frac{3 c^7}{4 \pi \hbar G^2}}[/tex]

    [tex]\boxed{\rho_p = 1.106 \cdot 10^{113} \; \frac{\text{j}}{\text{m}^3}}[/tex]

    Universe_mass-energy equivalence total energy:
    [tex]\boxed{E_t = \frac{4 \pi c^2 M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) R_u^3}[/tex]

    Total amount of energy in the Universe:
    [tex]\boxed{E_t = 3.764 \cdot 10^{73} \; \text{j}}[/tex]

    Universe total energy density:
    [tex]\rho_u = \frac{E_t}{V_u} = \frac{3 E_t}{4 \pi R_u^3} = \frac{M_{\odot} c^2}{\Omega_s} \left( \frac{dN_s}{dV_s} \right)[/tex]

    LQC maximum energy density parameter: (ref. 10 p. 73 (5.7))
    [tex]\boxed{\Omega_{LQC} = \frac{\rho_{\text{max}}}{\rho_p} = \frac{\hbar G}{2 \gamma^2 \lambda^2 c^7} = 0.41}[/tex]

    Universe total energy density equivalent to LQC maximum energy density:
    [tex]\rho_u = \rho_{\text{max}}[/tex]

    Integration via substitution:
    [tex]\frac{3 E_t}{4 \pi R_{LQC}^3} = \Omega_{LQC} \rho_p[/tex]

    Universe LQC Lambda-CDM bounce radius:
    [tex]\boxed{R_{LQC} = \left( \frac{3 E_t}{4 \pi \Omega_{LQC} \rho_p} \right)^{\frac{1}{3}}}[/tex]

    [tex]\boxed{R_{LQC} = 5.829 \cdot 10^{-14} \; \text{m}}[/tex]

    Reference:
    Planck energy - Wikipedia
    Planck length - Wikipedia
    Lambda-CDM_model - Wikipedia
    Universe - Wikipedia
    Observable universe - Wikipedia
    Dark matter - Wikipedia
    Dark energy - Wikipedia
    Friedmann equations - Wikipedia
    Total amount of energy in the Universe - Orion1 #13
    Loop Quantum Cosmology: A Status Report - Abhay Ashtekar, Parampreet Singh
     
    Last edited: Feb 22, 2012
  2. jcsd
  3. Mar 1, 2012 #2
    May please Check with Maattihias Bartelmann of MPI for Astrophysics Garching Germany.

    I have his paper with me on this subject,and found promising like yours,but I have to compare.
     
  4. Mar 6, 2012 #3


    Universe total energy density equivalent to Planck energy density:
    [tex]\rho_u = \rho_{p}[/tex]

    Integration via substitution:
    [tex]\frac{3 E_t}{4 \pi R_{1}^3} = \rho_p[/tex]

    Universe Planck energy density bounce radius:
    [tex]\boxed{R_{1} = \left( \frac{3 E_t}{4 \pi \rho_p} \right)^{\frac{1}{3}}}[/tex]

    [tex]\boxed{R_{1} = 4.330 \cdot 10^{-14} \; \text{m}}[/tex]

    Reference:
    Cosmology - Matthias Bartelmann
     
    Last edited: Mar 6, 2012
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