Universe mass

Main Question or Discussion Point

This is my equation for the Universe mass based upon the Lambda-CDM model parameters and the Hubble Space Telescope (HST) and WMAP observational parameters in SI units.

Observable Universe mass composition:
$$H_0 = 2.32987690448613 \cdot 10^{- 18} \; \text{s}^{- 1}$$ - Hubble parameter (WMAP)
$$\Omega_b = 0.00444$$ - Baryon density
$$\Omega_{dm} = (\Omega_m - \Omega_b) = 0.2216$$ - dark matter density
$$dN_s = 10^{22}$$ - HST observable stellar number
$$dV_s = 3.3871 \cdot 10^{78} \; \text{m}^3 \; \; \; (4 \cdot 10^{30} \; \text{ly}^3)$$ - HST observable stellar volume
$$M_{\odot} = 1.9891 \cdot 10^{30} \; \text{kg}$$ - solar mass

Observable Universe mass:
$$\boxed{M_u = \frac{4 \pi M_{\odot}}{3 \Omega_b} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3}$$

$$\boxed{M_u = 1.18029735794067 \cdot 10^{55} \; \text{kg}}$$

Gravitationally observable dark matter mass:
$$\boxed{M_{dm} = \frac{4 \pi M_{\odot}}{3} \left( \frac{\Omega_{dm}}{\Omega_b} \right) \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3}$$

$$\boxed{M_{dm} = 2.61553894519654 \cdot 10^{54}}$$

Hubble critical mass:
$$\boxed{M_c = \frac{c^3}{2 G H_0}}$$
$$\boxed{M_c = 8.66352589042757 \cdot 10^{52} \; \text{kg}}$$

Reference:
"[URL [Broken] law - Wikipedia[/URL]
http://en.wikipedia.org/wiki/Lambda-CDM_model" [Broken]
http://en.wikipedia.org/wiki/Universe" [Broken]
http://en.wikipedia.org/wiki/Observable_universe" [Broken]
http://en.wikipedia.org/wiki/Dark_matter" [Broken]

Last edited by a moderator:

Correction, the Baryon density listed in post #1 is the stellar Baryon density, not the total Baryon density.

The stellar Baryon density ranges between:
$$\Omega_s = \int_{0.004}^{0.005}$$

Last edited:

$$\Omega_s = 0.005$$ - stellar Baryon density

Observable Universe mass:
$$\boxed{M_u = \frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3}$$

$$\boxed{M_u = 1.04810405385132 \cdot 10^{55} \; \text{kg}}$$

Gravitationally observable dark matter mass:
$$\boxed{M_{dm} = \frac{4 \pi M_{\odot}}{3} \left( \frac{\Omega_{dm}}{\Omega_s} \right) \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3}$$

$$\boxed{M_{dm} = 2.32259858333452 \cdot 10^{54} \; \text{kg}}$$

Hubble critical mass:
$$\boxed{M_c = \frac{c^3}{2 G H_0}}$$

$$\boxed{M_c = 8.66352589042757 \cdot 10^{52} \; \text{kg}}$$

Observable Universe mass greater than or equal to Hubble critical mass:
$$\boxed{M_u \geq M_c}$$

$$\boxed{\frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3 \geq \frac{c^3}{2 G H_0}}$$

Observable Universe mass equivalent to Hubble critical mass:
$$\boxed{M_u = M_c}$$

$$\frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3 = \frac{c^3}{2 G H_0}$$

Observable critical stellar Baryon density:
$$\boxed{\Omega_s = \frac{8 \pi G M_{\odot}}{3 H_0^2} \left( \frac{dN_s}{dV_s} \right)}$$

$$\boxed{\Omega_s = 0.604894627838177}$$

Total matter density:
$$\Omega_m = 0.266$$

According to my calculations, the observable Universe mass is greater than the Hubble critical mass.

What exactly are the cosmological theoretical implications for this criteria?

Last edited:

Observable stellar Baryon critical density:
$$\Omega_s = 0.604894627838177$$

Observable cosmological critical density:
$$\Omega_{\Lambda} = 0.7$$

Reference:
http://en.wikipedia.org/wiki/Lambda-CDM_model" [Broken]

Last edited by a moderator:
malawi_glenn
Homework Helper
Why don't you google 'Hubble critical mass' and publish 'your' results in an article?

Why don't you google 'Hubble critical mass' and publish 'your' results in an article?
All my equations require proofreading by a peer review, prior to any publication.

According to my calculations, the observable Universe mass is greater than the Hubble critical mass.

What exactly are the theoretical cosmological implications for this criteria?

Are my equations and calculations correct?

Last edited: