# LQC Lambda-CDM model bounce radius

1. Feb 22, 2012

### Orion1

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.

$$R_u = 4.399 \cdot 10^{26} \; \text{m}$$
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:
$$\frac{3 E_t}{4 \pi R_{LQC}^3} = \Omega_{LQC} \rho_p$$

$$\boxed{R_{LQC} = \left( \frac{3 E_t}{4 \pi \Omega_{LQC} \rho_p} \right)^{\frac{1}{3}}}$$

$$\boxed{R_{LQC} = 5.829 \cdot 10^{-14} \; \text{m}}$$

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

Last edited: Feb 22, 2012
2. Mar 1, 2012

### tapasbhattach

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.

3. Mar 6, 2012

### Orion1

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

Last edited: Mar 6, 2012