# LQC Lambda-CDM model bounce radius...

by Orion1
 P: 991 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: $$R_u = 4.399 \cdot 10^{26} \; \text{m}$$ Lambda-CDM stellar Baryon density parameter: $$\Omega_s = 0.005$$ Hubble Space Telescope observable stellar number: $$dN_s = 10^{22}$$ Hubble Space Telescope observable stellar volume: $$dV_s = 3.3871 \cdot 10^{78} \; \text{m}^3 \; \; \; (4 \cdot 10^{30} \; \text{ly}^3)$$ Solar mass: $$M_{\odot} = 1.9891 \cdot 10^{30} \; \text{kg}$$ Planck energy density: $$\boxed{\rho_p = \frac{E_p}{V_p} = \frac{3 c^7}{4 \pi \hbar G^2}}$$ $$\boxed{\rho_p = 1.106 \cdot 10^{113} \; \frac{\text{j}}{\text{m}^3}}$$ Universe_mass-energy equivalence total energy: $$\boxed{E_t = \frac{4 \pi c^2 M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) R_u^3}$$ Total amount of energy in the Universe: $$\boxed{E_t = 3.764 \cdot 10^{73} \; \text{j}}$$ Universe total energy density: $$\rho_u = \frac{E_t}{V_u} = \frac{3 E_t}{4 \pi R_u^3} = \frac{M_{\odot} c^2}{\Omega_s} \left( \frac{dN_s}{dV_s} \right)$$ LQC maximum energy density parameter: (ref. 10 p. 73 (5.7)) $$\boxed{\Omega_{LQC} = \frac{\rho_{\text{max}}}{\rho_p} = \frac{\hbar G}{2 \gamma^2 \lambda^2 c^7} = 0.41}$$ Universe total energy density equivalent to LQC maximum energy density: $$\rho_u = \rho_{\text{max}}$$ Integration via substitution: $$\frac{3 E_t}{4 \pi R_{LQC}^3} = \Omega_{LQC} \rho_p$$ Universe LQC Lambda-CDM bounce radius: $$\boxed{R_{LQC} = \left( \frac{3 E_t}{4 \pi \Omega_{LQC} \rho_p} \right)^{\frac{1}{3}}}$$ $$\boxed{R_{LQC} = 5.829 \cdot 10^{-14} \; \text{m}}$$ 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
 P: 991 Universe total energy density equivalent to Planck energy density: $$\rho_u = \rho_{p}$$ Integration via substitution: $$\frac{3 E_t}{4 \pi R_{1}^3} = \rho_p$$ Universe Planck energy density bounce radius: $$\boxed{R_{1} = \left( \frac{3 E_t}{4 \pi \rho_p} \right)^{\frac{1}{3}}}$$ $$\boxed{R_{1} = 4.330 \cdot 10^{-14} \; \text{m}}$$ Reference: Cosmology - Matthias Bartelmann